# Bengali (India) translation for genius.
# Copyright (C) 2025 genius's COPYRIGHT HOLDER
# This file is distributed under the same license as the genius package.
# FIRST AUTHOR <EMAIL@ADDRESS>, YEAR.
#
msgid ""
msgstr ""
"Project-Id-Version: genius master\n"
"POT-Creation-Date: 2025-07-07 22:46+0000\n"
"PO-Revision-Date: 2025-07-07 22:46+0000\n"
"Last-Translator: FULL NAME <EMAIL@ADDRESS>\n"
"Language-Team: Bengali (India) <Bengali (India)>\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"
"Language: bn\n"

#. (itstool) path: para/ulink
#: C/legal.xml:9
msgid "link"
msgstr ""

#. (itstool) path: legalnotice/para
#: C/legal.xml:2
msgid ""
"Permission is granted to copy, distribute and/or modify this document under "
"the terms of the GNU Free Documentation License (GFDL), Version 1.1 or any "
"later version published by the Free Software Foundation with no Invariant "
"Sections, no Front-Cover Texts, and no Back-Cover Texts. You can find a copy "
"of the GFDL at this <_:ulink-1/> or in the file COPYING-DOCS distributed "
"with this manual."
msgstr ""

#. (itstool) path: legalnotice/para
#: C/legal.xml:12
msgid ""
"This manual is part of a collection of GNOME manuals distributed under the "
"GFDL. If you want to distribute this manual separately from the collection, "
"you can do so by adding a copy of the license to the manual, as described in "
"section 6 of the license."
msgstr ""

#. (itstool) path: legalnotice/para
#: C/legal.xml:19
msgid ""
"Many of the names used by companies to distinguish their products and "
"services are claimed as trademarks. Where those names appear in any GNOME "
"documentation, and the members of the GNOME Documentation Project are made "
"aware of those trademarks, then the names are in capital letters or initial "
"capital letters."
msgstr ""

#. (itstool) path: listitem/para
#: C/legal.xml:35
msgid ""
"DOCUMENT IS PROVIDED ON AN \"AS IS\" BASIS, WITHOUT WARRANTY OF ANY KIND, "
"EITHER EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, WARRANTIES THAT "
"THE DOCUMENT OR MODIFIED VERSION OF THE DOCUMENT IS FREE OF DEFECTS "
"MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE OR NON-INFRINGING. THE ENTIRE "
"RISK AS TO THE QUALITY, ACCURACY, AND PERFORMANCE OF THE DOCUMENT OR "
"MODIFIED VERSION OF THE DOCUMENT IS WITH YOU. SHOULD ANY DOCUMENT OR "
"MODIFIED VERSION PROVE DEFECTIVE IN ANY RESPECT, YOU (NOT THE INITIAL "
"WRITER, AUTHOR OR ANY CONTRIBUTOR) ASSUME THE COST OF ANY NECESSARY "
"SERVICING, REPAIR OR CORRECTION. THIS DISCLAIMER OF WARRANTY CONSTITUTES AN "
"ESSENTIAL PART OF THIS LICENSE. NO USE OF ANY DOCUMENT OR MODIFIED VERSION "
"OF THE DOCUMENT IS AUTHORIZED HEREUNDER EXCEPT UNDER THIS DISCLAIMER; AND"
msgstr ""

#. (itstool) path: listitem/para
#: C/legal.xml:55
msgid ""
"UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, WHETHER IN TORT (INCLUDING "
"NEGLIGENCE), CONTRACT, OR OTHERWISE, SHALL THE AUTHOR, INITIAL WRITER, ANY "
"CONTRIBUTOR, OR ANY DISTRIBUTOR OF THE DOCUMENT OR MODIFIED VERSION OF THE "
"DOCUMENT, OR ANY SUPPLIER OF ANY OF SUCH PARTIES, BE LIABLE TO ANY PERSON "
"FOR ANY DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES OF "
"ANY CHARACTER INCLUDING, WITHOUT LIMITATION, DAMAGES FOR LOSS OF GOODWILL, "
"WORK STOPPAGE, COMPUTER FAILURE OR MALFUNCTION, OR ANY AND ALL OTHER DAMAGES "
"OR LOSSES ARISING OUT OF OR RELATING TO USE OF THE DOCUMENT AND MODIFIED "
"VERSIONS OF THE DOCUMENT, EVEN IF SUCH PARTY SHALL HAVE BEEN INFORMED OF THE "
"POSSIBILITY OF SUCH DAMAGES."
msgstr ""

#. (itstool) path: legalnotice/para
#: C/legal.xml:28
msgid ""
"DOCUMENT AND MODIFIED VERSIONS OF THE DOCUMENT ARE PROVIDED UNDER THE TERMS "
"OF THE GNU FREE DOCUMENTATION LICENSE WITH THE FURTHER UNDERSTANDING THAT: "
"<_:orderedlist-1/>"
msgstr ""

#. Put one translator per line, in the form NAME <EMAIL>, YEAR1, YEAR2
msgctxt "_"
msgid "translator-credits"
msgstr ""

#. (itstool) path: abstract/para
#: C/genius.xml:36
msgid "Manual for the Genius Math Tool."
msgstr ""

#. (itstool) path: bookinfo/title
#: C/genius.xml:37
msgid "Genius Manual"
msgstr ""

#. (itstool) path: bookinfo/copyright
#: C/genius.xml:39
msgid "<year>1997-2021</year> <holder>Jiří (George) Lebl</holder>"
msgstr ""

#. (itstool) path: bookinfo/copyright
#: C/genius.xml:43
msgid "<year>2004</year> <holder>Kai Willadsen</holder>"
msgstr ""

#. (itstool) path: authorgroup/author
#: C/genius.xml:64
msgid ""
"<firstname>Jiří</firstname> <surname>Lebl</surname> <affiliation> "
"<orgname>Oklahoma State University</orgname> <address> "
"<email>jiri.lebl@gmail.com</email> </address> </affiliation>"
msgstr ""

#. (itstool) path: authorgroup/author
#: C/genius.xml:72
msgid ""
"<firstname>Kai</firstname> <surname>Willadsen</surname> <affiliation> "
"<orgname>University of Queensland, Australia</orgname> <address> "
"<email>kaiw@itee.uq.edu.au</email> </address> </affiliation>"
msgstr ""

#. (itstool) path: revdescription/para
#: C/genius.xml:148
msgid "Jiri (George) Lebl <email>jiri.lebl@gmail.com</email>"
msgstr ""

#. (itstool) path: revhistory/revision
#: C/genius.xml:144
msgid ""
"<revnumber>0.2</revnumber> <date>October 2021</date> <_:revdescription-1/>"
msgstr ""

#. (itstool) path: bookinfo/releaseinfo
#: C/genius.xml:154
msgid "This manual describes version 1.0.27 of Genius."
msgstr ""

#. (itstool) path: legalnotice/title
#: C/genius.xml:157
msgid "Feedback"
msgstr ""

#. (itstool) path: legalnotice/para
#: C/genius.xml:158
msgid ""
"To report a bug or make a suggestion regarding the <application>Genius "
"Mathematics Tool</application> application or this manual, please visit the "
"<ulink url=\"http://www.jirka.org/genius.html\" type=\"http\">Genius Web "
"page</ulink> or email me at <email>jiri.lebl@gmail.com</email>."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:171
msgid "Introduction"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:172
msgid ""
"The <application>Genius Mathematics Tool</application> application is a "
"general calculator for use as a desktop calculator, an educational tool in "
"mathematics and other STEM fields, and has found use in research. The "
"language used in <application>Genius Mathematics Tool</application> is "
"designed to be ‘mathematical’ in the sense that it should be ‘what you mean "
"is what you get’. Of course, that is not an entirely attainable goal. "
"<application>Genius Mathematics Tool</application> features rationals, "
"arbitrary precision integers and multiple precision floats using the GMP "
"library. It handles complex numbers using cartesian notation. It has good "
"vector and matrix manipulation and can handle basic linear algebra. The "
"programming language allows user defined functions, variables, and "
"parameters."
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:186
msgid ""
"<application>Genius Mathematics Tool</application> comes in two versions. "
"One version is the graphical GNOME version, which features an IDE style "
"interface and the ability to plot functions of one or two variables. "
"Parametric plots of curves are also supported. It can plot slope fields, "
"vector fields and draw their solutions. The plots can be exported to several "
"formats. The command line version does not require GNOME, but does not "
"implement any feature that requires the graphical interface, such as plotting"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:198
msgid ""
"Parts of this manual describe the graphical version of the calculator. The "
"language that both versions use is the same, it is simply the graphical "
"features such as plotting that are unique to the GUI version."
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:204
msgid ""
"Generally, when some feature of the language (function, operator, etc...) is "
"new in some version past 1.0.5, it is mentioned, but below 1.0.5 you would "
"have to look at the NEWS file."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:214
msgid "Getting Started"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:217
msgid "To Start <application>Genius Mathematics Tool</application>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:218
msgid ""
"You can start <application>Genius Mathematics Tool</application> in the "
"following ways:"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:222
msgid "<guimenu>Applications</guimenu> menu"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:224
msgid ""
"Depending on your operating system and version, the menu item for "
"<application>Genius Mathematics Tool</application> could appear in a number "
"of different places. It can be in the <guisubmenu>Education</guisubmenu>, "
"<guisubmenu>Accessories</guisubmenu>, <guisubmenu>Office</guisubmenu>, "
"<guisubmenu>Science</guisubmenu>, or similar submenu, depending on your "
"particular setup. The menu item name you are looking for is "
"<guimenuitem>Genius Math Tool</guimenuitem>. Once you locate this menu item "
"click on it to start <application>Genius Mathematics Tool</application>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:240
msgid "<guilabel>Run</guilabel> dialog"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:242
msgid ""
"Depending on your system installation the menu item may not be available. If "
"it is not, you can open the Run dialog and execute <command>gnome-genius</"
"command>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:250
msgid "Command line"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:252
msgid ""
"To start the GNOME version of <application>Genius Mathematics Tool</"
"application> execute <command>gnome-genius</command> from the command line."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:256
msgid ""
"To start the command line only version, execute the following command: "
"<command>genius</command>. This version does not include the graphical "
"environment and some functionality such as plotting will not be available."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:268
msgid "When You Start Genius"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:269
msgid ""
"When you start the GNOME edition of <application>Genius Mathematics Tool</"
"application>, the window pictured in <xref linkend=\"mainwindow-fig\"/> is "
"displayed."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:274
msgid "<application>Genius Mathematics Tool</application> Window"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:279
msgctxt "_"
msgid ""
"external ref='figures/genius_window.png' "
"md5='30949c611b0d473aed2e1658e9d4bf49'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:276
msgid ""
"<imageobject> <imagedata fileref=\"figures/genius_window.png\" "
"format=\"PNG\" scalefit=\"1\"/> </imageobject> <textobject> <phrase>Shows "
"<application>Genius Mathematics Tool</application> main window. Contains "
"titlebar, menubar, toolbar and working area. Menubar contains "
"<guilabel>File</guilabel>, <guilabel>Edit</guilabel>, <guilabel>Calculator</"
"guilabel>, <guilabel>Examples</guilabel>, <guilabel>Programs</guilabel>, "
"<guilabel>Settings</guilabel>, and <guilabel>Help</guilabel> menus.</phrase> "
"</textobject>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:293
msgid ""
"The <application>Genius Mathematics Tool</application> window contains the "
"following elements:"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:297
msgid "Menubar."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:299
msgid ""
"The menus on the menubar contain all of the commands that you need to work "
"with files in <application>Genius Mathematics Tool</application>. The "
"<guilabel>File</guilabel> menu contains items for loading and saving items "
"and creating new programs. The <guilabel>Load and Run...</guilabel> command "
"does not open a new window for the program, but just executes the program "
"directly. It is equivalent to the <command>load</command> command."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:304
msgid ""
"The <guilabel>Calculator</guilabel> menu controls the calculator engine. It "
"allows you to run the currently selected program or to interrupt the current "
"calculation. You can also look at the full expression of the last answer "
"(useful if the last answer was too large to fit onto the console), or you "
"can view a listing of the values of all user defined variables. You can also "
"monitor user variables, which is especially useful while a long calculation "
"is running, or to debug a certain program. Finally the <guilabel>Calculator</"
"guilabel> allows plotting functions using a user friendly dialog box."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:314
msgid ""
"The <guilabel>Examples</guilabel> menu is a list of example programs or "
"demos. If you open the menu, it will load the example into a new program, "
"which you can run, edit, modify, and save. These programs should be well "
"documented and generally demonstrate either some feature of "
"<application>Genius Mathematics Tool</application> or some mathematical "
"concept."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:322
msgid ""
"The <guilabel>Programs</guilabel> menu lists the currently open programs and "
"allows you to switch between them."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:327
msgid "The other menus have same familiar functions as in other applications."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:333
msgid "Toolbar."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:335
msgid ""
"The toolbar contains a subset of the commands that you can access from the "
"menubar."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:339
msgid "Working area"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:341
msgid ""
"The working area is the primary method of interacting with the application."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:345
msgid ""
"The working area initially has just the <guilabel>Console</guilabel> tab, "
"which is the main way of interacting with the calculator. Here you type "
"expressions and the results are immediately returned after you hit the Enter "
"key."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:351
msgid ""
"Alternatively you can write longer programs and those can appear in separate "
"tabs. The programs are a set of commands or functions that can be run all at "
"once rather than entering them at the command line. The programs can be "
"saved in files for later retrieval."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:367
msgid "Basic Usage"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:370
msgid "Using the Work Area"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:372
msgid ""
"Normally you interact with the calculator in the <guilabel>Console</"
"guilabel> tab of the work area. If you are running the text only version "
"then the console will be the only thing that is available to you. If you "
"want to use <application>Genius Mathematics Tool</application> as a "
"calculator only, just type in your expression in the console, it will be "
"evaluated, and the returned value will be printed."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:385
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>30*70 + 67^3.0 + ln(7) * (88.8/100)</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:388
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>62734 + 812634 + 77^4 mod 5</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:391
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>| sin(37) - e^7 |</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:394
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>sum n=1 to 70 do 1/n</userinput>\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:380
msgid ""
"To evaluate an expression, type it into the <guilabel>Console</guilabel> "
"work area and press enter. Expressions are written in a language called GEL. "
"The most simple GEL expressions just looks like mathematics. For example "
"<_:screen-1/> or <_:screen-2/> or <_:screen-3/> or <_:screen-4/> (Last is "
"the harmonic sum from 1 to 70)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:400
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>help</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:403
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>help FunctionName</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:406
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>manual</userinput>\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:398
msgid ""
"To get a list of functions and commands, type: <_:screen-1/> If you wish to "
"get more help on a specific function, type: <_:screen-2/> To view this "
"manual, type: <_:screen-3/>"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:414
#, no-wrap
msgid "<prompt>genius&gt; </prompt><userinput>load path/to/program.gel</userinput>\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:409
msgid ""
"Suppose you have previously saved some GEL commands as a program to a file "
"and you now want to execute them. To load this program from the file "
"<filename>path/to/program.gel</filename>, type <_:screen-1/> "
"<application>Genius Mathematics Tool</application> keeps track of the "
"current directory. To list files in the current directory type <command>ls</"
"command>, to change directory do <userinput>cd directory</userinput> as in "
"the UNIX command shell."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:423
msgid "To Create a New Program"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:424
msgid ""
"If you wish to enter several more complicated commands, or perhaps write a "
"complicated function using the <link linkend=\"genius-gel\">GEL</link> "
"language, you can create a new program; really just a file with many "
"commands."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:429
msgid ""
"To start writing a new program, choose <menuchoice><guimenu>File</"
"guimenu><guimenuitem>New Program</guimenuitem></menuchoice>. A new tab will "
"appear in the work area. You can write a <link linkend=\"genius-gel\">GEL</"
"link> program in this work area. Once you have written your program you can "
"run it by <menuchoice><guimenu>Calculator</guimenu><guimenuitem>Run</"
"guimenuitem></menuchoice> (or the <guilabel>Run</guilabel> toolbar button). "
"This will execute your program and will display any output on the "
"<guilabel>Console</guilabel> tab. Executing a program is equivalent of "
"taking the text of the program and typing it into the console. The only "
"difference is that this input is done independent of the console and just "
"the output goes onto the console. <menuchoice><guimenu>Calculator</"
"guimenu><guimenuitem>Run</guimenuitem></menuchoice> will always run the "
"currently selected program even if you are on the <guilabel>Console</"
"guilabel> tab. The currently selected program has its tab in bold type. To "
"select a program, just click on its tab."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:446
msgid ""
"To save the program you've just written, choose <menuchoice><guimenu>File</"
"guimenu><guimenuitem>Save As...</guimenuitem></menuchoice>. Similarly as in "
"other programs you can choose <menuchoice><guimenu>File</"
"guimenu><guimenuitem>Save</guimenuitem></menuchoice> to save a program that "
"already has a filename attached to it. If you have many opened programs you "
"have edited and wish to save you can also choose <menuchoice><guimenu>File</"
"guimenu><guimenuitem>Save All Unsaved</guimenuitem></menuchoice>."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:453
msgid ""
"Programs that have unsaved changes will have a \"[+]\" next to their "
"filename. This way you can see if the file on disk and the currently opened "
"tab differ in content. Programs which have not yet had a filename associated "
"with them are always considered unsaved and no \"[+]\" is printed."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:461
msgid "To Open and Run a Program"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:462
msgid ""
"To open a file, choose <menuchoice><guimenu>File</guimenu><guimenuitem>Open</"
"guimenuitem></menuchoice>. A new tab containing the file will appear in the "
"work area. You can use this to edit the file."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:468
msgid ""
"To run a program from a file, choose <menuchoice><guimenu>File</"
"guimenu><guimenuitem>Load and Run...</guimenuitem></menuchoice>. This will "
"run the program without opening it in a separate tab. This is equivalent to "
"the <command>load</command> command."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:474
msgid ""
"If you have made edits to a file you wish to throw away and want to reload "
"to the version that's on disk, you can choose the <menuchoice><guimenu>File</"
"guimenu><guimenuitem>Reload from Disk</guimenuitem></menuchoice> menuitem. "
"This is useful for experimenting with a program and making temporary edits, "
"to run a program, but that you do not intend to keep."
msgstr ""

#. (itstool) path: chapter/title
#. (itstool) path: sect1/title
#: C/genius.xml:486 C/genius.xml:8870
msgid "Plotting"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:488
msgid ""
"Plotting support is only available in the graphical GNOME version. All "
"plotting accessible from the graphical interface is available from the "
"<guilabel>Create Plot</guilabel> window. You can access this window by "
"either clicking on the <guilabel>Plot</guilabel> button on the toolbar or "
"selecting <guilabel>Plot</guilabel> from the <guilabel>Calculator</guilabel> "
"menu. You can also access the plotting functionality by using the <link "
"linkend=\"genius-gel-function-list-plotting\">plotting functions</link> of "
"the GEL language. See <xref linkend=\"genius-gel\"/> to find out how to "
"enter expressions that Genius understands."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:501
msgid "Line Plots"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:502
msgid ""
"To graph real-valued functions of one variable, open the <guilabel>Create "
"Plot</guilabel> window. You can also use the <link linkend=\"gel-function-"
"LinePlot\"><function>LinePlot</function></link> function on the command line "
"(see its documentation). And by the words line plot, we mean plots in the "
"plane, as opposed to surface plots, which are in three dimensions."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:509
msgid ""
"Once you click the <guilabel>Plot</guilabel> button, a window opens up with "
"some notebooks in it. You want to be in the <guilabel>Function line plot</"
"guilabel> notebook tab, and inside you want to be on the "
"<guilabel>Functions / Expressions</guilabel> notebook tab. See <xref "
"linkend=\"lineplot-fig\"/>."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:517
msgid "Create Plot Window"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:521
msgctxt "_"
msgid ""
"external ref='figures/line_plot.png' md5='a9434af040a158a4d1440a03edd0e873'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:519
msgid ""
"<imageobject> <imagedata fileref=\"figures/line_plot.png\" format=\"PNG\" "
"scalefit=\"1\"/> </imageobject> <textobject> <phrase>Shows the line plotting "
"window.</phrase> </textobject>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:530
msgid ""
"Type expressions with <userinput>x</userinput> as the independent variable "
"into the textboxes. Alternatively you can give names of functions such as "
"<userinput>cos</userinput> rather then having to type <userinput>cos(x)</"
"userinput>. You can graph up to ten functions. If you make a mistake and "
"Genius cannot parse the input it will signify this with a warning icon on "
"the right of the text input box where the error occurred, as well as giving "
"you an error dialog. You can change the ranges of the dependent and "
"independent variables in the bottom part of the dialog. In the boxes for the "
"ranges, simple expressions are allowed, such as <userinput>2*pi</userinput> "
"or <userinput>10^3</userinput>. The <varname>y</varname> (dependent) range "
"can be set automatically by turning on the <guilabel>Fit dependent axis</"
"guilabel> checkbox. The names of the variables can also be changed. Pressing "
"the <guilabel>Plot</guilabel> button produces the graph shown in <xref "
"linkend=\"lineplot2-fig\"/>."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:545
msgid ""
"The variables can be renamed by clicking the <guilabel>Change variable "
"names...</guilabel> button, which is useful if you wish to print or save the "
"figure and don't want to use the standard names. Finally you can also avoid "
"printing the legend and the axis labels completely, which is also useful if "
"printing or saving, when the legend might simply be clutter."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:553
msgid "Plot Window"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:557
msgctxt "_"
msgid ""
"external ref='figures/line_plot_graph.png' "
"md5='38c25568f3143571cd5789f364e98776'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:555
msgid ""
"<imageobject> <imagedata fileref=\"figures/line_plot_graph.png\" "
"format=\"PNG\" scalefit=\"1\"/> </imageobject> <textobject> <phrase>The "
"graph produced.</phrase> </textobject>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:566
msgid ""
"From here you can print out the plot, create encapsulated postscript or a "
"PNG version of the plot or change the zoom. If the dependent axis was not "
"set correctly you can have Genius fit it by finding out the extrema of the "
"graphed functions."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:573
msgid ""
"For plotting using the command line see the documentation of the <link "
"linkend=\"gel-function-LinePlot\"><function>LinePlot</function></link> "
"function."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:580
msgid "Parametric Plots"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:581
msgid ""
"In the create plot window, you can also choose the <guilabel>Parametric</"
"guilabel> notebook tab to create two dimensional parametric plots. This way "
"you can plot a single parametric function. You can either specify the points "
"as <varname>x</varname> and <varname>y</varname>, or giving a single complex "
"number as a function of the variable <varname>t</varname>. The range of the "
"variable <varname>t</varname> is given explicitly, and the function is "
"sampled according to the given increment. The <varname>x</varname> and "
"<varname>y</varname> range can be set automatically by turning on the "
"<guilabel>Fit dependent axis</guilabel> checkbox, or it can be specified "
"explicitly. See <xref linkend=\"paramplot-fig\"/>."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:596
msgid "Parametric Plot Tab"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:600
msgctxt "_"
msgid ""
"external ref='figures/parametric.png' md5='a259ec34ff3909261009bf11b5054144'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:598
msgid ""
"<imageobject> <imagedata fileref=\"figures/parametric.png\" format=\"PNG\" "
"scalefit=\"1\"/> </imageobject> <textobject> <phrase>Parametric plotting tab "
"in the <guilabel>Create Plot</guilabel> window.</phrase> </textobject>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:609
msgid ""
"An example of a parametric plot is given in <xref linkend=\"paramplot2-fig\"/"
">. Similar operations can be done on such graphs as can be done on the other "
"line plots. For plotting using the command line see the documentation of the "
"<link linkend=\"gel-function-"
"LinePlotParametric\"><function>LinePlotParametric</function></link> or <link "
"linkend=\"gel-function-LinePlotCParametric\"><function>LinePlotCParametric</"
"function></link> function."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:620
msgid "Parametric Plot"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:624
msgctxt "_"
msgid ""
"external ref='figures/parametric_graph.png' "
"md5='3b291065f178a30e900948574ab0891a'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:622
msgid ""
"<imageobject> <imagedata fileref=\"figures/parametric_graph.png\" "
"format=\"PNG\" scalefit=\"1\"/> </imageobject> <textobject> "
"<phrase>Parametric plot produced</phrase> </textobject>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:636
msgid "Slopefield Plots"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:637
msgid ""
"In the create plot window, you can also choose the <guilabel>Slope field</"
"guilabel> notebook tab to create a two dimensional slope field plot. Similar "
"operations can be done on such graphs as can be done on the other line "
"plots. For plotting using the command line see the documentation of the "
"<link linkend=\"gel-function-SlopefieldPlot\"><function>SlopefieldPlot</"
"function></link> function."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:646
msgid ""
"When a slope field is active, there is an extra <guilabel>Solver</guilabel> "
"menu available, through which you can bring up the solver dialog. Here you "
"can have Genius plot specific solutions for the given initial conditions. "
"You can either specify initial conditions in the dialog, or you can click on "
"the plot directly to specify the initial point. While the solver dialog is "
"active, the zooming by clicking and dragging does not work. You have to "
"close the dialog first if you want to zoom using the mouse."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:655
msgid ""
"The solver uses the standard Runge-Kutta method. The plots will stay on the "
"screen until cleared. The solver will stop whenever it reaches the boundary "
"of the plot window. Zooming does not change the limits or parameters of the "
"solutions, you will have to clear and redraw them with appropriate "
"parameters. You can also use the <link linkend=\"gel-function-"
"SlopefieldDrawSolution\"><function>SlopefieldDrawSolution</function></link> "
"function to draw solutions from the command line or programs."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:668
msgid "Vectorfield Plots"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:669
msgid ""
"In the create plot window, you can also choose the <guilabel>Vector field</"
"guilabel> notebook tab to create a two dimensional vector field plot. "
"Similar operations can be done on such graphs as can be done on the other "
"line plots. For plotting using the command line see the documentation of the "
"<link linkend=\"gel-function-VectorfieldPlot\"><function>VectorfieldPlot</"
"function></link> function."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:678
msgid ""
"By default the direction and magnitude of the vector field is shown. To only "
"show direction and not the magnitude, check the appropriate checkbox to "
"normalize the arrow lengths."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:684
msgid ""
"When a vector field is active, there is an extra <guilabel>Solver</guilabel> "
"menu available, through which you can bring up the solver dialog. Here you "
"can have Genius plot specific solutions for the given initial conditions. "
"You can either specify initial conditions in the dialog, or you can click on "
"the plot directly to specify the initial point. While the solver dialog is "
"active, the zooming by clicking and dragging does not work. You have to "
"close the dialog first if you want to zoom using the mouse."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:693
msgid ""
"The solver uses the standard Runge-Kutta method. The plots will stay on the "
"screen until cleared. Zooming does not change the limits or parameters of "
"the solutions, you will have to clear and redraw them with appropriate "
"parameters. You can also use the <link linkend=\"gel-function-"
"VectorfieldDrawSolution\"><function>VectorfieldDrawSolution</function></"
"link> function to draw solutions from the command line or programs."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:706
msgid "Surface Plots"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:707
msgid ""
"Genius can also plot surfaces. Select the <guilabel>Surface plot</guilabel> "
"tab in the main notebook of the <guilabel>Create Plot</guilabel> window. "
"Here you can specify a single expression that should use either <varname>x</"
"varname> and <varname>y</varname> as real independent variables or "
"<varname>z</varname> as a complex variable (where <varname>x</varname> is "
"the real part of <varname>z</varname> and <varname>y</varname> is the "
"imaginary part). For example to plot the modulus of the cosine function for "
"complex parameters, you could enter <userinput>|cos(z)|</userinput>. This "
"would be equivalent to <userinput>|cos(x+1i*y)|</userinput>. See <xref "
"linkend=\"surfaceplot-fig\"/>. For plotting using the command line see the "
"documentation of the <link linkend=\"gel-function-"
"SurfacePlot\"><function>SurfacePlot</function></link> function."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:720
msgid ""
"The <varname>z</varname> range can be set automatically by turning on the "
"<guilabel>Fit dependent axis</guilabel> checkbox. The variables can be "
"renamed by clicking the <guilabel>Change variable names...</guilabel> "
"button, which is useful if you wish to print or save the figure and don't "
"want to use the standard names. Finally you can also avoid printing the "
"legend, which is also useful if printing or saving, when the legend might "
"simply be clutter."
msgstr ""

#. (itstool) path: figure/title
#: C/genius.xml:728
msgid "Surface Plot"
msgstr ""

#. (itstool) path: imageobject/imagedata
#. This is a reference to an external file such as an image or video. When
#. the file changes, the md5 hash will change to let you know you need to
#. update your localized copy. The msgstr is not used at all. Set it to
#. whatever you like once you have updated your copy of the file.
#: C/genius.xml:732
msgctxt "_"
msgid ""
"external ref='figures/surface_graph.png' "
"md5='3d94846b0f4103be5d99f502630185f9'"
msgstr ""

#. (itstool) path: screenshot/mediaobject
#: C/genius.xml:730
msgid ""
"<imageobject> <imagedata fileref=\"figures/surface_graph.png\" "
"format=\"PNG\" scalefit=\"1\"/> </imageobject> <textobject> <phrase>Modulus "
"of the complex cosine function.</phrase> </textobject>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:741
msgid ""
"In surface mode, left and right arrow keys on your keyboard will rotate the "
"view along the z axis. Alternatively you can rotate along any axis by "
"selecting <guilabel>Rotate axis...</guilabel> in the <guilabel>View</"
"guilabel> menu. The <guilabel>View</guilabel> menu also has a top view mode "
"which rotates the graph so that the z axis is facing straight out, that is, "
"we view the graph from the top and get essentially just the colors that "
"define the values of the function getting a temperature plot of the "
"function. Finally you should try <guilabel>Start rotate animation</"
"guilabel>, to start a continuous slow rotation. This is especially good if "
"using <application>Genius Mathematics Tool</application> to present to an "
"audience."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:759
msgid "GEL Basics"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:761
msgid ""
"GEL stands for Genius Extension Language. It is the language you use to "
"write programs in Genius. A program in GEL is simply an expression that "
"evaluates to a number, a matrix, or another object in GEL. "
"<application>Genius Mathematics Tool</application> can be used as a simple "
"calculator, or as a powerful theoretical research tool. The syntax is meant "
"to have as shallow of a learning curve as possible, especially for use as a "
"calculator."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:774
msgid "Values"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:776
msgid ""
"Values in GEL can be <link linkend=\"genius-gel-values-numbers\">numbers</"
"link>, <link linkend=\"genius-gel-values-booleans\">Booleans</link>, or "
"<link linkend=\"genius-gel-values-strings\">strings</link>. GEL also treats "
"<link linkend=\"genius-gel-matrices\">matrices</link> as values. Values can "
"be used in calculations, assigned to variables and returned from functions, "
"among other uses."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:783
msgid "Numbers"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:786
#, no-wrap
msgid "1234\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:789
#, no-wrap
msgid ""
"0x123ABC\n"
"01234\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:793
#, no-wrap
msgid "23\\1234ABCD\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:784
msgid ""
"Integers are the first type of number in GEL. Integers are written in the "
"normal way. <_:programlisting-1/> Hexadecimal and octal numbers can be "
"written using C notation. For example: <_:programlisting-2/> Or you can type "
"numbers in an arbitrary base using <literal>&lt;base&gt;\\&lt;number&gt;</"
"literal>. Digits higher than 10 use letters in a similar way to hexadecimal. "
"For example, a number in base 23 could be written: <_:programlisting-3/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:799
#, no-wrap
msgid "3/4\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:802
#, no-wrap
msgid "1 3/10\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:797
msgid ""
"The second type of GEL number is rationals. Rationals are simply achieved by "
"dividing two integers. So one could write: <_:programlisting-1/> to get "
"three quarters. Rationals also accept mixed fraction notation. So in order "
"to get one and three tenths you could write: <_:programlisting-2/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:808
#, no-wrap
msgid ""
"1.315\n"
"7.887e77\n"
"7.887e-77\n"
".3\n"
"0.3\n"
"77e5\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:806
msgid ""
"The next type of number is floating point. These are entered in a similar "
"fashion to C notation. You can use <literal>E</literal>, <literal>e</"
"literal> or <literal>@</literal> as the exponent delimiter. Note that using "
"the exponent delimiter gives a float even if there is no decimal point in "
"the number. Examples: <_:programlisting-1/> When Genius prints a floating "
"point number it will always append a <computeroutput>.0</computeroutput> "
"even if the number is whole. This is to indicate that floating point numbers "
"are taken as imprecise quantities. When a number is written in the "
"scientific notation, it is always a floating point number and thus Genius "
"does not print the <computeroutput>.0</computeroutput>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:824
#, no-wrap
msgid ""
"1+2i\n"
"8.01i\n"
"77*e^(1.3i)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:822
msgid ""
"The final type of number in GEL is the complex numbers. You can enter a "
"complex number as a sum of real and imaginary parts. To add an imaginary "
"part, append an <literal>i</literal>. Here are examples of entering complex "
"numbers: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: important/para
#: C/genius.xml:831
msgid ""
"When entering imaginary numbers, a number must be in front of the "
"<literal>i</literal>. If you use <literal>i</literal> by itself, Genius will "
"interpret this as referring to the variable <varname>i</varname>. If you "
"need to refer to <literal>i</literal> by itself, use <literal>1i</literal> "
"instead."
msgstr ""

#. (itstool) path: important/para
#: C/genius.xml:835
msgid ""
"In order to use mixed fraction notation with imaginary numbers you must have "
"the mixed fraction in parentheses. (i.e., <userinput>(1 2/5)i</userinput>)"
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:844
msgid "Booleans"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:845
msgid ""
"Genius also supports native Boolean values. The two Boolean constants are "
"defined as <constant>true</constant> and <constant>false</constant>; these "
"identifiers can be used like any other variable. You can also use the "
"identifiers <constant>True</constant>, <constant>TRUE</constant>, "
"<constant>False</constant> and <constant>FALSE</constant> as aliases for the "
"above."
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:853
msgid ""
"At any place where a Boolean expression is expected, you can use a Boolean "
"value or any expression that produces either a number or a Boolean. If "
"Genius needs to evaluate a number as a Boolean it will interpret 0 as "
"<constant>false</constant> and any other number as <constant>true</constant>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:862
#, no-wrap
msgid "( (1 + true) - false ) * true\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:865
#, no-wrap
msgid "( (true or true) or not false ) and true\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:868
#, no-wrap
msgid "1 == true\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:860
msgid ""
"In addition, you can do arithmetic with Boolean values. For example: "
"<_:programlisting-1/> is the same as: <_:programlisting-2/> Only addition, "
"subtraction and multiplication are supported. If you mix numbers with "
"Booleans in an expression then the numbers are converted to Booleans as "
"described above. This means that, for example: <_:programlisting-3/> always "
"evaluates to <constant>true</constant> since 1 will be converted to "
"<constant>true</constant> before being compared to <constant>true</constant>."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:876
msgid "Strings"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:879
#, no-wrap
msgid "a=2+3;\"The result is: \"+a\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:882
#, no-wrap
msgid "The result is: 5\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:885
#, no-wrap
msgid "\"Slash: \\\\ Quotes: \\\" Tabs: \\t1\\t2\\t3\"\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:888
#, no-wrap
msgid "Slash: \\ Quotes: \" Tabs: \t1\t2\t3\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:877
msgid ""
"Like numbers and Booleans, strings in GEL can be stored as values inside "
"variables and passed to functions. You can also concatenate a string with "
"another value using the plus operator. For example: <_:programlisting-1/> "
"will create the string: <_:programlisting-2/> You can also use C-like escape "
"sequences such as <literal>\\n</literal>,<literal>\\t</literal>,"
"<literal>\\b</literal>,<literal>\\a</literal> and <literal>\\r</literal>. To "
"get a <literal>\\</literal> or <literal>\"</literal> into the string you can "
"quote it with a <literal>\\</literal>. For example: <_:programlisting-3/> "
"will make a string: <_:programlisting-4/> Do note however that when a string "
"is returned from a function, escapes are quoted, so that the output can be "
"used as input. If you wish to print the string as it is (without escapes), "
"use the <link linkend=\"gel-function-print\"><function>print</function></"
"link> or <link linkend=\"gel-function-printn\"><function>printn</function></"
"link> functions."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:899
#, no-wrap
msgid "string(22)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:902
#, no-wrap
msgid "\"22\"\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:897
msgid ""
"In addition, you can use the library function <link linkend=\"gel-function-"
"string\"><function>string</function></link> to convert anything to a string. "
"For example: <_:programlisting-1/> will return <_:programlisting-2/> Strings "
"can also be compared with <literal>==</literal> (equal), <literal>!=</"
"literal> (not equal) and <literal>&lt;=&gt;</literal> (comparison) operators"
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:910
msgid "Null"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:911
msgid ""
"There is a special value called <constant>null</constant>. No operations can "
"be performed on it, and nothing is printed when it is returned. Therefore, "
"<constant>null</constant> is useful when you do not want output from an "
"expression. The value <constant>null</constant> can be obtained as an "
"expression when you type <literal>.</literal>, the constant <constant>null</"
"constant> or nothing. By nothing we mean that if you end an expression with "
"a separator <literal>;</literal>, it is equivalent to ending it with a "
"separator followed by a <constant>null</constant>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:924
#, no-wrap
msgid ""
"x=5;.\n"
"x=5;\n"
msgstr ""

#. (itstool) path: sect2/para
#. (itstool) path: sect1/para
#: C/genius.xml:922 C/genius.xml:2254
msgid "Example: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:928
msgid ""
"Some functions return <constant>null</constant> when no value can be "
"returned or an error happened. Also <constant>null</constant> is used as an "
"empty vector or matrix, or an empty reference."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:938
msgid "Using Variables"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:942
#, no-wrap
msgid "VariableName\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:945
#, no-wrap
msgid ""
"<prompt>genius&gt; </prompt><userinput>e</userinput>\n"
"= 2.71828182846\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:940
msgid "Syntax: <_:programlisting-1/> Example: <_:screen-2/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:950
msgid ""
"To evaluate a variable by itself, just enter the name of the variable. This "
"will return the value of the variable. You can use a variable anywhere you "
"would normally use a number or string. In addition, variables are necessary "
"when defining functions that take arguments (see <xref linkend=\"genius-gel-"
"functions-defining\"/>)."
msgstr ""

#. (itstool) path: tip/title
#: C/genius.xml:955 C/genius.xml:1044
msgid "Using Tab completion"
msgstr ""

#. (itstool) path: tip/para
#: C/genius.xml:956
msgid ""
"You can use Tab completion to get Genius to complete variable names for you. "
"Try typing the first few letters of the name and pressing <userinput>Tab</"
"userinput>."
msgstr ""

#. (itstool) path: important/title
#: C/genius.xml:962
msgid "Variable names are case sensitive"
msgstr ""

#. (itstool) path: important/para
#: C/genius.xml:963
msgid ""
"The names of variables are case sensitive. That means that variables named "
"<varname>hello</varname>, <varname>HELLO</varname> and <varname>Hello</"
"varname> are all different variables."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:970
msgid "Setting Variables"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:973
#, no-wrap
msgid ""
"&lt;identifier&gt; = &lt;value&gt;\n"
"&lt;identifier&gt; := &lt;value&gt;\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:977
#, no-wrap
msgid ""
"x = 3\n"
"x := 3\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:971
msgid "Syntax: <_:programlisting-1/> Example: <_:programlisting-2/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:984
#, no-wrap
msgid "a = b = 5\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:982
msgid ""
"To assign a value to a variable, use the <literal>=</literal> or "
"<literal>:=</literal> operators. These operators set the value of the "
"variable and return the value you set, so you can do things like "
"<_:programlisting-1/> This will set <varname>b</varname> to 5 and then also "
"set <varname>a</varname> to 5."
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:989
msgid ""
"The <literal>=</literal> and <literal>:=</literal> operators can both be "
"used to set variables. The difference between them is that the <literal>:=</"
"literal> operator always acts as an assignment operator, whereas the "
"<literal>=</literal> operator may be interpreted as testing for equality "
"when used in a context where a Boolean expression is expected."
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:993
msgid ""
"For more information about the scope of variables, that is when are what "
"variables visible, see <xref linkend=\"genius-gel-variables-global\"/>."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1000
msgid "Built-in Variables"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1001
msgid ""
"GEL has a number of built-in ‘variables’, such as <varname>e</varname>, "
"<varname>pi</varname> or <varname>GoldenRatio</varname>. These are widely "
"used constants with a preset value, and they cannot be assigned new values. "
"There are a number of other built-in variables. See <xref linkend=\"genius-"
"gel-function-list-constants\"/> for a full list. Note that <varname>i</"
"varname> is not by default the square root of negative one (the imaginary "
"number), and is undefined to allow its use as a counter. If you wish to "
"write the imaginary number you need to use <userinput>1i</userinput>."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1014
msgid "Previous Result Variable"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1017
#, no-wrap
msgid "Ans+389\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1015
msgid ""
"The <varname>Ans</varname> and <varname>ans</varname> variables can be used "
"to get the result of the last expression. For example, if you had performed "
"some calculation, to add 389 to the result you could do: <_:programlisting-1/"
">"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1024
msgid "Using Functions"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1028
#, no-wrap
msgid "FunctionName(argument1, argument2, ...)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1031
#, no-wrap
msgid ""
"Factorial(5)\n"
"cos(2*pi)\n"
"gcd(921,317)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1026
msgid ""
"Syntax: <_:programlisting-1/> Example: <_:programlisting-2/> To evaluate a "
"function, enter the name of the function, followed by the arguments (if any) "
"to the function in parentheses. This will return the result of applying the "
"function to its arguments. The number of arguments to the function is, of "
"course, different for each function."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1039
msgid ""
"There are many built-in functions, such as <link linkend=\"gel-function-"
"sin\"><function>sin</function></link>, <link linkend=\"gel-function-"
"cos\"><function>cos</function></link> and <link linkend=\"gel-function-"
"tan\"><function>tan</function></link>. You can use the <link linkend=\"gel-"
"command-help\"><function>help</function></link> built-in command to get a "
"list of available functions, or see <xref linkend=\"genius-gel-function-"
"list\"/> for a full listing."
msgstr ""

#. (itstool) path: tip/para
#: C/genius.xml:1045
msgid ""
"You can use Tab completion to get Genius to complete function names for you. "
"Try typing the first few letters of the name and pressing <userinput>Tab</"
"userinput>."
msgstr ""

#. (itstool) path: important/title
#: C/genius.xml:1051
msgid "Function names are case sensitive"
msgstr ""

#. (itstool) path: important/para
#: C/genius.xml:1052
msgid ""
"The names of functions are case sensitive. That means that functions named "
"<function>dosomething</function>, <function>DOSOMETHING</function> and "
"<function>DoSomething</function> are all different functions."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1059
msgid "Defining Functions"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1062
#, no-wrap
msgid ""
"function &lt;identifier&gt;(&lt;comma separated arguments&gt;) = &lt;function body&gt;\n"
"&lt;identifier&gt; = (`() = &lt;function body&gt;)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1060
msgid ""
"Syntax: <_:programlisting-1/> The <literal>`</literal> is the backquote "
"character, and signifies an anonymous function. By setting it to a variable "
"name you effectively define a function."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1071
#, no-wrap
msgid "function addup(a,b,c) = a+b+c\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1068
msgid ""
"A function takes zero or more comma separated arguments, and returns the "
"result of the function body. Defining your own functions is primarily a "
"matter of convenience; one possible use is to have sets of functions defined "
"in GEL files that Genius can load in order to make them available. Example: "
"<_:programlisting-1/> then <userinput>addup(1,4,9)</userinput> yields 14"
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1078
msgid "Variable Argument Lists"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1081
#, no-wrap
msgid "function f(a,b...) = b\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1079
msgid ""
"If you include <literal>...</literal> after the last argument name in the "
"function declaration, then Genius will allow any number of arguments to be "
"passed in place of that argument. If no arguments were passed then that "
"argument will be set to <constant>null</constant>. Otherwise, it will be a "
"horizontal vector containing all the arguments. For example: "
"<_:programlisting-1/> Then <userinput>f(1,2,3)</userinput> yields "
"<computeroutput>[2,3]</computeroutput>, while <userinput>f(1)</userinput> "
"yields a <constant>null</constant>."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1089
msgid "Passing Functions to Functions"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1091
msgid ""
"In Genius, it is possible to pass a function as an argument to another "
"function. This can be done using either ‘function nodes’ or anonymous "
"functions."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1098
#, no-wrap
msgid ""
"function f(a,b) = a(b)+1;\n"
"function b(x) = x*x;\n"
"f(b,2)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1095
msgid ""
"If you do not enter the parentheses after a function name, instead of being "
"evaluated, the function will instead be returned as a ‘function node’. The "
"function node can then be passed to another function. Example: "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1107
#, no-wrap
msgid ""
"function(&lt;comma separated arguments&gt;) = &lt;function body&gt;\n"
"`(&lt;comma separated arguments&gt;) = &lt;function body&gt;\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1111
#, no-wrap
msgid ""
"function f(a,b) = a(b)+1;\n"
"f(`(x) = x*x,2)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1103
msgid ""
"To pass functions that are not defined, you can use an anonymous function "
"(see <xref linkend=\"genius-gel-functions-defining\"/>). That is, you want "
"to pass a function without giving it a name. Syntax: <_:programlisting-1/> "
"Example: <_:programlisting-2/> This will return 5."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1120
msgid "Operations on Functions"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1123
#, no-wrap
msgid "exp(sin*cos+4)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1127
#, no-wrap
msgid "`(x) = exp(sin(x)*cos(x)+4)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1132
#, no-wrap
msgid "f = exp(sin*cos+4)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1135
#, no-wrap
msgid "LinePlot(sin^2)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1121
msgid ""
"Some functions allow arithmetic operations, and some single argument "
"functions such as <link linkend=\"gel-function-exp\"><function>exp</"
"function></link> or <link linkend=\"gel-function-ln\"><function>ln</"
"function></link>, to operate on the function. For example, "
"<_:programlisting-1/> will return a function that takes <varname>x</varname> "
"and returns <userinput>exp(sin(x)*cos(x)+4)</userinput>. It is functionally "
"equivalent to typing <_:programlisting-2/> This operation can be useful when "
"quickly defining functions. For example to create a function called "
"<varname>f</varname> to perform the above operation, you can just type: "
"<_:programlisting-3/> It can also be used in plotting. For example, to plot "
"sin squared you can enter: <_:programlisting-4/>"
msgstr ""

#. (itstool) path: warning/para
#: C/genius.xml:1140
msgid ""
"Not all functions can be used in this way. For example, when you use a "
"binary operation the functions must take the same number of arguments."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1150
msgid "Separator"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1159
#, no-wrap
msgid "3 ; 5\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1151
msgid ""
"GEL is somewhat different from other languages in how it deals with multiple "
"commands and functions. In GEL you must chain commands together with a "
"separator operator. That is, if you want to type more than one expression "
"you have to use the <literal>;</literal> operator in between the "
"expressions. This is a way in which both expressions are evaluated and the "
"result of the second one (or the last one if there is more than two "
"expressions) is returned. Suppose you type the following: "
"<_:programlisting-1/> This expression will yield 5."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1163
msgid ""
"This will require some parenthesizing to make it unambiguous sometimes, "
"especially if the <literal>;</literal> is not the top most primitive. This "
"slightly differs from other programming languages where the <literal>;</"
"literal> is a terminator of statements, whereas in GEL it’s actually a "
"binary operator. If you are familiar with pascal this should be second "
"nature. However genius can let you pretend it is a terminator to some "
"degree. If a <literal>;</literal> is found at the end of a parenthesis or a "
"block, genius will append a null to it as if you would have written "
"<userinput>;null</userinput>. This is useful in case you do not want to "
"return a value from a loop, or if you handle the return differently."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1175
msgid ""
"If you are typing expressions in a program file you do not have to add a "
"semicolon. In this case genius will simply print the return value whenever "
"it executes the expression. This is the same as when typing on the command "
"line. However, do note that if you are defining a function, the body of the "
"function is a single expression. Usually, therefore, if a function body is "
"long, you will need to enclose it in parentheses."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1185
msgid "Comments"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1190
#, no-wrap
msgid ""
"# This is just a comment\n"
"# every line in a comment must have its own pound sign\n"
"# in the next line we set x to the value 123\n"
"x=123;\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1186
msgid ""
"GEL is similar to other scripting languages in that <literal>#</literal> "
"denotes a comment, that is text that is not meant to be evaluated. "
"Everything beyond the pound sign till the end of line will just be ignored. "
"For example, <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1199
msgid "Modular Evaluation"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1200
msgid ""
"Genius implements modular arithmetic. To use it you just add \"mod "
"&lt;integer&gt;\" after the expression. Example: <userinput>2^(5!) * 3^(6!) "
"mod 5</userinput> It could be possible to do modular arithmetic by computing "
"with integers and then modding in the end with the <literal>%</literal> "
"operator, which simply gives the remainder, but that may be time consuming "
"if not impossible when working with larger numbers. For example, "
"<userinput>10^(10^10) % 6</userinput> will simply not work (the exponent "
"will be too large), while <userinput>10^(10^10) mod 6</userinput> is "
"instantaneous. The first expression first tries to compute the integer "
"<userinput>10^(10^10)</userinput> and then find remainder after division by "
"6, while the second expression evaluates everything modulo 6 to begin with."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1218
#, no-wrap
msgid ""
"10^-1 mod 101\n"
"1/10 mod 101"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1223
#, no-wrap
msgid ""
"A = [1,2;3,4]\n"
"B = A^-1 mod 5\n"
"A*B mod 5"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1214
msgid ""
"The inverses of numbers mod some integer are computed by writing them as "
"rational numbers (as long as the desired inverse exists, of course). "
"Examples: <_:programlisting-1/> Modular evaluation also works with matrices "
"including taking inverses, powers, and dividing. Example: "
"<_:programlisting-2/> This should yield the identity matrix as B will be the "
"inverse of A mod 5."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1235
#, no-wrap
msgid ""
"genius&gt; sqrt(4) mod 7\n"
"=\n"
"[2, 5]\n"
"genius&gt; 2*2 mod 7\n"
"= 4"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1228
msgid ""
"Some functions such as <link linkend=\"gel-function-sqrt\"><function>sqrt</"
"function></link> or <link linkend=\"gel-function-log\"><function>log</"
"function></link> work in a different way when in modulo mode. These will "
"then work like their discrete versions working within the ring of integers "
"you selected. For example: <_:programlisting-1/> <function>sqrt</function> "
"will actually return all the possible square roots."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1243
msgid ""
"Do not chain mod operators, simply place it at the end of the computation, "
"all computations in the expression on the left will be carried out in mod "
"arithmetic. If you place a mod inside a mod, you will get unexpected "
"results. If you simply want to mod a single number and control exactly when "
"remainders are taken, best to use the <literal>%</literal> operator. When "
"you need to chain several expressions in modular arithmetic with different "
"divisors, it may be best to just split up the expression into several and "
"use temporary variables to avoid a mod inside a mod."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1256
msgid "List of GEL Operators"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1258
msgid ""
"Everything in GEL is really just an expression. Expressions are stringed "
"together with different operators. As we have seen, even the separator is "
"simply a binary operator in GEL. Here is a list of the operators in GEL."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1266
msgid "<userinput>a;b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1268
msgid ""
"The separator, just evaluates both <varname>a</varname> and <varname>b</"
"varname>, but returns only the result of <varname>b</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1280
msgid "<userinput>a=b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1282
msgid ""
"The assignment operator. This assigns <varname>b</varname> to <varname>a</"
"varname> (<varname>a</varname> must be a valid <link linkend=\"genius-gel-"
"lvalues\">lvalue</link>) (note however that this operator may be translated "
"to <literal>==</literal> if used in a place where boolean expression is "
"expected)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1294
msgid "<userinput>a:=b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1296
msgid ""
"The assignment operator. Assigns <varname>b</varname> to <varname>a</"
"varname> (<varname>a</varname> must be a valid <link linkend=\"genius-gel-"
"lvalues\">lvalue</link>). This is different from <literal>=</literal> "
"because it never gets translated to a <literal>==</literal>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1307
msgid "<userinput>|a|</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1309
msgid ""
"Absolute value. In case the expression is a complex number the result will "
"be the modulus (distance from the origin). For example: <userinput>|3 * "
"e^(1i*pi)|</userinput> returns 3."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1316
msgid ""
"See <ulink url=\"http://mathworld.wolfram.com/"
"AbsoluteValue.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1325
msgid "<userinput>a^b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1327
msgid ""
"Exponentiation, raises <varname>a</varname> to the <varname>b</varname>th "
"power."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1335
msgid "<userinput>a.^b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1337
msgid ""
"Element by element exponentiation. Raise each element of a matrix "
"<varname>a</varname> to the <varname>b</varname>th power. Or if <varname>b</"
"varname> is a matrix of the same size as <varname>a</varname>, then do the "
"operation element by element. If <varname>a</varname> is a number and "
"<varname>b</varname> is a matrix then it creates matrix of the same size as "
"<varname>b</varname> with <varname>a</varname> raised to all the different "
"powers in <varname>b</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1352
msgid "<userinput>a+b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1354
msgid ""
"Addition. Adds two numbers, matrices, functions or strings. If you add a "
"string to anything the result will just be a string. If one is a square "
"matrix and the other a number, then the number is multiplied by the identity "
"matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1365
msgid "<userinput>a-b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1367
msgid "Subtraction. Subtract two numbers, matrices or functions."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1375
msgid "<userinput>a*b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1377
msgid "Multiplication. This is the normal matrix multiplication."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1385
msgid "<userinput>a.*b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1387
msgid ""
"Element by element multiplication if <varname>a</varname> and <varname>b</"
"varname> are matrices."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1396
msgid "<userinput>a/b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1398
msgid ""
"Division. When <varname>a</varname> and <varname>b</varname> are just "
"numbers this is the normal division. When they are matrices, then this is "
"equivalent to <userinput>a*b^-1</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1408
msgid "<userinput>a./b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1410
msgid ""
"Element by element division. Same as <userinput>a/b</userinput> for numbers, "
"but operates element by element on matrices."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1419
msgid "<userinput>a\\b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1421
msgid "Back division. That is this is the same as <userinput>b/a</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1429
msgid "<userinput>a.\\b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1431
msgid "Element by element back division."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1439
msgid "<userinput>a%b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1441
msgid ""
"The mod operator. This does not turn on the <link linkend=\"genius-gel-"
"modular-evaluation\">modular mode</link>, but just returns the remainder of "
"integer division <userinput>a/b</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1452
msgid "<userinput>a.%b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1454
msgid ""
"Element by element mod operator. Returns the remainder after element by "
"element integer division <userinput>a./b</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1464
msgid "<userinput>a mod b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1466
msgid ""
"Modular evaluation operator. The expression <varname>a</varname> is "
"evaluated modulo <varname>b</varname>. See <xref linkend=\"genius-gel-"
"modular-evaluation\"/>. Some functions and operators behave differently "
"modulo an integer."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1477
msgid "<userinput>a!</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1479
msgid ""
"Factorial operator. This is like <userinput>1*...*(n-2)*(n-1)*n</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1488
msgid "<userinput>a!!</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1490
msgid ""
"Double factorial operator. This is like <userinput>1*...*(n-4)*(n-2)*n</"
"userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1499
msgid "<userinput>a==b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1501
msgid ""
"Equality operator. Returns <constant>true</constant> or <constant>false</"
"constant> depending on <varname>a</varname> and <varname>b</varname> being "
"equal or not."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1511
msgid "<userinput>a!=b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1513
msgid ""
"Inequality operator, returns <constant>true</constant> if <varname>a</"
"varname> does not equal <varname>b</varname> else returns <constant>false</"
"constant>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1523
msgid "<userinput>a&lt;&gt;b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1525
msgid ""
"Alternative inequality operator, returns <constant>true</constant> if "
"<varname>a</varname> does not equal <varname>b</varname> else returns "
"<constant>false</constant>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1535
msgid "<userinput>a&lt;=b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1537
msgid ""
"Less than or equal operator, returns <constant>true</constant> if "
"<varname>a</varname> is less than or equal to <varname>b</varname> else "
"returns <constant>false</constant>. These can be chained as in <userinput>a "
"&lt;= b &lt;= c</userinput> (can also be combined with the less than "
"operator)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1550
msgid "<userinput>a&gt;=b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1552
msgid ""
"Greater than or equal operator, returns <constant>true</constant> if "
"<varname>a</varname> is greater than or equal to <varname>b</varname> else "
"returns <constant>false</constant>. These can be chained as in <userinput>a "
"&gt;= b &gt;= c</userinput> (and they can also be combined with the greater "
"than operator)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1564
msgid "<userinput>a&lt;b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1566
msgid ""
"Less than operator, returns <constant>true</constant> if <varname>a</"
"varname> is less than <varname>b</varname> else returns <constant>false</"
"constant>. These can be chained as in <userinput>a &lt; b &lt; c</userinput> "
"(they can also be combined with the less than or equal to operator)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1579
msgid "<userinput>a&gt;b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1581
msgid ""
"Greater than operator, returns <constant>true</constant> if <varname>a</"
"varname> is greater than <varname>b</varname> else returns <constant>false</"
"constant>. These can be chained as in <userinput>a &gt; b &gt; c</userinput> "
"(they can also be combined with the greater than or equal to operator)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1594
msgid "<userinput>a&lt;=&gt;b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1596
msgid ""
"Comparison operator. If <varname>a</varname> is equal to <varname>b</"
"varname> it returns 0, if <varname>a</varname> is less than <varname>b</"
"varname> it returns -1 and if <varname>a</varname> is greater than "
"<varname>b</varname> it returns 1."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1608
msgid "<userinput>a and b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1610
msgid ""
"Logical and. Returns true if both <varname>a</varname> and <varname>b</"
"varname> are true, else returns false. If given numbers, nonzero numbers are "
"treated as true."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1621
msgid "<userinput>a or b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1623
msgid ""
"Logical or. Returns true if either <varname>a</varname> or <varname>b</"
"varname> is true, else returns false. If given numbers, nonzero numbers are "
"treated as true."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1635
msgid "<userinput>a xor b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1637
msgid ""
"Logical xor. Returns true if exactly one of <varname>a</varname> or "
"<varname>b</varname> is true, else returns false. If given numbers, nonzero "
"numbers are treated as true."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1649
msgid "<userinput>not a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1651
msgid "Logical not. Returns the logical negation of <varname>a</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1659
msgid "<userinput>-a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1661
msgid ""
"Negation operator. Returns the negative of a number or a matrix (works "
"element-wise on a matrix)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1669
msgid "<userinput>&amp;a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1671
msgid ""
"Variable referencing (to pass a reference to a variable). See <xref "
"linkend=\"genius-gel-references\"/>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1680 C/genius.xml:2327
msgid "<userinput>*a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1682
msgid ""
"Variable dereferencing (to access a referenced variable). See <xref "
"linkend=\"genius-gel-references\"/>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1691
msgid "<userinput>a'</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1693
msgid ""
"Matrix conjugate transpose. That is, rows and columns get swapped and we "
"take complex conjugate of all entries. That is if the i,j element of "
"<varname>a</varname> is x+iy, then the j,i element of <userinput>a'</"
"userinput> is x-iy."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1702
msgid "<userinput>a.'</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1704
msgid ""
"Matrix transpose, does not conjugate the entries. That is, the i,j element "
"of <varname>a</varname> becomes the j,i element of <userinput>a.'</"
"userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1713
msgid "<userinput>a@(b,c)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1715
msgid ""
"Get element of a matrix in row <varname>b</varname> and column <varname>c</"
"varname>. If <varname>b</varname>, <varname>c</varname> are vectors, then "
"this gets the corresponding rows, columns or submatrices."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1726
msgid "<userinput>a@(b,)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1728
msgid ""
"Get row of a matrix (or multiple rows if <varname>b</varname> is a vector)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1736
msgid "<userinput>a@(b,:)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1738 C/genius.xml:1759
msgid "Same as above."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1746
msgid "<userinput>a@(,c)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1748
msgid ""
"Get column of a matrix (or columns if <varname>c</varname> is a vector)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1757
msgid "<userinput>a@(:,c)</userinput>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1767
msgid "<userinput>a@(b)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1769
msgid ""
"Get an element from a matrix treating it as a vector. This will traverse the "
"matrix row-wise."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1778
msgid "<userinput>a:b</userinput>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1782
#, no-wrap
msgid ""
"A@(2:4,)\n"
"\t     "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1780
msgid ""
"Build a vector from <varname>a</varname> to <varname>b</varname> (or specify "
"a row, column region for the <literal>@</literal> operator). For example to "
"get rows 2 to 4 of matrix <varname>A</varname> we could do "
"<_:programlisting-1/> as <userinput>2:4</userinput> will return a vector "
"<userinput>[2,3,4]</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1792
msgid "<userinput>a:b:c</userinput>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1797
#, no-wrap
msgid ""
"genius&gt; 1:2:9\n"
"=\n"
"`[1, 3, 5, 7, 9]\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1794
msgid ""
"Build a vector from <varname>a</varname> to <varname>c</varname> with "
"<varname>b</varname> as a step. That is for example <_:programlisting-1/>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1802
msgid ""
"When the numbers involved are floating point numbers, for example "
"<userinput>1.0:0.4:3.0</userinput>, the output is what is expected even "
"though adding 0.4 to 1.0 five times is actually just slightly more than 3.0 "
"due to the way that floating point numbers are stored in base 2 (there is no "
"0.4, the actual number stored is just ever so slightly bigger). The way this "
"is handled is the same as in the for, sum, and prod loops. If the end is "
"within <userinput>2^-20</userinput> times the step size of the endpoint, the "
"endpoint is used and we assume there were roundoff errors. This is not "
"perfect, but it handles the majority of the cases. This check is done only "
"from version 1.0.18 onwards, so execution of your code may differ on older "
"versions. If you want to avoid dealing with this issue, use actual rational "
"numbers, possibly using the <function>float</function> if you wish to get "
"floating point numbers in the end. For example <userinput>1:2/5:3</"
"userinput> does the right thing and <userinput>float(1:2/5:3)</userinput> "
"even gives you floating point numbers and is ever so slightly more precise "
"than <userinput>1.0:0.4:3.0</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1828
msgid "<userinput>(a)i</userinput>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1834
#, no-wrap
msgid ""
"(a)*1i\n"
"\t     "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1830
msgid ""
"Make <varname>a</varname> into an imaginary number (multiply <varname>a</"
"varname> by the imaginary). Normally the imaginary number <varname>i</"
"varname> is written as <userinput>1i</userinput>. So the above is equal to "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1842
msgid "<userinput>`a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1844
msgid ""
"Quote an identifier so that it doesn't get evaluated. Or quote a matrix so "
"that it doesn't get expanded."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1852
msgid "<userinput>a swapwith b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1854
msgid ""
"Swap value of <varname>a</varname> with the value of <varname>b</varname>. "
"Currently does not operate on ranges of matrix elements. It returns "
"<constant>null</constant>. Available from version 1.0.13."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1865
msgid "<userinput>increment a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1867
msgid ""
"Increment the variable <varname>a</varname> by 1. If <varname>a</varname> is "
"a matrix, then increment each element. This is equivalent to "
"<userinput>a=a+1</userinput>, but it is somewhat faster. It returns "
"<constant>null</constant>. Available from version 1.0.13."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:1878
msgid "<userinput>increment a by b</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:1880
msgid ""
"Increment the variable <varname>a</varname> by <varname>b</varname>. If "
"<varname>a</varname> is a matrix, then increment each element. This is "
"equivalent to <userinput>a=a+b</userinput>, but it is somewhat faster. It "
"returns <constant>null</constant>. Available from version 1.0.13."
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:1894
msgid ""
"The @() operator makes the : operator most useful. With this you can specify "
"regions of a matrix. So that a@(2:4,6) is the rows 2,3,4 of the column 6. Or "
"a@(,1:2) will get you the first two columns of a matrix. You can also assign "
"to the @() operator, as long as the right value is a matrix that matches the "
"region in size, or if it is any other type of value."
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:1900
msgid ""
"The comparison operators (except for the &lt;=&gt; operator, which behaves "
"normally), are not strictly binary operators, they can in fact be grouped in "
"the normal mathematical way, e.g.: (1&lt;x&lt;=y&lt;5) is a legal boolean "
"expression and means just what it should, that is (1&lt;x and x≤y and y&lt;5)"
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:1906
msgid ""
"The unitary minus operates in a different fashion depending on where it "
"appears. If it appears before a number it binds very closely, if it appears "
"in front of an expression it binds less than the power and factorial "
"operators. So for example <userinput>-1^k</userinput> is really "
"<userinput>(-1)^k</userinput>, but <userinput>-foo(1)^k</userinput> is "
"really <userinput>-(foo(1)^k)</userinput>. So be careful how you use it and "
"if in doubt, add parentheses."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:1921
msgid "Programming with GEL"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1924
msgid "Conditionals"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1927
#, no-wrap
msgid "if &lt;expression1&gt; then &lt;expression2&gt; [else &lt;expression3&gt;]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1925
msgid ""
"Syntax: <_:programlisting-1/> If <literal>else</literal> is omitted, then if "
"the <literal>expression1</literal> yields <constant>false</constant> or 0, "
"<literal>NULL</literal> is returned."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1933
#, no-wrap
msgid ""
"if(a==5)then(a=a-1)\n"
"if b&lt;a then b=a\n"
"if c&gt;0 then c=c-1 else c=0\n"
"a = ( if b&gt;0 then b else 1 )\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1939
#, no-wrap
msgid "if a=5 then a=a-1\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1942
#, no-wrap
msgid "if a==5 then a:=a-1\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:1931
msgid ""
"Examples: <_:programlisting-1/> Note that <literal>=</literal> will be "
"translated to <literal>==</literal> if used inside the expression for "
"<literal>if</literal>, so <_:programlisting-2/> will be interpreted as: "
"<_:programlisting-3/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:1948
msgid "Loops"
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1951
msgid "While Loops"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1954
#, no-wrap
msgid ""
"while &lt;expression1&gt; do &lt;expression2&gt;\n"
"until &lt;expression1&gt; do &lt;expression2&gt;\n"
"do &lt;expression2&gt; while &lt;expression1&gt;\n"
"do &lt;expression2&gt; until &lt;expression1&gt;"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1952
msgid ""
"Syntax: <_:programlisting-1/> These are similar to other languages. However, "
"as in GEL it is simply an expression that must have some return value, these "
"constructs will simply return the result of the last iteration or "
"<literal>NULL</literal> if no iteration was done. In the boolean expression, "
"<literal>=</literal> is translated into <literal>==</literal> just as for "
"the <literal>if</literal> statement."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1965
msgid "For Loops"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1968
#, no-wrap
msgid ""
"for &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; do &lt;body&gt;\n"
"for &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; by &lt;increment&gt; do &lt;body&gt;"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1972
#, no-wrap
msgid "for i = 1 to 20 by 2 do print(i)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1966
msgid ""
"Syntax: <_:programlisting-1/> Loop with identifier being set to all values "
"from <literal>&lt;from&gt;</literal> to <literal>&lt;to&gt;</literal>, "
"optionally using an increment other than 1. These are faster, nicer and more "
"compact than the normal loops such as above, but less flexible. The "
"identifier must be an identifier and can't be a dereference. The value of "
"identifier is the last value of identifier, or <literal>&lt;from&gt;</"
"literal> if body was never evaluated. The variable is guaranteed to be "
"initialized after a loop, so you can safely use it. Also the "
"<literal>&lt;from&gt;</literal>, <literal>&lt;to&gt;</literal> and "
"<literal>&lt;increment&gt;</literal> must be non complex values. The "
"<literal>&lt;to&gt;</literal> is not guaranteed to be hit, but will never be "
"overshot, for example the following prints out odd numbers from 1 to 19: "
"<_:programlisting-2/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1980
#, no-wrap
msgid "for x = 0 to 1 by 0.1 do print(x)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1985
#, no-wrap
msgid "for x = 0 to 1 by 1/10 do print(x)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1975
msgid ""
"When one of the values is a floating point number, then the final check is "
"done to within 2^-20 of the step size. That is, even if we overshoot by "
"2^-20 times the \"by\" above, we still execute the last iteration. This way "
"<_:programlisting-1/> does the expected even though adding 0.1 ten times "
"becomes just slightly more than 1.0 due to the way that floating point "
"numbers are stored in base 2 (there is no 0.1, the actual number stored is "
"just ever so slightly bigger). This is not perfect but it handles the "
"majority of the cases. If you want to avoid dealing with this issue, use "
"actual rational numbers for example: <_:programlisting-2/> This check is "
"done only from version 1.0.16 onwards, so execution of your code may differ "
"on older versions."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:1992
msgid "Foreach Loops"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:1995
#, no-wrap
msgid "for &lt;identifier&gt; in &lt;matrix&gt; do &lt;body&gt;"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2000
#, no-wrap
msgid "for n in [1,2:3,4] do print(n)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2005
#, no-wrap
msgid "for n in RowsOf ([1,2:3,4]) do print(n)\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:1993
msgid ""
"Syntax: <_:programlisting-1/> For each element in the matrix, going row by "
"row from left to right we execute the body with the identifier set to the "
"current element. To print numbers 1,2,3 and 4 in this order you could do: "
"<_:programlisting-2/> If you wish to run through the rows and columns of a "
"matrix, you can use the RowsOf and ColumnsOf functions, which return a "
"vector of the rows or columns of the matrix. So, <_:programlisting-3/> will "
"print out [1,2] and then [3,4]."
msgstr ""

#. (itstool) path: sect2/title
#: C/genius.xml:2012
msgid "Break and Continue"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2015
#, no-wrap
msgid ""
"while(&lt;expression1&gt;) do (\n"
"  if(&lt;expression2&gt;) break\n"
"  else if(&lt;expression3&gt;) continue;\n"
"  &lt;expression4&gt;\n"
")\n"
msgstr ""

#. (itstool) path: sect2/para
#: C/genius.xml:2013
msgid ""
"You can also use the <literal>break</literal> and <literal>continue</"
"literal> commands in loops. The continue <literal>continue</literal> command "
"will restart the current loop at its next iteration, while the "
"<literal>break</literal> command exits the current loop. <_:programlisting-1/"
">"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2026
msgid "Sums and Products"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2029
#, no-wrap
msgid ""
"sum &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; do &lt;body&gt;\n"
"sum &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; by &lt;increment&gt; do &lt;body&gt;\n"
"sum &lt;identifier&gt; in &lt;matrix&gt; do &lt;body&gt;\n"
"prod &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; do &lt;body&gt;\n"
"prod &lt;identifier&gt; = &lt;from&gt; to &lt;to&gt; by &lt;increment&gt; do &lt;body&gt;\n"
"prod &lt;identifier&gt; in &lt;matrix&gt; do &lt;body&gt;"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2027
msgid ""
"Syntax: <_:programlisting-1/> If you substitute <literal>for</literal> with "
"<literal>sum</literal> or <literal>prod</literal>, then you will get a sum "
"or a product instead of a <literal>for</literal> loop. Instead of returning "
"the last value, these will return the sum or the product of the values "
"respectively."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2038
msgid ""
"If no body is executed (for example <userinput>sum i=1 to 0 do ...</"
"userinput>) then <literal>sum</literal> returns 0 and <literal>prod</"
"literal> returns 1 as is the standard convention."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2041
msgid ""
"For floating point numbers the same roundoff error protection is done as in "
"the for loop. See <xref linkend=\"genius-gel-loops-for\"/>."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2048
msgid "Comparison Operators"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2049
msgid ""
"The following standard comparison operators are supported in GEL and have "
"the obvious meaning: <literal>==</literal>, <literal>&gt;=</literal>, "
"<literal>&lt;=</literal>, <literal>!=</literal>, <literal>&lt;&gt;</"
"literal>, <literal>&lt;</literal>, <literal>&gt;</literal>. They return "
"<constant>true</constant> or <constant>false</constant>. The operators "
"<literal>!=</literal> and <literal>&lt;&gt;</literal> are the same thing and "
"mean \"is not equal to\". GEL also supports the operator <literal>&lt;=&gt;</"
"literal>, which returns -1 if left side is smaller, 0 if both sides are "
"equal, 1 if left side is larger."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2068
#, no-wrap
msgid ""
"if a=b then c\n"
"if a==b then c\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2064
msgid ""
"Normally <literal>=</literal> is translated to <literal>==</literal> if it "
"happens to be somewhere where GEL is expecting a condition such as in the if "
"condition. For example <_:programlisting-1/> are the same thing in GEL. "
"However you should really use <literal>==</literal> or <literal>:=</literal> "
"when you want to compare or assign respectively if you want your code to be "
"easy to read and to avoid mistakes."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2077
msgid ""
"All the comparison operators (except for the <literal>&lt;=&gt;</literal> "
"operator, which behaves normally), are not strictly binary operators, they "
"can in fact be grouped in the normal mathematical way, e.g.: "
"(<literal>1&lt;x&lt;=y&lt;5</literal>) is a legal boolean expression and "
"means just what it should, that is (1&lt;x and x≤y and y&lt;5)"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2086
msgid ""
"To build up logical expressions use the words <literal>not</literal>, "
"<literal>and</literal>, <literal>or</literal>, <literal>xor</literal>. The "
"operators <literal>or</literal> and <literal>and</literal> are special "
"beasts as they evaluate their arguments one by one, so the usual trick for "
"conditional evaluation works here as well. For example, <literal>1 or a=1</"
"literal> will not set <literal>a=1</literal> since the first argument was "
"true."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2097
msgid "Global Variables and Scope of Variables"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2098
msgid ""
"GEL is a <ulink url=\"https://en.wikipedia.org/wiki/"
"Scope_%28programming%29\"> dynamically scoped language</ulink>. We will "
"explain what this means below. That is, normal variables and functions are "
"dynamically scoped. The exception are <link linkend=\"genius-gel-"
"parameters\">parameter variables</link>, which are always global."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2121
#, no-wrap
msgid ""
"function f() = (a:=5; g());\n"
"function g() = print(a);\n"
"f();\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2107
msgid ""
"Like most programming languages, GEL has different types of variables. "
"Normally when a variable is defined in a function, it is visible from that "
"function and from all functions that are called (all higher contexts). For "
"example, suppose a function <function>f</function> defines a variable "
"<varname>a</varname> and then calls function <function>g</function>. Then "
"function <function>g</function> can reference <varname>a</varname>. But once "
"<function>f</function> returns, the variable <varname>a</varname> goes out "
"of scope. For example, the following code will print out 5. The function "
"<function>g</function> cannot be called on the top level (outside "
"<function>f</function> as <varname>a</varname> will not be defined). "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2130
#, no-wrap
msgid ""
"function f() = (a:=5; g());\n"
"function g() = print(a);\n"
"a:=10;\n"
"f();\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2126
msgid ""
"If you define a variable inside a function it will override any variables "
"defined in calling functions. For example, we modify the above code and "
"write: <_:programlisting-1/> This code will still print out 5. But if you "
"call <function>g</function> outside of <function>f</function> then you will "
"get a printout of 10. Note that setting <varname>a</varname> to 5 inside "
"<function>f</function> does not change the value of <varname>a</varname> at "
"the top (global) level, so if you now check the value of <varname>a</"
"varname> it will still be 10."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2144
msgid ""
"Function arguments are exactly like variables defined inside the function, "
"except that they are initialized with the value that was passed to the "
"function. Other than this point, they are treated just like all other "
"variables defined inside the function."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:2156
#, no-wrap
msgid ""
"<prompt>genius&gt; </prompt><userinput>function f(x) = sin(x)^2</userinput>\n"
"= (`(x)=(sin(x)^2))\n"
"<prompt>genius&gt; </prompt><userinput>function f(x) = sin(x)^2</userinput>\n"
"= (`(x)=(sin(x)^2))\n"
"<prompt>genius&gt; </prompt><userinput>function g(x) = ((function sin(x)=x^10);f(x))</userinput>\n"
"= (`(x)=((sin:=(`(x)=(x^10)));f(x)))\n"
"<prompt>genius&gt; </prompt><userinput>g(10)</userinput>\n"
"= 1e20\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2151
msgid ""
"Functions are treated exactly like variables. Hence you can locally redefine "
"functions. Normally (on the top level) you cannot redefine protected "
"variables and functions. But locally you can do this. Consider the following "
"session: <_:screen-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2171
#, no-wrap
msgid ""
"a=6;\n"
"function f() = (a:=5);\n"
"f();\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2182
#, no-wrap
msgid "set(`a,3)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2185
#, no-wrap
msgid "set(\"a\",3)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2166
msgid ""
"Functions and variables defined at the top level are considered global. They "
"are visible from anywhere. As we said the following function <function>f</"
"function> will not change the value of <varname>a</varname> to 5. "
"<_:programlisting-1/> Sometimes, however, it is necessary to set a global "
"variable from inside a function. When this behavior is needed, use the <link "
"linkend=\"gel-function-set\"><function>set</function></link> function. "
"Passing a string or a quoted identifier to this function sets the variable "
"globally (on the top level). For example, to set <varname>a</varname> to the "
"value 3 you could call: <_:programlisting-2/> or: <_:programlisting-3/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2188
msgid ""
"The <function>set</function> function always sets the toplevel global. There "
"is no way to set a local variable in some function from a subroutine. If "
"this is required, must use passing by reference."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2194
msgid ""
"See also the <link linkend=\"gel-function-SetElement\"><function>SetElement</"
"function></link> and <link linkend=\"gel-function-"
"SetVElement\"><function>SetVElement</function></link> functions."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2199
msgid ""
"So to recap in a more technical language: Genius operates with different "
"numbered contexts. The top level is the context 0 (zero). Whenever a "
"function is entered, the context is raised, and when the function returns "
"the context is lowered. A function or a variable is always visible from all "
"higher numbered contexts. When a variable was defined in a lower numbered "
"context, then setting this variable has the effect of creating a new local "
"variable in the current context number and this variable will now be visible "
"from all higher numbered contexts."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2210
msgid ""
"There are also true local variables that are not seen from anywhere but the "
"current context. Also when returning functions by value it may reference "
"variables not visible from higher context and this may be a problem. See the "
"sections <link linkend=\"genius-gel-true-local-variables\">True Local "
"Variables</link> and <link linkend=\"genius-gel-returning-"
"functions\">Returning Functions</link>."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2223
msgid "Parameter variables"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2228
#, no-wrap
msgid "parameter foo = 1\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2224
msgid ""
"As we said before, there exist special variables called parameters that "
"exist in all scopes. To declare a parameter called <varname>foo</varname> "
"with the initial value 1, we write <_:programlisting-1/> From then on, "
"<varname>foo</varname> is a strictly global variable. Setting <varname>foo</"
"varname> inside any function will modify the variable in all contexts, that "
"is, functions do not have a private copy of parameters."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2235
msgid ""
"When you undefine a parameter using the <link linkend=\"gel-function-"
"undefine\"> <function>undefine</function></link> function, it stops being a "
"parameter."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2241
msgid "Some parameters are built-in and modify the behavior of genius."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2247
msgid "Returning"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2248
msgid ""
"Normally a function is one or several expressions separated by a semicolon, "
"and the value of the last expression is returned. This is fine for simple "
"functions, but sometimes you do not want a function to return the last thing "
"calculated. You may, for example, want to return from a middle of a "
"function. In this case, you can use the <literal>return</literal> keyword. "
"<literal>return</literal> takes one argument, which is the value to be "
"returned."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2256
#, no-wrap
msgid ""
"function f(x) = (\n"
"  y=1;\n"
"  while true do (\n"
"    if x&gt;50 then return y;\n"
"    y=y+1;\n"
"    x=x+1\n"
"  )\n"
")\n"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2270
msgid "References"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2271
msgid ""
"It may be necessary for some functions to return more than one value. This "
"may be accomplished by returning a vector of values, but many times it is "
"convenient to use passing a reference to a variable. You pass a reference to "
"a variable to a function, and the function will set the variable for you "
"using a dereference. You do not have to use references only for this "
"purpose, but this is their main use."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2286
#, no-wrap
msgid "RayleighQuotientIteration (A,x,0.001,100,&amp;v)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2279
msgid ""
"When using functions that return values through references in the argument "
"list, just pass the variable name with an ampersand. For example the "
"following code will compute an eigenvalue of a matrix <varname>A</varname> "
"with initial eigenvector guess <varname>x</varname>, and store the computed "
"eigenvector into the variable named <varname>v</varname>: "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2289
msgid ""
"The details of how references work and the syntax is similar to the C "
"language. The operator <literal>&amp;</literal> references a variable and "
"<literal>*</literal> dereferences a variable. Both can only be applied to an "
"identifier, so <literal>**a</literal> is not a legal expression in GEL."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2298
#, no-wrap
msgid ""
"a=1;\n"
"b=&amp;a;\n"
"*b=2;\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2303
#, no-wrap
msgid ""
"function f(x) = x+1;\n"
"t=&amp;f;\n"
"*t(3)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2296
msgid ""
"References are best explained by an example: <_:programlisting-1/> now "
"<varname>a</varname> contains 2. You can also reference functions: "
"<_:programlisting-2/> gives us 4."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2312
msgid "Lvalues"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2318
msgid "<userinput>a</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2320
msgid ""
"Identifier. Here we would be setting the variable of name <varname>a</"
"varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2329
msgid ""
"Dereference of an identifier. This will set whatever variable <varname>a</"
"varname> points to."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2336
msgid "<userinput>a@(&lt;region&gt;)</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2338
msgid ""
"A region of a matrix. Here the region is specified normally as with the "
"regular @() operator, and can be a single entry, or an entire region of the "
"matrix."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2313
msgid ""
"An lvalue is the left hand side of an assignment. In other words, an lvalue "
"is what you assign something to. Valid lvalues are: <_:variablelist-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2349
#, no-wrap
msgid ""
"a:=4\n"
"*tmp := 89\n"
"a@(1,1) := 5\n"
"a@(4:8,3) := [1,2,3,4,5]'\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2347
msgid ""
"Examples: <_:programlisting-1/> Note that both <literal>:=</literal> and "
"<literal>=</literal> can be used interchangeably. Except if the assignment "
"appears in a condition. It is thus always safer to just use <literal>:=</"
"literal> when you mean assignment, and <literal>==</literal> when you mean "
"comparison."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:2365
msgid "Advanced Programming with GEL"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2368
msgid "Error Handling"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2369
msgid ""
"If you detect an error in your function, you can bail out of it. For normal "
"errors, such as wrong types of arguments, you can fail to compute the "
"function by adding the statement <literal>bailout</literal>. If something "
"went really wrong and you want to completely kill the current computation, "
"you can use <literal>exception</literal>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2379
#, no-wrap
msgid ""
"function f(M) = (\n"
"  if not IsMatrix (M) then (\n"
"    error (\"M not a matrix!\");\n"
"    bailout\n"
"  );\n"
"  ...\n"
")\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2376
msgid ""
"For example if you want to check for arguments in your function. You could "
"use the following code. <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2391
msgid "Toplevel Syntax"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2392
msgid ""
"The syntax is slightly different if you enter statements on the top level "
"versus when they are inside parentheses or inside functions. On the top "
"level, enter acts the same as if you press return on the command line. "
"Therefore think of programs as just a sequence of lines as if they were "
"entered on the command line. In particular, you do not need to enter the "
"separator at the end of the line (unless it is part of several statements "
"inside parentheses). When a statement does not end with a separator on the "
"top level, the result is printed after being executed."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2405
#, no-wrap
msgid ""
"function f(x)=x^2\n"
"f(3)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2412
#, no-wrap
msgid ""
"function f(x)=x^2;\n"
"f(3)\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2417
#, no-wrap
msgid ""
"function f(x)=(\n"
"  y=1;\n"
"  for j=1 to x do\n"
"    y = y+j;\n"
"  y^2\n"
");\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2403
msgid ""
"For example, <_:programlisting-1/> will print first the result of setting a "
"function (a representation of the function, in this case "
"<computeroutput>(`(x)=(x^2))</computeroutput>) and then the expected 9. To "
"avoid this, enter a separator after the function definition. "
"<_:programlisting-2/> If you need to put a separator into your function then "
"you have to surround with parenthesis. For example: <_:programlisting-3/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2428
#, no-wrap
msgid ""
"if Something() then\n"
"  DoSomething()\n"
"else\n"
"  DoSomethingElse()\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2425
msgid ""
"The following code will produce an error when entered on the top level of a "
"program, while it will work just fine in a function. <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2442
#, no-wrap
msgid ""
"if Something() then (\n"
"  DoSomething()\n"
") else (\n"
"  DoSomethingElse()\n"
")\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2434
msgid ""
"The problem is that after <application>Genius Mathematics Tool</application> "
"sees the end of line after the second line, it will decide that we have "
"whole statement and it will execute it. After the execution is done, "
"<application>Genius Mathematics Tool</application> will go on to the next "
"line, it will see <literal>else</literal>, and it will produce a parsing "
"error. To fix this, use parentheses. <application>Genius Mathematics Tool</"
"application> will not be satisfied until it has found that all parentheses "
"are closed. <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2452
msgid "Returning Functions"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2465
#, no-wrap
msgid ""
"function f() = (\n"
"  k = 5;\n"
"  `(x) = (x+k)\n"
")\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2472
#, no-wrap
msgid ""
"g = f();\n"
"g(5)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2453
msgid ""
"It is possible to return functions as value. This way you can build "
"functions that construct special purpose functions according to some "
"parameters. The tricky bit is what variables does the function see. The way "
"this works in GEL is that when a function returns another function, all "
"identifiers referenced in the function body that went out of scope are "
"prepended a private dictionary of the returned function. So the function "
"will see all variables that were in scope when it was defined. For example, "
"we define a function that returns a function that adds 5 to its argument. "
"<_:programlisting-1/> Notice that the function adds <varname>k</varname> to "
"<varname>x</varname>. You could use this as follows. <_:programlisting-2/> "
"And <userinput>g(5)</userinput> should return 10."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2481
#, no-wrap
msgid ""
"function f() = (\n"
"  k := 5;\n"
"  function r(x) = (x+k);\n"
"  k := 10;\n"
"  r\n"
")\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2477
msgid ""
"One thing to note is that the value of <varname>k</varname> that is used is "
"the one that's in effect when the <function>f</function> returns. For "
"example: <_:programlisting-1/> will return a function that adds 10 to its "
"argument rather than 5. This is because the extra dictionary is created only "
"when the context in which the function was defined ends, which is when the "
"function <function>f</function> returns. This is consistent with how you "
"would expect the function <function>r</function> to work inside the function "
"<function>f</function> according to the rules of scope of variables in GEL. "
"Only those variables are added to the extra dictionary that are in the "
"context that just ended and no longer exists. Variables used in the function "
"that are in still valid contexts will work as usual, using the current value "
"of the variable. The only difference is with global variables and functions. "
"All identifiers that referenced global variables at time of the function "
"definition are not added to the private dictionary. This is to avoid much "
"unnecessary work when returning functions and would rarely be a problem. For "
"example, suppose that you delete the \"k=5\" from the function <function>f</"
"function>, and at the top level you define <varname>k</varname> to be say 5. "
"Then when you run <function>f</function>, the function <function>r</"
"function> will not put <varname>k</varname> into the private dictionary "
"because it was global (toplevel) at the time of definition of <function>r</"
"function>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2523
#, no-wrap
msgid ""
"function f() = (\n"
"  k := 5;\n"
"  function r(x) [k] = (x+k);\n"
"  k := 10;\n"
"  r\n"
")\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2512
msgid ""
"Sometimes it is better to have more control over how variables are copied "
"into the private dictionary. Since version 1.0.7, you can specify which "
"variables are copied into the private dictionary by putting extra square "
"brackets after the arguments with the list of variables to be copied "
"separated by commas. If you do this, then variables are copied into the "
"private dictionary at time of the function definition, and the private "
"dictionary is not touched afterwards. For example <_:programlisting-1/> will "
"return a function that when called will add 5 to its argument. The local "
"copy of <varname>k</varname> was created when the function was defined."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2545
#, no-wrap
msgid ""
"function f() = (\n"
"  k := 5;\n"
"  function r(x) [] = (x+k);\n"
"  r\n"
");\n"
"k := 10;\n"
"g = f();\n"
"g(10)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2534
msgid ""
"When you want the function to not have any private dictionary then put empty "
"square brackets after the argument list. Then no private dictionary will be "
"created at all. Doing this is good to increase efficiency when a private "
"dictionary is not needed or when you want the function to lookup all "
"variables as it sees them when called. For example suppose you want the "
"function returned from <function>f</function> to see the value of "
"<varname>k</varname> from the toplevel despite there being a local variable "
"of the same name during definition. So the code <_:programlisting-1/> will "
"return 20 and not 15, which would happen if <varname>k</varname> with a "
"value of 5 was added to the private dictionary."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2561
msgid "True Local Variables"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2565
#, no-wrap
msgid ""
"k := 10;\n"
"function r(x) = (x+k);\n"
"function f(g,x) = (\n"
"  k := 5;\n"
"  g(x)\n"
");\n"
"f(r,1)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2562
msgid ""
"When passing functions into other functions, the normal scoping of variables "
"might be undesired. For example: <_:programlisting-1/> you probably want the "
"function <function>r</function> when passed as <function>g</function> into "
"<function>f</function> to see <varname>k</varname> as 10 rather than 5, so "
"that the code returns 11 and not 6. However, as written, the function when "
"executed will see the <varname>k</varname> that is equal to 5. There are two "
"ways to solve this. One would be to have <function>r</function> get "
"<varname>k</varname> in a private dictionary using the square bracket "
"notation section <link linkend=\"genius-gel-returning-functions\">Returning "
"Functions</link>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2594
#, no-wrap
msgid ""
"function f(g,x) = (\n"
"  local g,x,k;\n"
"  k := 5;\n"
"  g(x)\n"
");\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2584
msgid ""
"But there is another solution. Since version 1.0.7 there are true local "
"variables. These are variables that are visible only from the current "
"context and not from any called functions. We could define <varname>k</"
"varname> as a local variable in the function <function>f</function>. To do "
"this add a <command>local</command> statement as the first statement in the "
"function (it must always be the first statement in the function). You can "
"also make any arguments be local variables as well. That is, "
"<_:programlisting-1/> Then the code will work as expected and prints out 11. "
"Note that the <command>local</command> statement initializes all the "
"referenced variables (except for function arguments) to a <constant>null</"
"constant>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2611
#, no-wrap
msgid ""
"function f(g,x) = (\n"
"  local *;\n"
"  k := 5;\n"
"  g(x)\n"
");\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2605
msgid ""
"If all variables are to be created as locals you can just pass an asterisk "
"instead of a list of variables. In this case the variables will not be "
"initialized until they are actually set. So the following definition of "
"<function>f</function> will also work: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2618
msgid ""
"It is good practice that all functions that take other functions as "
"arguments use local variables. This way the passed function does not see "
"implementation details and get confused."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2626
msgid "GEL Startup Procedure"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2627
msgid ""
"First the program looks for the installed library file (the compiled version "
"<filename>lib.cgel</filename>) in the installed directory, then it looks "
"into the current directory, and then it tries to load an uncompiled file "
"called <filename>~/.geniusinit</filename>."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2631
msgid ""
"If you ever change the library in its installed place, you’ll have to first "
"compile it with <command>genius --compile loader.gel &gt; lib.cgel</command>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2638
msgid "Loading Programs"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2641
#, no-wrap
msgid ""
"load program1.gel program2.gel\n"
"load \"Weird File Name With SPACES.gel\"\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2645
#, no-wrap
msgid ""
"cd directory_with_gel_programs\n"
"ls *.gel\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2639
msgid ""
"Sometimes you have a larger program you wrote into a file and want to read "
"that file into <application>Genius Mathematics Tool</application>. In these "
"situations, you have two options. You can keep the functions you use most "
"inside the <filename>~/.geniusinit</filename> file. Or if you want to load "
"up a file in a middle of a session (or from within another file), you can "
"type <command>load &lt;list of filenames&gt;</command> at the prompt. This "
"has to be done on the top level and not inside any function or whatnot, and "
"it cannot be part of any expression. It also has a slightly different syntax "
"than the rest of genius, more similar to a shell. You can enter the file in "
"quotes. If you use the '' quotes, you will get exactly the string that you "
"typed, if you use the \"\" quotes, special characters will be unescaped as "
"they are for strings. Example: <_:programlisting-1/> There are also "
"<command>cd</command>, <command>pwd</command> and <command>ls</command> "
"commands built in. <command>cd</command> will take one argument, "
"<command>ls</command> will take an argument that is like the glob in the "
"UNIX shell (i.e., you can use wildcards). <command>pwd</command> takes no "
"arguments. For example: <_:programlisting-2/>"
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:2655
msgid "Matrices in GEL"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:2657
msgid ""
"Genius has support for vectors and matrices and possesses a sizable library "
"of matrix manipulation and linear algebra functions."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2663
msgid "Entering Matrices"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2672
#, no-wrap
msgid "[1,2,3;4,5,6;7,8,9]\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2675
#, no-wrap
msgid ""
"[1, 2, 3\n"
" 4, 5, 6\n"
" 7, 8, 9]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2664
msgid ""
"To enter matrices, you can use one of the following two syntaxes. You can "
"either enter the matrix on one line, separating values by commas and rows by "
"semicolons. Or you can enter each row on one line, separating values by "
"commas. You can also just combine the two methods. So to enter a 3x3 matrix "
"of numbers 1-9 you could do <_:programlisting-1/> or <_:programlisting-2/> "
"Do not use both ';' and return at once on the same line though."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2685
#, no-wrap
msgid ""
"a = [ 1, 2, 3\n"
"      4, 5, 6\n"
"      7, 8, 9]\n"
"b = [ a,  10\n"
"      11, 12]\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2692
#, no-wrap
msgid ""
"[1,   2,  3, 10\n"
" 4,   5,  6, 10\n"
" 7,   8,  9, 10\n"
" 11, 11, 11, 12]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2682
msgid ""
"You can also use the matrix expansion functionality to enter matrices. For "
"example you can do: <_:programlisting-1/> and you should get "
"<_:programlisting-2/> similarly you can build matrices out of vectors and "
"other stuff like that."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2702
#, no-wrap
msgid ""
"[1, 2, 3\n"
" 4, 5\n"
" 6]\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2707
#, no-wrap
msgid ""
"\n"
"[1, 2, 3\n"
" 4, 5, 0\n"
" 6, 0, 0]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2700
msgid ""
"Another thing is that non-specified spots are initialized to 0, so "
"<_:programlisting-1/> will end up being <_:programlisting-2/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2714
msgid ""
"When matrices are evaluated, they are evaluated and traversed row-wise. This "
"is just like the <literal>M@(j)</literal> operator, which traverses the "
"matrix row-wise."
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:2720
msgid ""
"Be careful about using returns for expressions inside the <literal>[ ]</"
"literal> brackets, as they have a slightly different meaning there. You will "
"start a new row."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2730
msgid "Conjugate Transpose and Transpose Operator"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2738
#, no-wrap
msgid "[1,2,3]*[4,5,6]'\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2743
#, no-wrap
msgid "[1,2,3]*[4,5,6i].'\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2731
msgid ""
"You can conjugate transpose a matrix by using the <literal>'</literal> "
"operator. That is the entry in the <varname>i</varname>th column and the "
"<varname>j</varname>th row will be the complex conjugate of the entry in the "
"<varname>j</varname>th column and the <varname>i</varname>th row of the "
"original matrix. For example: <_:programlisting-1/> We transpose the second "
"vector to make matrix multiplication possible. If you just want to transpose "
"a matrix without conjugating it, you would use the <literal>.'</literal> "
"operator. For example: <_:programlisting-2/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2746
msgid ""
"Note that normal transpose, that is the <literal>.'</literal> operator, is "
"much faster and will not create a new copy of the matrix in memory. The "
"conjugate transpose does create a new copy unfortunately. It is recommended "
"to always use the <literal>.'</literal> operator when working with real "
"matrices and vectors."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2756 C/genius.xml:5945
msgid "Linear Algebra"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2757
msgid ""
"Genius implements many useful linear algebra and matrix manipulation "
"routines. See the <link linkend=\"genius-gel-function-list-linear-"
"algebra\">Linear Algebra</link> and <link linkend=\"genius-gel-function-list-"
"matrix\">Matrix Manipulation</link> sections of the GEL function listing."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2764
msgid ""
"The linear algebra routines implemented in GEL do not currently come from a "
"well tested numerical package, and thus should not be used for critical "
"numerical computation. On the other hand, Genius implements very well many "
"linear algebra operations with rational and integer coefficients. These are "
"inherently exact and in fact will give you much better results than common "
"double precision routines for linear algebra."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2772
msgid ""
"For example, it is pointless to compute the rank and nullspace of a floating "
"point matrix since for all practical purposes, we need to consider the "
"matrix as having some slight errors. You are likely to get a different "
"result than you expect. The problem is that under a small perturbation every "
"matrix is of full rank and invertible. If the matrix however is of rational "
"numbers, then the rank and nullspace are always exact."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2780
msgid ""
"In general when Genius computes the basis of a certain vectorspace (for "
"example with the <link linkend=\"gel-function-"
"NullSpace\"><function>NullSpace</function></link>) it will give the basis as "
"a matrix, in which the columns are the vectors of the basis. That is, when "
"Genius talks of a linear subspace it means a matrix whose column space is "
"the given linear subspace."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2787
msgid ""
"It should be noted that Genius can remember certain properties of a matrix. "
"For example, it will remember that a matrix is in row reduced form. If many "
"calls are made to functions that internally use row reduced form of the "
"matrix, we can just row reduce the matrix beforehand once. Successive calls "
"to <link linkend=\"gel-function-rref\"><function>rref</function></link> will "
"be very fast."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:2800
msgid "Polynomials in GEL"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:2802
msgid ""
"Currently Genius can handle polynomials of one variable written out as "
"vectors, and do some basic operations with these. It is planned to expand "
"this support further."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2809
msgid "Using Polynomials"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2815
#, no-wrap
msgid "[1,2,3]\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2818
#, no-wrap
msgid "1 + 2*x + 3*x^2\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2810
msgid ""
"Currently polynomials in one variable are just horizontal vectors with value "
"only nodes. The power of the term is the position in the vector, with the "
"first position being 0. So, <_:programlisting-1/> translates to a polynomial "
"of <_:programlisting-2/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2830
#, no-wrap
msgid "PolyToString([1,2,3],\"y\")\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2833
#, no-wrap
msgid "3*y^2 + 2*y + 1\n"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2840
#, no-wrap
msgid ""
"f = PolyToFunction([0,1,1])\n"
"f(2)\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2821
msgid ""
"You can add, subtract and multiply polynomials using the <link linkend=\"gel-"
"function-AddPoly\"><function>AddPoly</function></link>, <link linkend=\"gel-"
"function-SubtractPoly\"><function>SubtractPoly</function></link>, and <link "
"linkend=\"gel-function-MultiplyPoly\"><function>MultiplyPoly</function></"
"link> functions respectively. You can print a polynomial using the <link "
"linkend=\"gel-function-PolyToString\"><function>PolyToString</function></"
"link> function. For example, <_:programlisting-1/> gives <_:programlisting-2/"
"> You can also get a function representation of the polynomial so that you "
"can evaluate it. This is done by using <link linkend=\"gel-function-"
"PolyToFunction\"><function>PolyToFunction</function></link>, which returns "
"an anonymous function. <_:programlisting-3/>"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2844
msgid ""
"It is also possible to find roots of polynomials of degrees 1 through 4 by "
"using the function <link linkend=\"gel-function-"
"PolynomialRoots\"><function>PolynomialRoots</function></link>, which calls "
"the appropriate formula function. Higher degree polynomials must be "
"converted to functions and solved numerically using a function such as <link "
"linkend=\"gel-function-FindRootBisection\"><function>FindRootBisection</"
"function></link>, <link linkend=\"gel-function-"
"FindRootFalsePosition\"><function>FindRootFalsePosition</function></link>, "
"<link linkend=\"gel-function-"
"FindRootMullersMethod\"><function>FindRootMullersMethod</function></link>, "
"or <link linkend=\"gel-function-FindRootSecant\"><function>FindRootSecant</"
"function></link>."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2856
msgid ""
"See <xref linkend=\"genius-gel-function-list-polynomials\"/> in the function "
"list for the rest of functions acting on polynomials."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:2866
msgid "Set Theory in GEL"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:2868
msgid ""
"Genius has some basic set theoretic functionality built in. Currently a set "
"is just a vector (or a matrix). Every distinct object is treated as a "
"different element."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2874
msgid "Using Sets"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2875
msgid ""
"Just like vectors, objects in sets can include numbers, strings, "
"<constant>null</constant>, matrices and vectors. It is planned in the future "
"to have a dedicated type for sets, rather than using vectors. Note that "
"floating point numbers are distinct from integers, even if they appear the "
"same. That is, Genius will treat <constant>0</constant> and <constant>0.0</"
"constant> as two distinct elements. The <constant>null</constant> is treated "
"as an empty set."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:2887
#, no-wrap
msgid ""
"<prompt>genius&gt; </prompt><userinput>MakeSet([1,2,2,3])</userinput>\n"
"= [1, 2, 3]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2883
msgid ""
"To build a set out of a vector, use the <link linkend=\"gel-function-"
"MakeSet\"><function>MakeSet</function></link> function. Currently, it will "
"just return a new vector where every element is unique. <_:screen-1/>"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:2898
#, no-wrap
msgid ""
"<prompt>genius&gt; </prompt><userinput>Union([1,2,3], [1,2,4])</userinput>\n"
"= [1, 2, 4, 3]\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2892
msgid ""
"Similarly there are functions <link linkend=\"gel-function-"
"Union\"><function>Union</function></link>, <link linkend=\"gel-function-"
"Intersection\"><function>Intersection</function></link>, <link linkend=\"gel-"
"function-SetMinus\"><function>SetMinus</function></link>, which are rather "
"self explanatory. For example: <_:screen-1/> Note that no order is "
"guaranteed for the return values. If you wish to sort the vector you should "
"use the <link linkend=\"gel-function-SortVector\"><function>SortVector</"
"function></link> function."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:2911
#, no-wrap
msgid ""
"<prompt>genius&gt; </prompt><userinput>IsIn (1, [0,1,2])</userinput>\n"
"= true\n"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:2906
msgid ""
"For testing membership, there are functions <link linkend=\"gel-function-"
"IsIn\"><function>IsIn</function></link> and <link linkend=\"gel-function-"
"IsSubset\"><function>IsSubset</function></link>, which return a boolean "
"value. For example: <_:screen-1/> The input <userinput>IsIn(x,X)</userinput> "
"is equivalent to <userinput>IsSubset([x],X)</userinput>. Note that since the "
"empty set is a subset of every set, <userinput>IsSubset(null,X)</userinput> "
"is always true."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:2925
msgid "List of GEL functions"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:2931
#, no-wrap
msgid "help FunctionName\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:2929
msgid ""
"To get help on a specific function from the console type: "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2936
msgid "Commands"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2939
msgid "<anchor id=\"gel-command-help\"/>help"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2941
#, no-wrap
msgid "help"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2942
#, no-wrap
msgid "help FunctionName"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2943
msgid "Print help (or help on a function/command)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2948
msgid "<anchor id=\"gel-command-load\"/>load"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2950
#, no-wrap
msgid "load \"file.gel\""
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2951
msgid ""
"Load a file into the interpreter. The file will execute as if it were typed "
"onto the command line."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2957
msgid "<anchor id=\"gel-command-cd\"/>cd"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2959
#, no-wrap
msgid "cd /directory/name"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2960
msgid "Change working directory to <filename>/directory/name</filename>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2965
msgid "<anchor id=\"gel-command-pwd\"/>pwd"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2967
#, no-wrap
msgid "pwd"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2968
msgid "Print the current working directory."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2973
msgid "<anchor id=\"gel-command-ls\"/>ls"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2975
#, no-wrap
msgid "ls"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2976
msgid "List files in the current directory."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2981
msgid "<anchor id=\"gel-command-plugin\"/>plugin"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2983
#, no-wrap
msgid "plugin plugin_name"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2984
msgid ""
"Load a plugin. Plugin of that name must be installed on the system in the "
"proper directory."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:2992
msgid "Basic"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:2995
msgid "<anchor id=\"gel-function-AskButtons\"/>AskButtons"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2997
#, no-wrap
msgid "AskButtons (query)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:2998
#, no-wrap
msgid "AskButtons (query, button1, ...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:2999
msgid ""
"Asks a question and presents a list of buttons to the user (or a menu of "
"options in text mode). Returns the 1-based index of the button pressed. That "
"is, returns 1 if the first button was pressed, 2 if the second button was "
"pressed, and so on. If the user closes the window (or simply hits enter in "
"text mode), then <constant>null</constant> is returned. The execution of the "
"program is blocked until the user responds."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3005 C/genius.xml:3623 C/genius.xml:3753 C/genius.xml:3801
#: C/genius.xml:3830 C/genius.xml:8123 C/genius.xml:8366
msgid "Version 1.0.10 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3010
msgid "<anchor id=\"gel-function-AskString\"/>AskString"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3012
#, no-wrap
msgid "AskString (query)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3013
#, no-wrap
msgid "AskString (query, default)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3014
msgid ""
"Asks a question and lets the user enter a string, which it then returns. If "
"the user cancels or closes the window, then <constant>null</constant> is "
"returned. The execution of the program is blocked until the user responds. "
"If <varname>default</varname> is given, then it is pre-typed in for the user "
"to just press enter on (version 1.0.6 onwards)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3022
msgid "<anchor id=\"gel-function-Compose\"/>Compose"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3024
#, no-wrap
msgid "Compose (f,g)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3025
msgid ""
"Compose two functions and return a function that is the composition of "
"<function>f</function> and <function>g</function>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3030
msgid "<anchor id=\"gel-function-ComposePower\"/>ComposePower"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3032
#, no-wrap
msgid "ComposePower (f,n,x)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:3036
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>function f(x) = x^2 ;</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>ComposePower (f,3,7)</userinput>\n"
"= 5764801\n"
"<prompt>genius&gt;</prompt> <userinput>f(f(f(7)))</userinput>\n"
"= 5764801\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3033
msgid ""
"Compose and execute a function with itself <varname>n</varname> times, "
"passing <varname>x</varname> as argument. Returning <varname>x</varname> if "
"<varname>n</varname> equals 0. Example: <_:screen-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3047
msgid "<anchor id=\"gel-function-Evaluate\"/>Evaluate"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3049
#, no-wrap
msgid "Evaluate (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3050
msgid "Parses and evaluates a string."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3056
msgid "<anchor id=\"gel-function-GetCurrentModulo\"/>GetCurrentModulo"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3058
#, no-wrap
msgid "GetCurrentModulo"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3059
msgid ""
"Get current modulo from the context outside the function. That is, if "
"outside of the function was executed in modulo (using <literal>mod</"
"literal>) then this returns what this modulo was. Normally the body of the "
"function called is not executed in modular arithmetic, and this builtin "
"function makes it possible to make GEL functions aware of modular arithmetic."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3067
msgid "<anchor id=\"gel-function-Identity\"/>Identity"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3069
#, no-wrap
msgid "Identity (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3070
msgid ""
"Identity function, returns its argument. It is equivalent to "
"<userinput>function Identity(x)=x</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3075
msgid "<anchor id=\"gel-function-IntegerFromBoolean\"/>IntegerFromBoolean"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3077
#, no-wrap
msgid "IntegerFromBoolean (bval)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3078
msgid ""
"Make integer (0 for <constant>false</constant> or 1 for <constant>true</"
"constant>) from a boolean value. <varname>bval</varname> can also be a "
"number in which case a non-zero value will be interpreted as <constant>true</"
"constant> and zero will be interpreted as <constant>false</constant>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3089
msgid "<anchor id=\"gel-function-IsBoolean\"/>IsBoolean"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3091
#, no-wrap
msgid "IsBoolean (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3092
msgid "Check if argument is a boolean (and not a number)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3097
msgid "<anchor id=\"gel-function-IsDefined\"/>IsDefined"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3099
#, no-wrap
msgid "IsDefined (id)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3100
msgid ""
"Check if an id is defined. You should pass a string or and identifier. If "
"you pass a matrix, each entry will be evaluated separately and the matrix "
"should contain strings or identifiers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3108
msgid "<anchor id=\"gel-function-IsFunction\"/>IsFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3110
#, no-wrap
msgid "IsFunction (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3111
msgid "Check if argument is a function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3116
msgid ""
"<anchor id=\"gel-function-IsFunctionOrIdentifier\"/>IsFunctionOrIdentifier"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3118
#, no-wrap
msgid "IsFunctionOrIdentifier (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3119
msgid "Check if argument is a function or an identifier."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3124
msgid "<anchor id=\"gel-function-IsFunctionRef\"/>IsFunctionRef"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3126
#, no-wrap
msgid "IsFunctionRef (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3127
msgid ""
"Check if argument is a function reference. This includes variable references."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3133
msgid "<anchor id=\"gel-function-IsMatrix\"/>IsMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3135
#, no-wrap
msgid "IsMatrix (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3136
msgid ""
"Check if argument is a matrix. Even though <constant>null</constant> is "
"sometimes considered an empty matrix, the function <function>IsMatrix</"
"function> does not consider <constant>null</constant> a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3143
msgid "<anchor id=\"gel-function-IsNull\"/>IsNull"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3145
#, no-wrap
msgid "IsNull (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3146
msgid "Check if argument is a <constant>null</constant>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3151
msgid "<anchor id=\"gel-function-IsString\"/>IsString"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3153
#, no-wrap
msgid "IsString (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3154
msgid "Check if argument is a text string."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3159
msgid "<anchor id=\"gel-function-IsValue\"/>IsValue"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3161
#, no-wrap
msgid "IsValue (arg)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3162
msgid "Check if argument is a number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3167
msgid "<anchor id=\"gel-function-Parse\"/>Parse"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3169
#, no-wrap
msgid "Parse (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3170
msgid ""
"Parses but does not evaluate a string. Note that certain pre-computation is "
"done during the parsing stage."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3176
msgid "<anchor id=\"gel-function-SetFunctionFlags\"/>SetFunctionFlags"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3178
#, no-wrap
msgid "SetFunctionFlags (id,flags...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3179
msgid ""
"Set flags for a function, currently <literal>\"PropagateMod\"</literal> and "
"<literal>\"NoModuloArguments\"</literal>. If <literal>\"PropagateMod\"</"
"literal> is set, then the body of the function is evaluated in modular "
"arithmetic when the function is called inside a block that was evaluated "
"using modular arithmetic (using <literal>mod</literal>). If "
"<literal>\"NoModuloArguments\"</literal>, then the arguments of the function "
"are never evaluated using modular arithmetic."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3188
msgid "<anchor id=\"gel-function-SetHelp\"/>SetHelp"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3190
#, no-wrap
msgid "SetHelp (id,category,desc)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3191
msgid "Set the category and help description line for a function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3196
msgid "<anchor id=\"gel-function-SetHelpAlias\"/>SetHelpAlias"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3198
#, no-wrap
msgid "SetHelpAlias (id,alias)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3199
msgid "Sets up a help alias."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3204
msgid "<anchor id=\"gel-function-chdir\"/>chdir"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3206
#, no-wrap
msgid "chdir (dir)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3207
msgid "Changes current directory, same as the <command>cd</command>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3212
msgid "<anchor id=\"gel-function-CurrentTime\"/>CurrentTime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3214
#, no-wrap
msgid "CurrentTime"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3215
msgid ""
"Returns the current UNIX time with microsecond precision as a floating point "
"number. That is, returns the number of seconds since January 1st 1970."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3216 C/genius.xml:8680 C/genius.xml:8689 C/genius.xml:8698
msgid "Version 1.0.15 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3221
msgid "<anchor id=\"gel-function-display\"/>display"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3223
#, no-wrap
msgid "display (str,expr)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3224
msgid "Display a string and an expression with a colon to separate them."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3229
msgid "<anchor id=\"gel-function-DisplayVariables\"/>DisplayVariables"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3231
#, no-wrap
msgid "DisplayVariables (var1,var2,...)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3234
#, no-wrap
msgid ""
"DisplayVariables(`x,`y,`z)\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3232
msgid ""
"Display set of variables. The variables can be given as strings or "
"identifiers. For example: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3239
#, no-wrap
msgid ""
"DisplayVariables()\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3237
msgid ""
"If called without arguments (must supply empty argument list) as "
"<_:programlisting-1/> then all variables are printed including a stacktrace "
"similar to <guilabel>Show user variables</guilabel> in the graphical version."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3244 C/genius.xml:3312 C/genius.xml:5768 C/genius.xml:5777
#: C/genius.xml:6422 C/genius.xml:7832 C/genius.xml:8196 C/genius.xml:8222
#: C/genius.xml:9201 C/genius.xml:9215
msgid "Version 1.0.18 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3249
msgid "<anchor id=\"gel-function-error\"/>error"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3251
#, no-wrap
msgid "error (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3252
msgid "Prints a string to the error stream (onto the console)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3257
msgid "<anchor id=\"gel-function-exit\"/>exit"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3259
#, no-wrap
msgid "exit"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3260
msgid "Aliases: <function>quit</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3261
msgid "Exits the program."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3266
msgid "<anchor id=\"gel-function-false\"/>false"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3268
#, no-wrap
msgid "false"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3269
msgid "Aliases: <function>False</function> <function>FALSE</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3270
msgid "The <constant>false</constant> boolean value."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3275
msgid "<anchor id=\"gel-function-manual\"/>manual"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3277
#, no-wrap
msgid "manual"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3278
msgid "Displays the user manual."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3283
msgid "<anchor id=\"gel-function-print\"/>print"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3285
#, no-wrap
msgid "print (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3286
msgid ""
"Prints an expression and then print a newline. The argument <varname>str</"
"varname> can be any expression. It is made into a string before being "
"printed."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3292
msgid "<anchor id=\"gel-function-printn\"/>printn"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3294
#, no-wrap
msgid "printn (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3295
msgid ""
"Prints an expression without a trailing newline. The argument <varname>str</"
"varname> can be any expression. It is made into a string before being "
"printed."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3301
msgid "<anchor id=\"gel-function-PrintTable\"/>PrintTable"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3303
#, no-wrap
msgid "PrintTable (f,v)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3307
#, no-wrap
msgid ""
"PrintTable (f,[0:10])\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3304
msgid ""
"Print a table of values for a function. The values are in the vector "
"<varname>v</varname>. You can use the vector building notation as follows: "
"<_:programlisting-1/> If <varname>v</varname> is a positive integer, then "
"the table of integers from 1 up to and including v will be used."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3317
msgid "<anchor id=\"gel-function-protect\"/>protect"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3319
#, no-wrap
msgid "protect (id)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3320
msgid ""
"Protect a variable from being modified. This is used on the internal GEL "
"functions to avoid them being accidentally overridden."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3326
msgid "<anchor id=\"gel-function-ProtectAll\"/>ProtectAll"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3328
#, no-wrap
msgid "ProtectAll ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3329
msgid ""
"Protect all currently defined variables, parameters and functions from being "
"modified. This is used on the internal GEL functions to avoid them being "
"accidentally overridden. Normally <application>Genius Mathematics Tool</"
"application> considers unprotected variables as user defined."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3333 C/genius.xml:3434 C/genius.xml:3452 C/genius.xml:7284
#: C/genius.xml:7419 C/genius.xml:7439 C/genius.xml:7464 C/genius.xml:7485
#: C/genius.xml:7507 C/genius.xml:7528 C/genius.xml:7580 C/genius.xml:7613
msgid "Version 1.0.7 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3338
msgid "<anchor id=\"gel-function-set\"/>set"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3340
#, no-wrap
msgid "set (id,val)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3344
#, no-wrap
msgid ""
"set(`x,1)\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3341
msgid ""
"Set a global variable. The <varname>id</varname> can be either a string or a "
"quoted identifier. For example: <_:programlisting-1/> will set the global "
"variable <varname>x</varname> to the value 1."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3348 C/genius.xml:3367 C/genius.xml:3387
msgid ""
"The function returns the <varname>val</varname>, to be usable in chaining."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3354
msgid "<anchor id=\"gel-function-SetElement\"/>SetElement"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3356
#, no-wrap
msgid "SetElement (id,row,col,val)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3361
#, no-wrap
msgid ""
"SetElement(`x,2,3,1)\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3357
msgid ""
"Set an element of a global variable which is a matrix. The <varname>id</"
"varname> can be either a string or a quoted identifier. For example: "
"<_:programlisting-1/> will set the second row third column element of the "
"global variable <varname>x</varname> to the value 1. If no global variable "
"of the name exists, or if it is set to something that's not a matrix, a new "
"zero matrix of appropriate size will be created."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3365
msgid ""
"The <varname>row</varname> and <varname>col</varname> can also be ranges, "
"and the semantics are the same as for regular setting of the elements with "
"an equals sign."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3369 C/genius.xml:3389
msgid "Available from 1.0.18 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3374
msgid "<anchor id=\"gel-function-SetVElement\"/>SetVElement"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3376
#, no-wrap
msgid "SetElement (id,elt,val)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3381
#, no-wrap
msgid ""
"SetElement(`x,2,1)\n"
"\t    "
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3377
msgid ""
"Set an element of a global variable which is a vector. The <varname>id</"
"varname> can be either a string or a quoted identifier. For example: "
"<_:programlisting-1/> will set the second element of the global vector "
"variable <varname>x</varname> to the value 1. If no global variable of the "
"name exists, or if it is set to something that's not a vector (matrix), a "
"new zero row vector of appropriate size will be created."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3385
msgid ""
"The <varname>elt</varname> can also be a range, and the semantics are the "
"same as for regular setting of the elements with an equals sign."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3394
msgid "<anchor id=\"gel-function-string\"/>string"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3396
#, no-wrap
msgid "string (s)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3397
msgid "Make a string. This will make a string out of any argument."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3402
msgid "<anchor id=\"gel-function-true\"/>true"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3404
#, no-wrap
msgid "true"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3405
msgid "Aliases: <function>True</function> <function>TRUE</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3406
msgid "The <constant>true</constant> boolean value."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3411
msgid "<anchor id=\"gel-function-undefine\"/>undefine"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3413
#, no-wrap
msgid "undefine (id)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3414
msgid "Alias: <function>Undefine</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3415
msgid ""
"Undefine a variable. This includes locals and globals, every value on all "
"context levels is wiped. This function should really not be used on local "
"variables. A vector of identifiers can also be passed to undefine several "
"variables."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3424
msgid "<anchor id=\"gel-function-UndefineAll\"/>UndefineAll"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3426
#, no-wrap
msgid "UndefineAll ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3427
msgid ""
"Undefine all unprotected global variables (including functions and "
"parameters). Normally <application>Genius Mathematics Tool</application> "
"considers protected variables as system defined functions and variables. "
"Note that <function>UndefineAll</function> only removes the global "
"definition of symbols not local ones, so that it may be run from inside "
"other functions safely."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3439
msgid "<anchor id=\"gel-function-unprotect\"/>unprotect"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3441
#, no-wrap
msgid "unprotect (id)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3442
msgid "Unprotect a variable from being modified."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3447
msgid "<anchor id=\"gel-function-UserVariables\"/>UserVariables"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3449
#, no-wrap
msgid "UserVariables ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3450
msgid ""
"Return a vector of identifiers of user defined (unprotected) global "
"variables."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3457
msgid "<anchor id=\"gel-function-wait\"/>wait"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3459
#, no-wrap
msgid "wait (secs)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3460
msgid ""
"Waits a specified number of seconds. <varname>secs</varname> must be non-"
"negative. Zero is accepted and nothing happens in this case, except possibly "
"user interface events are processed."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3463
msgid ""
"Since version 1.0.18, <varname>secs</varname> can be a noninteger number, so "
"<userinput>wait(0.1)</userinput> will wait for one tenth of a second."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3469
msgid "<anchor id=\"gel-function-version\"/>version"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3471
#, no-wrap
msgid "version"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3472
msgid ""
"Returns the version of Genius as a horizontal 3-vector with major version "
"first, then minor version and finally the patch level."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3478
msgid "<anchor id=\"gel-function-warranty\"/>warranty"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3480
#, no-wrap
msgid "warranty"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3481
msgid "Gives the warranty information."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:3489
msgid "Parameters"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3492
msgid "<anchor id=\"gel-function-ChopTolerance\"/>ChopTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3494
#, no-wrap
msgid "ChopTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3495
msgid "Tolerance of the <function>Chop</function> function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3500
msgid ""
"<anchor id=\"gel-function-ContinuousNumberOfTries\"/>ContinuousNumberOfTries"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3502
#, no-wrap
msgid "ContinuousNumberOfTries = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3503
msgid "How many iterations to try to find the limit for continuity and limits."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3508
msgid "<anchor id=\"gel-function-ContinuousSFS\"/>ContinuousSFS"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3510
#, no-wrap
msgid "ContinuousSFS = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3511
msgid ""
"How many successive steps to be within tolerance for calculation of "
"continuity."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3516
msgid "<anchor id=\"gel-function-ContinuousTolerance\"/>ContinuousTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3518
#, no-wrap
msgid "ContinuousTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3519
msgid "Tolerance for continuity of functions and for calculating the limit."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3524
msgid ""
"<anchor id=\"gel-function-DerivativeNumberOfTries\"/>DerivativeNumberOfTries"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3526
#, no-wrap
msgid "DerivativeNumberOfTries = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3527
msgid "How many iterations to try to find the limit for derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3532
msgid "<anchor id=\"gel-function-DerivativeSFS\"/>DerivativeSFS"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3534
#, no-wrap
msgid "DerivativeSFS = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3535
msgid ""
"How many successive steps to be within tolerance for calculation of "
"derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3540
msgid "<anchor id=\"gel-function-DerivativeTolerance\"/>DerivativeTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3542
#, no-wrap
msgid "DerivativeTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3543
msgid "Tolerance for calculating the derivatives of functions."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3548
msgid ""
"<anchor id=\"gel-function-ErrorFunctionTolerance\"/>ErrorFunctionTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3550
#, no-wrap
msgid "ErrorFunctionTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3551
msgid ""
"Tolerance of the <link linkend=\"gel-function-"
"ErrorFunction\"><function>ErrorFunction</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3556
msgid "<anchor id=\"gel-function-FloatPrecision\"/>FloatPrecision"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3558
#, no-wrap
msgid "FloatPrecision = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3559
msgid "Floating point precision."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3564
msgid "<anchor id=\"gel-function-FullExpressions\"/>FullExpressions"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3566
#, no-wrap
msgid "FullExpressions = boolean"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3567
msgid "Print full expressions, even if more than a line."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3572
msgid ""
"<anchor id=\"gel-function-GaussDistributionTolerance\"/"
">GaussDistributionTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3574
#, no-wrap
msgid "GaussDistributionTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3575
msgid ""
"Tolerance of the <link linkend=\"gel-function-"
"GaussDistribution\"><function>GaussDistribution</function></link> function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3580
msgid "<anchor id=\"gel-function-IntegerOutputBase\"/>IntegerOutputBase"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3582
#, no-wrap
msgid "IntegerOutputBase = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3583
msgid "Integer output base."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3588
msgid ""
"<anchor id=\"gel-function-IsPrimeMillerRabinReps\"/>IsPrimeMillerRabinReps"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3590
#, no-wrap
msgid "IsPrimeMillerRabinReps = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3591
msgid ""
"Number of extra Miller-Rabin tests to run on a number before declaring it a "
"prime in <link linkend=\"gel-function-IsPrime\"><function>IsPrime</"
"function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3596
msgid "<anchor id=\"gel-function-LinePlotDrawLegends\"/>LinePlotDrawLegends"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3598
#, no-wrap
msgid "LinePlotDrawLegends = true"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3599
msgid ""
"Tells genius to draw the legends for <link linkend=\"genius-gel-function-"
"list-plotting\">line plotting functions</link> such as <link linkend=\"gel-"
"function-LinePlot\"><function>LinePlot</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3606
msgid ""
"<anchor id=\"gel-function-LinePlotDrawAxisLabels\"/>LinePlotDrawAxisLabels"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3608
#, no-wrap
msgid "LinePlotDrawAxisLabels = true"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3609
msgid ""
"Tells genius to draw the axis labels for <link linkend=\"genius-gel-function-"
"list-plotting\">line plotting functions</link> such as <link linkend=\"gel-"
"function-LinePlot\"><function>LinePlot</function></link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3612 C/genius.xml:3788 C/genius.xml:7681 C/genius.xml:7694
#: C/genius.xml:7707 C/genius.xml:7720 C/genius.xml:7733 C/genius.xml:7746
#: C/genius.xml:8008 C/genius.xml:8897 C/genius.xml:9376 C/genius.xml:9413
msgid "Version 1.0.16 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3617
msgid ""
"<anchor id=\"gel-function-LinePlotVariableNames\"/>LinePlotVariableNames"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3619
#, no-wrap
msgid "LinePlotVariableNames = [\"x\",\"y\",\"z\",\"t\"]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3620
msgid ""
"Tells genius which variable names are used as default names for <link "
"linkend=\"genius-gel-function-list-plotting\">line plotting functions</link> "
"such as <link linkend=\"gel-function-LinePlot\"><function>LinePlot</"
"function></link> and friends."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3628
msgid "<anchor id=\"gel-function-LinePlotWindow\"/>LinePlotWindow"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3630
#, no-wrap
msgid "LinePlotWindow = [x1,x2,y1,y2]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3631
msgid ""
"Sets the limits for <link linkend=\"genius-gel-function-list-plotting\">line "
"plotting functions</link> such as <link linkend=\"gel-function-"
"LinePlot\"><function>LinePlot</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3639
msgid "<anchor id=\"gel-function-MaxDigits\"/>MaxDigits"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3641
#, no-wrap
msgid "MaxDigits = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3642
msgid "Maximum digits to display."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3647
msgid "<anchor id=\"gel-function-MaxErrors\"/>MaxErrors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3649
#, no-wrap
msgid "MaxErrors = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3650
msgid "Maximum errors to display."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3655
msgid "<anchor id=\"gel-function-MixedFractions\"/>MixedFractions"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3657
#, no-wrap
msgid "MixedFractions = boolean"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3658
msgid "If true, mixed fractions are printed."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3663
msgid ""
"<anchor id=\"gel-function-NumericalIntegralFunction\"/"
">NumericalIntegralFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3665
#, no-wrap
msgid "NumericalIntegralFunction = function"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3666
msgid ""
"The function used for numerical integration in <link linkend=\"gel-function-"
"NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3671
msgid ""
"<anchor id=\"gel-function-NumericalIntegralSteps\"/>NumericalIntegralSteps"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3673
#, no-wrap
msgid "NumericalIntegralSteps = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3674
msgid ""
"Steps to perform in <link linkend=\"gel-function-"
"NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3679
msgid "<anchor id=\"gel-function-OutputChopExponent\"/>OutputChopExponent"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3681
#, no-wrap
msgid "OutputChopExponent = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3682
msgid ""
"When another number in the object being printed (a matrix or a value) is "
"greater than 10<superscript>-OutputChopWhenExponent</superscript>, and the "
"number being printed is less than 10<superscript>-OutputChopExponent</"
"superscript>, then display <computeroutput>0.0</computeroutput> instead of "
"the number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3689
msgid ""
"Output is never chopped if <function>OutputChopExponent</function> is zero. "
"It must be a non-negative integer."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3693
msgid ""
"If you want output always chopped according to <function>OutputChopExponent</"
"function>, then set <function>OutputChopWhenExponent</function>, to "
"something greater than or equal to <function>OutputChopExponent</function>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3704
msgid ""
"<anchor id=\"gel-function-OutputChopWhenExponent\"/>OutputChopWhenExponent"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3706
#, no-wrap
msgid "OutputChopWhenExponent = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3707
msgid ""
"When to chop output. See <link linkend=\"gel-function-"
"OutputChopExponent\"><function>OutputChopExponent</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3714
msgid "<anchor id=\"gel-function-OutputStyle\"/>OutputStyle"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3716
#, no-wrap
msgid "OutputStyle = string"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3717
msgid ""
"Output style, this can be <literal>normal</literal>, <literal>latex</"
"literal>, <literal>mathml</literal> or <literal>troff</literal>."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:3724
#, no-wrap
msgid "OutputStyle = \"latex\"\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3720
msgid ""
"This affects mostly how matrices and fractions are printed out and is useful "
"for pasting into documents. For example you can set this to the latex by: "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3731
msgid "<anchor id=\"gel-function-ResultsAsFloats\"/>ResultsAsFloats"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3733
#, no-wrap
msgid "ResultsAsFloats = boolean"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3734
msgid "Convert all results to floats before printing."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3739
msgid "<anchor id=\"gel-function-ScientificNotation\"/>ScientificNotation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3741
#, no-wrap
msgid "ScientificNotation = boolean"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3742
msgid "Use scientific notation."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3747
msgid "<anchor id=\"gel-function-SlopefieldTicks\"/>SlopefieldTicks"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3749
#, no-wrap
msgid "SlopefieldTicks = [vertical,horizontal]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3750
msgid ""
"Sets the number of vertical and horizontal ticks in a slopefield plot. (See "
"<link linkend=\"gel-function-SlopefieldPlot\"><function>SlopefieldPlot</"
"function></link>)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3758
msgid ""
"<anchor id=\"gel-function-SumProductNumberOfTries\"/>SumProductNumberOfTries"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3760
#, no-wrap
msgid "SumProductNumberOfTries = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3761
msgid ""
"How many iterations to try for <link linkend=\"gel-function-"
"InfiniteSum\"><function>InfiniteSum</function></link> and <link "
"linkend=\"gel-function-InfiniteProduct\"><function>InfiniteProduct</"
"function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3766
msgid "<anchor id=\"gel-function-SumProductSFS\"/>SumProductSFS"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3768
#, no-wrap
msgid "SumProductSFS = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3769
msgid ""
"How many successive steps to be within tolerance for <link linkend=\"gel-"
"function-InfiniteSum\"><function>InfiniteSum</function></link> and <link "
"linkend=\"gel-function-InfiniteProduct\"><function>InfiniteProduct</"
"function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3774
msgid "<anchor id=\"gel-function-SumProductTolerance\"/>SumProductTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3776
#, no-wrap
msgid "SumProductTolerance = number"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3777
msgid ""
"Tolerance for <link linkend=\"gel-function-"
"InfiniteSum\"><function>InfiniteSum</function></link> and <link "
"linkend=\"gel-function-InfiniteProduct\"><function>InfiniteProduct</"
"function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3782
msgid ""
"<anchor id=\"gel-function-SurfacePlotDrawLegends\"/>SurfacePlotDrawLegends"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3784
#, no-wrap
msgid "SurfacePlotDrawLegends = true"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3785
msgid ""
"Tells genius to draw the legends for <link linkend=\"genius-gel-function-"
"list-plotting\">surface plotting functions</link> such as <link "
"linkend=\"gel-function-SurfacePlot\"><function>SurfacePlot</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3793
msgid ""
"<anchor id=\"gel-function-SurfacePlotVariableNames\"/"
">SurfacePlotVariableNames"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3795
#, no-wrap
msgid "SurfacePlotVariableNames = [\"x\",\"y\",\"z\"]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3796
msgid ""
"Tells genius which variable names are used as default names for <link "
"linkend=\"genius-gel-function-list-plotting\">surface plotting functions</"
"link> using <link linkend=\"gel-function-"
"SurfacePlot\"><function>SurfacePlot</function></link>. Note that the "
"<varname>z</varname> does not refer to the dependent (vertical) axis, but to "
"the independent complex variable <userinput>z=x+iy</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3806
msgid "<anchor id=\"gel-function-SurfacePlotWindow\"/>SurfacePlotWindow"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3808
#, no-wrap
msgid "SurfacePlotWindow = [x1,x2,y1,y2,z1,z2]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3809
msgid ""
"Sets the limits for surface plotting (See <link linkend=\"gel-function-"
"SurfacePlot\"><function>SurfacePlot</function></link>)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3814
msgid ""
"<anchor id=\"gel-function-VectorfieldNormalized\"/>VectorfieldNormalized"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3816
#, no-wrap
msgid "VectorfieldNormalized = true"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3817
msgid ""
"Should the vectorfield plotting have normalized arrow length. If true, "
"vector fields will only show direction and not magnitude. (See <link "
"linkend=\"gel-function-VectorfieldPlot\"><function>VectorfieldPlot</"
"function></link>)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3824
msgid "<anchor id=\"gel-function-VectorfieldTicks\"/>VectorfieldTicks"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3826
#, no-wrap
msgid "VectorfieldTicks = [vertical,horizontal]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3827
msgid ""
"Sets the number of vertical and horizontal ticks in a vectorfield plot. (See "
"<link linkend=\"gel-function-VectorfieldPlot\"><function>VectorfieldPlot</"
"function></link>)."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:3838
msgid "Constants"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3841
msgid "<anchor id=\"gel-function-CatalanConstant\"/>CatalanConstant"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3843
#, no-wrap
msgid "CatalanConstant"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3844
msgid ""
"Catalan's Constant, approximately 0.915... It is defined to be the series "
"where terms are <userinput>(-1^k)/((2*k+1)^2)</userinput>, where <varname>k</"
"varname> ranges from 0 to infinity."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3847
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Catalan%27s_constant\">Wikipedia</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/CatalansConstant.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3856
msgid "<anchor id=\"gel-function-EulerConstant\"/>EulerConstant"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3858
#, no-wrap
msgid "EulerConstant"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3859
msgid "Aliases: <function>gamma</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3860
msgid "Euler's constant gamma. Sometimes called the Euler-Mascheroni constant."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3864
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Euler-"
"Mascheroni_constant\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/MascheroniConstant\">Planetmath</ulink> or <ulink "
"url=\"http://mathworld.wolfram.com/Euler-"
"MascheroniConstant.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3874
msgid "<anchor id=\"gel-function-GoldenRatio\"/>GoldenRatio"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3876
#, no-wrap
msgid "GoldenRatio"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3877
msgid "The Golden Ratio."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3878
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Golden_ratio\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/GoldenRatio\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"GoldenRatio.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3888
msgid "<anchor id=\"gel-function-Gravity\"/>Gravity"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3890
#, no-wrap
msgid "Gravity"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3891
msgid ""
"Free fall acceleration at sea level in meters per second squared. This is "
"the standard gravity constant 9.80665. The gravity in your particular neck "
"of the woods might be different due to different altitude and the fact that "
"the earth is not perfectly round and uniform."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3894
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Standard_gravity\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3902
msgid "<anchor id=\"gel-function-e\"/>e"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3904
#, no-wrap
msgid "e"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3905
msgid ""
"The base of the natural logarithm. <userinput>e^x</userinput> is the "
"exponential function <link linkend=\"gel-function-exp\"><function>exp</"
"function></link>. It is approximately 2.71828182846... This number is "
"sometimes called Euler's number, although there are several numbers that are "
"also called Euler's. An example is the gamma constant: <link linkend=\"gel-"
"function-EulerConstant\"><function>EulerConstant</function></link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3912
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/E_(mathematical_constant)"
"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/E\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/e.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3922
msgid "<anchor id=\"gel-function-pi\"/>pi"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3924
#, no-wrap
msgid "pi"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3925
msgid ""
"The number pi, that is the ratio of a circle's circumference to its "
"diameter. This is approximately 3.14159265359..."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3929
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Pi\">Wikipedia</ulink> or "
"<ulink url=\"http://planetmath.org/Pi\">Planetmath</ulink> or <ulink "
"url=\"http://mathworld.wolfram.com/Pi.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:3942
msgid "Numeric"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3945
msgid "<anchor id=\"gel-function-AbsoluteValue\"/>AbsoluteValue"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3947
#, no-wrap
msgid "AbsoluteValue (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3948
msgid "Aliases: <function>abs</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3949
msgid ""
"Absolute value of a number and if <varname>x</varname> is a complex value "
"the modulus of <varname>x</varname>. I.e. this the distance of <varname>x</"
"varname> to the origin. This is equivalent to <userinput>|x|</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3955
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Absolute_value\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/AbsoluteValue\">Planetmath "
"(absolute value)</ulink>, <ulink url=\"http://planetmath.org/"
"ModulusOfComplexNumber\">Planetmath (modulus)</ulink>, <ulink url=\"http://"
"mathworld.wolfram.com/AbsoluteValue.html\">Mathworld (absolute value)</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"ComplexModulus.html\">Mathworld (complex modulus)</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3968
msgid "<anchor id=\"gel-function-Chop\"/>Chop"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3970
#, no-wrap
msgid "Chop (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3971
msgid "Replace very small number with zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3976
msgid "<anchor id=\"gel-function-ComplexConjugate\"/>ComplexConjugate"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3978
#, no-wrap
msgid "ComplexConjugate (z)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3979
msgid "Aliases: <function>conj</function> <function>Conj</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3980
msgid ""
"Calculates the complex conjugate of the complex number <varname>z</varname>. "
"If <varname>z</varname> is a vector or matrix, all its elements are "
"conjugated."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3982
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Complex_conjugate\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:3990
msgid "<anchor id=\"gel-function-Denominator\"/>Denominator"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:3992
#, no-wrap
msgid "Denominator (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3993
msgid "Get the denominator of a rational number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:3994
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Denominator\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4002
msgid "<anchor id=\"gel-function-FractionalPart\"/>FractionalPart"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4004
#, no-wrap
msgid "FractionalPart (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4005
msgid "Return the fractional part of a number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4006
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Fractional_part\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4014
msgid "<anchor id=\"gel-function-Im\"/>Im"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4016
#, no-wrap
msgid "Im (z)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4017
msgid "Aliases: <function>ImaginaryPart</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4018
msgid ""
"Get the imaginary part of a complex number. For example <userinput>Re(3+4i)</"
"userinput> yields 4."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4019
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Imaginary_part\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4027
msgid "<anchor id=\"gel-function-IntegerQuotient\"/>IntegerQuotient"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4029
#, no-wrap
msgid "IntegerQuotient (m,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4030
msgid "Division without remainder."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4035
msgid "<anchor id=\"gel-function-IsComplex\"/>IsComplex"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4037
#, no-wrap
msgid "IsComplex (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4038
msgid ""
"Check if argument is a complex (non-real) number. Do note that we really "
"mean nonreal number. That is, <userinput>IsComplex(3)</userinput> yields "
"false, while <userinput>IsComplex(3-1i)</userinput> yields true."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4045
msgid "<anchor id=\"gel-function-IsComplexRational\"/>IsComplexRational"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4047
#, no-wrap
msgid "IsComplexRational (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4048
msgid ""
"Check if argument is a possibly complex rational number. That is, if both "
"real and imaginary parts are given as rational numbers. Of course rational "
"simply means \"not stored as a floating point number.\""
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4054
msgid "<anchor id=\"gel-function-IsFloat\"/>IsFloat"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4056
#, no-wrap
msgid "IsFloat (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4057
msgid "Check if argument is a real floating point number (non-complex)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4062
msgid "<anchor id=\"gel-function-IsGaussInteger\"/>IsGaussInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4064
#, no-wrap
msgid "IsGaussInteger (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4065
msgid "Aliases: <function>IsComplexInteger</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4066
msgid ""
"Check if argument is a possibly complex integer. That is a complex integer "
"is a number of the form <userinput>n+1i*m</userinput> where <varname>n</"
"varname> and <varname>m</varname> are integers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4073
msgid "<anchor id=\"gel-function-IsInteger\"/>IsInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4075
#, no-wrap
msgid "IsInteger (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4076
msgid "Check if argument is an integer (non-complex)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4081
msgid "<anchor id=\"gel-function-IsNonNegativeInteger\"/>IsNonNegativeInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4083
#, no-wrap
msgid "IsNonNegativeInteger (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4084
msgid ""
"Check if argument is a non-negative real integer. That is, either a positive "
"integer or zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4089
msgid "<anchor id=\"gel-function-IsPositiveInteger\"/>IsPositiveInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4091
#, no-wrap
msgid "IsPositiveInteger (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4092
msgid "Aliases: <function>IsNaturalNumber</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4093
msgid ""
"Check if argument is a positive real integer. Note that we accept the "
"convention that 0 is not a natural number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4099
msgid "<anchor id=\"gel-function-IsRational\"/>IsRational"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4101
#, no-wrap
msgid "IsRational (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4102
msgid ""
"Check if argument is a rational number (non-complex). Of course rational "
"simply means \"not stored as a floating point number.\""
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4107
msgid "<anchor id=\"gel-function-IsReal\"/>IsReal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4109
#, no-wrap
msgid "IsReal (num)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4110
msgid "Check if argument is a real number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4115
msgid "<anchor id=\"gel-function-Numerator\"/>Numerator"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4117
#, no-wrap
msgid "Numerator (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4118
msgid "Get the numerator of a rational number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4119
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Numerator\">Wikipedia</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4127
msgid "<anchor id=\"gel-function-Re\"/>Re"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4129
#, no-wrap
msgid "Re (z)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4130
msgid "Aliases: <function>RealPart</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4131
msgid ""
"Get the real part of a complex number. For example <userinput>Re(3+4i)</"
"userinput> yields 3."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4132
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Real_part\">Wikipedia</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4140
msgid "<anchor id=\"gel-function-Sign\"/>Sign"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4142
#, no-wrap
msgid "Sign (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4143
msgid "Aliases: <function>sign</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4144
msgid ""
"Return the sign of a number. That is returns <literal>-1</literal> if value "
"is negative, <literal>0</literal> if value is zero and <literal>1</literal> "
"if value is positive. If <varname>x</varname> is a complex value then "
"<function>Sign</function> returns the direction or 0."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4154
msgid "<anchor id=\"gel-function-ceil\"/>ceil"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4156
#, no-wrap
msgid "ceil (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4157
msgid "Aliases: <function>Ceiling</function>"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:4159
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>ceil(1.1)</userinput>\n"
"= 2\n"
"<prompt>genius&gt;</prompt> <userinput>ceil(-1.1)</userinput>\n"
"= -1\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4158
msgid ""
"Get the lowest integer more than or equal to <varname>n</varname>. Examples: "
"<_:screen-1/>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4165
msgid ""
"Note that you should be careful and notice that floating point numbers are "
"stored in binary and so may not be what you expect. For example "
"<userinput>ceil(420/4.2)</userinput> returns 101 instead of the expected "
"100. This is because 4.2 is actually very slightly less than 4.2. Use "
"rational representation <userinput>42/10</userinput> if you want exact "
"arithmetic."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4177
msgid "<anchor id=\"gel-function-exp\"/>exp"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4179
#, no-wrap
msgid "exp (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4180
msgid ""
"The exponential function. This is the function <userinput>e^x</userinput> "
"where <varname>e</varname> is the <link linkend=\"gel-function-e\">base of "
"the natural logarithm</link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4186
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Exponential_function\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/LogarithmFunction\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/ExponentialFunction.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4196
msgid "<anchor id=\"gel-function-float\"/>float"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4198
#, no-wrap
msgid "float (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4199
msgid ""
"Make number a floating point value. That is returns the floating point "
"representation of the number <varname>x</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4204
msgid "<anchor id=\"gel-function-floor\"/>floor"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4206
#, no-wrap
msgid "floor (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4207
msgid "Aliases: <function>Floor</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4208
msgid "Get the highest integer less than or equal to <varname>n</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4213
msgid "<anchor id=\"gel-function-ln\"/>ln"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4215
#, no-wrap
msgid "ln (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4216
msgid "The natural logarithm, the logarithm to base <varname>e</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4217
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Natural_logarithm\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/"
"LogarithmFunction\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/NaturalLogarithm.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4227
msgid "<anchor id=\"gel-function-log\"/>log"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4229
#, no-wrap
msgid "log (x)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4230
#, no-wrap
msgid "log (x,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4231
msgid ""
"Logarithm of <varname>x</varname> base <varname>b</varname> (calls <link "
"linkend=\"gel-function-DiscreteLog\"><function>DiscreteLog</function></link> "
"if in modulo mode), if base is not given, <link linkend=\"gel-function-"
"e\"><varname>e</varname></link> is used."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4236
msgid "<anchor id=\"gel-function-log10\"/>log10"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4238
#, no-wrap
msgid "log10 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4239
msgid "Logarithm of <varname>x</varname> base 10."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4244
msgid "<anchor id=\"gel-function-log2\"/>log2"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4246
#, no-wrap
msgid "log2 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4247
msgid "Aliases: <function>lg</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4248
msgid "Logarithm of <varname>x</varname> base 2."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4253
msgid "<anchor id=\"gel-function-max\"/>max"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4255
#, no-wrap
msgid "max (a,args...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4256
msgid "Aliases: <function>Max</function> <function>Maximum</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4257
msgid "Returns the maximum of arguments or matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4262
msgid "<anchor id=\"gel-function-min\"/>min"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4264
#, no-wrap
msgid "min (a,args...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4265
msgid "Aliases: <function>Min</function> <function>Minimum</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4266
msgid "Returns the minimum of arguments or matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4271
msgid "<anchor id=\"gel-function-rand\"/>rand"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4273
#, no-wrap
msgid "rand (size...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4274
msgid ""
"Generate random float in the range <literal>[0,1)</literal>. If size is "
"given then a matrix (if two numbers are specified) or vector (if one number "
"is specified) of the given size returned."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4281
msgid "<anchor id=\"gel-function-randint\"/>randint"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4283
#, no-wrap
msgid "randint (max,size...)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:4288
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>randint(4)</userinput>\n"
"= 3\n"
"<prompt>genius&gt;</prompt> <userinput>randint(4,2)</userinput>\n"
"=\n"
"[0      1]\n"
"<prompt>genius&gt;</prompt> <userinput>randint(4,2,3)</userinput>\n"
"=\n"
"[2      2       1\n"
" 0      0       3]\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4284
msgid ""
"Generate random integer in the range <literal>[0,max)</literal>. If size is "
"given then a matrix (if two numbers are specified) or vector (if one number "
"is specified) of the given size returned. For example, <_:screen-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4303
msgid "<anchor id=\"gel-function-round\"/>round"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4305
#, no-wrap
msgid "round (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4306
msgid "Aliases: <function>Round</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4307
msgid "Round a number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4312
msgid "<anchor id=\"gel-function-sqrt\"/>sqrt"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4314
#, no-wrap
msgid "sqrt (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4315
msgid "Aliases: <function>SquareRoot</function>"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:4317
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>sqrt(2)</userinput>\n"
"= 1.41421356237\n"
"<prompt>genius&gt;</prompt> <userinput>sqrt(-1)</userinput>\n"
"= 1i\n"
"<prompt>genius&gt;</prompt> <userinput>sqrt(4) mod 7</userinput>\n"
"=\n"
"[2      5]\n"
"<prompt>genius&gt;</prompt> <userinput>2*2 mod 7</userinput>\n"
"= 4\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4316
msgid ""
"The square root. When operating modulo some integer will return either a "
"<constant>null</constant> or a vector of the square roots. Examples: "
"<_:screen-1/>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4328
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Square_root\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/SquareRoot\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4337
msgid "<anchor id=\"gel-function-trunc\"/>trunc"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4339
#, no-wrap
msgid "trunc (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4340
msgid "Aliases: <function>Truncate</function> <function>IntegerPart</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4341
msgid "Truncate number to an integer (return the integer part)."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:4349
msgid "Trigonometry"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4352
msgid "<anchor id=\"gel-function-acos\"/>acos"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4354
#, no-wrap
msgid "acos (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4355
msgid "Aliases: <function>arccos</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4356
msgid "The arccos (inverse cos) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4361
msgid "<anchor id=\"gel-function-acosh\"/>acosh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4363
#, no-wrap
msgid "acosh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4364
msgid "Aliases: <function>arccosh</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4365
msgid "The arccosh (inverse cosh) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4370
msgid "<anchor id=\"gel-function-acot\"/>acot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4372
#, no-wrap
msgid "acot (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4373
msgid "Aliases: <function>arccot</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4374
msgid "The arccot (inverse cot) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4379
msgid "<anchor id=\"gel-function-acoth\"/>acoth"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4381
#, no-wrap
msgid "acoth (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4382
msgid "Aliases: <function>arccoth</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4383
msgid "The arccoth (inverse coth) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4388
msgid "<anchor id=\"gel-function-acsc\"/>acsc"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4390
#, no-wrap
msgid "acsc (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4391
msgid "Aliases: <function>arccsc</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4392
msgid "The inverse cosecant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4397
msgid "<anchor id=\"gel-function-acsch\"/>acsch"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4399
#, no-wrap
msgid "acsch (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4400
msgid "Aliases: <function>arccsch</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4401
msgid "The inverse hyperbolic cosecant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4406
msgid "<anchor id=\"gel-function-asec\"/>asec"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4408
#, no-wrap
msgid "asec (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4409
msgid "Aliases: <function>arcsec</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4410
msgid "The inverse secant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4415
msgid "<anchor id=\"gel-function-asech\"/>asech"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4417
#, no-wrap
msgid "asech (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4418
msgid "Aliases: <function>arcsech</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4419
msgid "The inverse hyperbolic secant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4424
msgid "<anchor id=\"gel-function-asin\"/>asin"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4426
#, no-wrap
msgid "asin (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4427
msgid "Aliases: <function>arcsin</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4428
msgid "The arcsin (inverse sin) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4433
msgid "<anchor id=\"gel-function-asinh\"/>asinh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4435
#, no-wrap
msgid "asinh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4436
msgid "Aliases: <function>arcsinh</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4437
msgid "The arcsinh (inverse sinh) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4442
msgid "<anchor id=\"gel-function-atan\"/>atan"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4444
#, no-wrap
msgid "atan (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4445
msgid "Aliases: <function>arctan</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4446
msgid "Calculates the arctan (inverse tan) function."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4447
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Arctangent\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"InverseTangent.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4456
msgid "<anchor id=\"gel-function-atanh\"/>atanh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4458
#, no-wrap
msgid "atanh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4459
msgid "Aliases: <function>arctanh</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4460
msgid "The arctanh (inverse tanh) function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4465
msgid "<anchor id=\"gel-function-atan2\"/>atan2"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4467
#, no-wrap
msgid "atan2 (y, x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4468
msgid "Aliases: <function>arctan2</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4469
msgid ""
"Calculates the arctan2 function. If <userinput>x&gt;0</userinput> then it "
"returns <userinput>atan(y/x)</userinput>. If <userinput>x&lt;0</userinput> "
"then it returns <userinput>sign(y) * (pi - atan(|y/x|)</userinput>. When "
"<userinput>x=0</userinput> it returns <userinput>sign(y) * pi/2</userinput>. "
"<userinput>atan2(0,0)</userinput> returns 0 rather than failing."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4477
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Atan2\">Wikipedia</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/InverseTangent.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4486
msgid "<anchor id=\"gel-function-cos\"/>cos"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4488
#, no-wrap
msgid "cos (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4489
msgid "Calculates the cosine function."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4490 C/genius.xml:4516 C/genius.xml:4542 C/genius.xml:4568
#: C/genius.xml:4594 C/genius.xml:4620
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Trigonometric_functions\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/DefinitionsInTrigonometry\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4499
msgid "<anchor id=\"gel-function-cosh\"/>cosh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4501
#, no-wrap
msgid "cosh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4502
msgid "Calculates the hyperbolic cosine function."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4503 C/genius.xml:4529 C/genius.xml:4555 C/genius.xml:4581
#: C/genius.xml:4607 C/genius.xml:4633
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Hyperbolic_function\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/HyperbolicFunctions\">Planetmath</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4512
msgid "<anchor id=\"gel-function-cot\"/>cot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4514
#, no-wrap
msgid "cot (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4515
msgid "The cotangent function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4525
msgid "<anchor id=\"gel-function-coth\"/>coth"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4527
#, no-wrap
msgid "coth (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4528
msgid "The hyperbolic cotangent function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4538
msgid "<anchor id=\"gel-function-csc\"/>csc"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4540
#, no-wrap
msgid "csc (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4541
msgid "The cosecant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4551
msgid "<anchor id=\"gel-function-csch\"/>csch"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4553
#, no-wrap
msgid "csch (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4554
msgid "The hyperbolic cosecant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4564
msgid "<anchor id=\"gel-function-sec\"/>sec"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4566
#, no-wrap
msgid "sec (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4567
msgid "The secant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4577
msgid "<anchor id=\"gel-function-sech\"/>sech"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4579
#, no-wrap
msgid "sech (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4580
msgid "The hyperbolic secant function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4590
msgid "<anchor id=\"gel-function-sin\"/>sin"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4592
#, no-wrap
msgid "sin (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4593
msgid "Calculates the sine function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4603
msgid "<anchor id=\"gel-function-sinh\"/>sinh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4605
#, no-wrap
msgid "sinh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4606
msgid "Calculates the hyperbolic sine function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4616
msgid "<anchor id=\"gel-function-tan\"/>tan"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4618
#, no-wrap
msgid "tan (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4619
msgid "Calculates the tan function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4629
msgid "<anchor id=\"gel-function-tanh\"/>tanh"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4631
#, no-wrap
msgid "tanh (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4632
msgid "The hyperbolic tangent function."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:4645
msgid "Number Theory"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4648
msgid "<anchor id=\"gel-function-AreRelativelyPrime\"/>AreRelativelyPrime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4650
#, no-wrap
msgid "AreRelativelyPrime (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4651
msgid ""
"Are the real integers <varname>a</varname> and <varname>b</varname> "
"relatively prime? Returns <constant>true</constant> or <constant>false</"
"constant>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4655
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Coprime_integers\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/RelativelyPrime\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"RelativelyPrime.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4665
msgid "<anchor id=\"gel-function-BernoulliNumber\"/>BernoulliNumber"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4667
#, no-wrap
msgid "BernoulliNumber (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4668
msgid "Return the <varname>n</varname>th Bernoulli number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4669
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Bernoulli_number\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"BernoulliNumber.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4678
msgid "<anchor id=\"gel-function-ChineseRemainder\"/>ChineseRemainder"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4680
#, no-wrap
msgid "ChineseRemainder (a,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4681
msgid "Aliases: <function>CRT</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4682
msgid ""
"Find the <varname>x</varname> that solves the system given by the vector "
"<varname>a</varname> and modulo the elements of <varname>m</varname>, using "
"the Chinese Remainder Theorem."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4686
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Chinese_remainder_theorem\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/ChineseRemainderTheorem\">Planetmath</ulink> or <ulink "
"url=\"http://mathworld.wolfram.com/ChineseRemainderTheorem.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4696
msgid ""
"<anchor id=\"gel-function-CombineFactorizations\"/>CombineFactorizations"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4698
#, no-wrap
msgid "CombineFactorizations (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4699
msgid "Given two factorizations, give the factorization of the product."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4701
msgid "See <link linkend=\"gel-function-Factorize\">Factorize</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4706
msgid "<anchor id=\"gel-function-ConvertFromBase\"/>ConvertFromBase"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4708
#, no-wrap
msgid "ConvertFromBase (v,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4709
msgid "Convert a vector of values indicating powers of b to a number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4714
msgid "<anchor id=\"gel-function-ConvertToBase\"/>ConvertToBase"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4716
#, no-wrap
msgid "ConvertToBase (n,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4717
msgid ""
"Convert a number to a vector of powers for elements in base <varname>b</"
"varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4722
msgid "<anchor id=\"gel-function-DiscreteLog\"/>DiscreteLog"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4724
#, no-wrap
msgid "DiscreteLog (n,b,q)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4725
msgid ""
"Find discrete log of <varname>n</varname> base <varname>b</varname> in "
"F<subscript>q</subscript>, the finite field of order <varname>q</varname>, "
"where <varname>q</varname> is a prime, using the Silver-Pohlig-Hellman "
"algorithm."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4728
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Discrete_logarithm\">Wikipedia</ulink>, <ulink url=\"http://planetmath.org/"
"DiscreteLogarithm\">Planetmath</ulink>, or <ulink url=\"http://"
"mathworld.wolfram.com/DiscreteLogarithm.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4738
msgid "<anchor id=\"gel-function-Divides\"/>Divides"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4740
#, no-wrap
msgid "Divides (m,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4741
msgid ""
"Checks divisibility (if <varname>m</varname> divides <varname>n</varname>)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4746
msgid "<anchor id=\"gel-function-EulerPhi\"/>EulerPhi"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4748
#, no-wrap
msgid "EulerPhi (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4749
msgid ""
"Compute the Euler phi function for <varname>n</varname>, that is the number "
"of integers between 1 and <varname>n</varname> relatively prime to "
"<varname>n</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4754
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Euler_phi\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/EulerPhifunction\">Planetmath</"
"ulink>, or <ulink url=\"http://mathworld.wolfram.com/"
"TotientFunction.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4764
msgid "<anchor id=\"gel-function-ExactDivision\"/>ExactDivision"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4766
#, no-wrap
msgid "ExactDivision (n,d)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4767
msgid ""
"Return <userinput>n/d</userinput> but only if <varname>d</varname> divides "
"<varname>n</varname>. If <varname>d</varname> does not divide <varname>n</"
"varname> then this function returns garbage. This is a lot faster for very "
"large numbers than the operation <userinput>n/d</userinput>, but it is only "
"useful if you know that the division is exact."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4779
msgid "<anchor id=\"gel-function-Factorize\"/>Factorize"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4781
#, no-wrap
msgid "Factorize (n)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:4786
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>Factorize(11*11*13)</userinput>\n"
"=\n"
"[1      11      13\n"
" 1      2       1]"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4782
msgid ""
"Return factorization of a number as a matrix. The first row is the primes in "
"the factorization (including 1) and the second row are the powers. So for "
"example: <_:screen-1/>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4791
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Factorization\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4799
msgid "<anchor id=\"gel-function-Factors\"/>Factors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4801
#, no-wrap
msgid "Factors (n)"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:4808
#, no-wrap
msgid ""
"for n=1 to 1000 do (\n"
"    if MatrixSum (Factors(n)) == 2*n then\n"
"        print(n)\n"
")\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4802
msgid ""
"Return all factors of <varname>n</varname> in a vector. This includes all "
"the non-prime factors as well. It includes 1 and the number itself. So to "
"print all the perfect numbers (those that are sums of their factors) up to "
"the number 1000 you could do (this is clearly very inefficient) "
"<_:programlisting-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4818
msgid "<anchor id=\"gel-function-FermatFactorization\"/>FermatFactorization"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4820
#, no-wrap
msgid "FermatFactorization (n,tries)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4821
msgid ""
"Attempt Fermat factorization of <varname>n</varname> into <userinput>(t-"
"s)*(t+s)</userinput>, returns <varname>t</varname> and <varname>s</varname> "
"as a vector if possible, <constant>null</constant> otherwise. "
"<varname>tries</varname> specifies the number of tries before giving up."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4828
msgid ""
"This is a fairly good factorization if your number is the product of two "
"factors that are very close to each other."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4832
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Fermat_factorization\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4840
msgid ""
"<anchor id=\"gel-function-FindPrimitiveElementMod\"/>FindPrimitiveElementMod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4842
#, no-wrap
msgid "FindPrimitiveElementMod (q)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4843
msgid ""
"Find the first primitive element in F<subscript>q</subscript>, the finite "
"group of order <varname>q</varname>. Of course <varname>q</varname> must be "
"a prime."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4849
msgid ""
"<anchor id=\"gel-function-FindRandomPrimitiveElementMod\"/"
">FindRandomPrimitiveElementMod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4851
#, no-wrap
msgid "FindRandomPrimitiveElementMod (q)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4852
msgid ""
"Find a random primitive element in F<subscript>q</subscript>, the finite "
"group of order <varname>q</varname> (q must be a prime)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4858
msgid "<anchor id=\"gel-function-IndexCalculus\"/>IndexCalculus"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4860
#, no-wrap
msgid "IndexCalculus (n,b,q,S)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4861
msgid ""
"Compute discrete log base <varname>b</varname> of n in F<subscript>q</"
"subscript>, the finite group of order <varname>q</varname> (<varname>q</"
"varname> a prime), using the factor base <varname>S</varname>. <varname>S</"
"varname> should be a column of primes possibly with second column "
"precalculated by <link linkend=\"gel-function-"
"IndexCalculusPrecalculation\"><function>IndexCalculusPrecalculation</"
"function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4870
msgid ""
"<anchor id=\"gel-function-IndexCalculusPrecalculation\"/"
">IndexCalculusPrecalculation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4872
#, no-wrap
msgid "IndexCalculusPrecalculation (b,q,S)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4873
msgid ""
"Run the precalculation step of <link linkend=\"gel-function-"
"IndexCalculus\"><function>IndexCalculus</function></link> for logarithms "
"base <varname>b</varname> in F<subscript>q</subscript>, the finite group of "
"order <varname>q</varname> (<varname>q</varname> a prime), for the factor "
"base <varname>S</varname> (where <varname>S</varname> is a column vector of "
"primes). The logs will be precalculated and returned in the second column."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4883
msgid "<anchor id=\"gel-function-IsEven\"/>IsEven"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4885
#, no-wrap
msgid "IsEven (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4886
msgid "Tests if an integer is even."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4891
msgid ""
"<anchor id=\"gel-function-IsMersennePrimeExponent\"/>IsMersennePrimeExponent"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4893
#, no-wrap
msgid "IsMersennePrimeExponent (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4894
msgid ""
"Tests if a positive integer <varname>p</varname> is a Mersenne prime "
"exponent. That is if 2<superscript>p</superscript>-1 is a prime. It does "
"this by looking it up in a table of known values, which is relatively short. "
"See also <link linkend=\"gel-function-"
"MersennePrimeExponents\">MersennePrimeExponents</link> and <link "
"linkend=\"gel-function-LucasLehmer\">LucasLehmer</link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4905 C/genius.xml:5121
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Mersenne_prime\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/MersenneNumbers\">Planetmath</"
"ulink>, <ulink url=\"http://mathworld.wolfram.com/"
"MersennePrime.html\">Mathworld</ulink> or <ulink url=\"http://"
"www.mersenne.org/\">GIMPS</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4917
msgid "<anchor id=\"gel-function-IsNthPower\"/>IsNthPower"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4919
#, no-wrap
msgid "IsNthPower (m,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4920
msgid ""
"Tests if a rational number <varname>m</varname> is a perfect <varname>n</"
"varname>th power. See also <link linkend=\"gel-function-"
"IsPerfectPower\">IsPerfectPower</link> and <link linkend=\"gel-function-"
"IsPerfectSquare\">IsPerfectSquare</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4931
msgid "<anchor id=\"gel-function-IsOdd\"/>IsOdd"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4933
#, no-wrap
msgid "IsOdd (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4934
msgid "Tests if an integer is odd."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4939
msgid "<anchor id=\"gel-function-IsPerfectPower\"/>IsPerfectPower"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4941
#, no-wrap
msgid "IsPerfectPower (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4942
msgid ""
"Check an integer for being any perfect power, a<superscript>b</superscript>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4947
msgid "<anchor id=\"gel-function-IsPerfectSquare\"/>IsPerfectSquare"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4949
#, no-wrap
msgid "IsPerfectSquare (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4950
msgid ""
"Check an integer for being a perfect square of an integer. The number must "
"be an integer. Negative integers are never perfect squares of integers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4959
msgid "<anchor id=\"gel-function-IsPrime\"/>IsPrime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4961
#, no-wrap
msgid "IsPrime (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4962
msgid ""
"Tests primality of integers, for numbers less than 2.5e10 the answer is "
"deterministic (if Riemann hypothesis is true). For numbers larger, the "
"probability of a false positive depends on <link linkend=\"gel-function-"
"IsPrimeMillerRabinReps\"> <function>IsPrimeMillerRabinReps</function></"
"link>. That is the probability of false positive is 1/4 to the power "
"<function>IsPrimeMillerRabinReps</function>. The default value of 22 yields "
"a probability of about 5.7e-14."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4973
msgid ""
"If <constant>false</constant> is returned, you can be sure that the number "
"is a composite. If you want to be absolutely sure that you have a prime you "
"can use <link linkend=\"gel-function-MillerRabinTestSure\"> "
"<function>MillerRabinTestSure</function></link> but it may take a lot longer."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4981 C/genius.xml:5219 C/genius.xml:5260
msgid ""
"See <ulink url=\"http://planetmath.org/PrimeNumber\">Planetmath</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/PrimeNumber.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4990
msgid "<anchor id=\"gel-function-IsPrimitiveMod\"/>IsPrimitiveMod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:4992
#, no-wrap
msgid "IsPrimitiveMod (g,q)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:4993
msgid ""
"Check if <varname>g</varname> is primitive in F<subscript>q</subscript>, the "
"finite group of order <varname>q</varname>, where <varname>q</varname> is a "
"prime. If <varname>q</varname> is not prime results are bogus."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:4999
msgid ""
"<anchor id=\"gel-function-IsPrimitiveModWithPrimeFactors\"/"
">IsPrimitiveModWithPrimeFactors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5001
#, no-wrap
msgid "IsPrimitiveModWithPrimeFactors (g,q,f)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5002
msgid ""
"Check if <varname>g</varname> is primitive in F<subscript>q</subscript>, the "
"finite group of order <varname>q</varname>, where <varname>q</varname> is a "
"prime and <varname>f</varname> is a vector of prime factors of <varname>q</"
"varname>-1. If <varname>q</varname> is not prime results are bogus."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5010
msgid "<anchor id=\"gel-function-IsPseudoprime\"/>IsPseudoprime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5012
#, no-wrap
msgid "IsPseudoprime (n,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5013
msgid ""
"If <varname>n</varname> is a pseudoprime base <varname>b</varname> but not a "
"prime, that is if <userinput>b^(n-1) == 1 mod n</userinput>. This calls the "
"<link linkend=\"gel-function-PseudoprimeTest\"><function>PseudoprimeTest</"
"function></link>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5019
msgid "<anchor id=\"gel-function-IsStrongPseudoprime\"/>IsStrongPseudoprime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5021
#, no-wrap
msgid "IsStrongPseudoprime (n,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5022
msgid ""
"Test if <varname>n</varname> is a strong pseudoprime to base <varname>b</"
"varname> but not a prime."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5027
msgid "<anchor id=\"gel-function-Jacobi\"/>Jacobi"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5029
#, no-wrap
msgid "Jacobi (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5030
msgid "Aliases: <function>JacobiSymbol</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5031
msgid "Calculate the Jacobi symbol (a/b) (b should be odd)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5036
msgid "<anchor id=\"gel-function-JacobiKronecker\"/>JacobiKronecker"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5038
#, no-wrap
msgid "JacobiKronecker (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5039
msgid "Aliases: <function>JacobiKroneckerSymbol</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5040
msgid ""
"Calculate the Jacobi symbol (a/b) with the Kronecker extension (a/2)=(2/a) "
"when a odd, or (a/2)=0 when a even."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5045
msgid "<anchor id=\"gel-function-LeastAbsoluteResidue\"/>LeastAbsoluteResidue"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5047
#, no-wrap
msgid "LeastAbsoluteResidue (a,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5048
msgid ""
"Return the residue of <varname>a</varname> mod <varname>n</varname> with the "
"least absolute value (in the interval -n/2 to n/2)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5053
msgid "<anchor id=\"gel-function-Legendre\"/>Legendre"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5055
#, no-wrap
msgid "Legendre (a,p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5056
msgid "Aliases: <function>LegendreSymbol</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5057
msgid "Calculate the Legendre symbol (a/p)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5058
msgid ""
"See <ulink url=\"http://planetmath.org/LegendreSymbol\">Planetmath</ulink> "
"or <ulink url=\"http://mathworld.wolfram.com/"
"LegendreSymbol.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5067
msgid "<anchor id=\"gel-function-LucasLehmer\"/>LucasLehmer"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5069
#, no-wrap
msgid "LucasLehmer (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5070
msgid ""
"Test if 2<superscript>p</superscript>-1 is a Mersenne prime using the Lucas-"
"Lehmer test. See also <link linkend=\"gel-function-"
"MersennePrimeExponents\">MersennePrimeExponents</link> and <link "
"linkend=\"gel-function-IsMersennePrimeExponent\">IsMersennePrimeExponent</"
"link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5076
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Lucas%E2%80%93Lehmer_primality_test\">Wikipedia</ulink>, <ulink url=\"http://"
"planetmath.org/LucasLhemer\">Planetmath</ulink>, or <ulink url=\"http://"
"mathworld.wolfram.com/Lucas-LehmerTest.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5086
msgid "<anchor id=\"gel-function-LucasNumber\"/>LucasNumber"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5088
#, no-wrap
msgid "LucasNumber (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5089
msgid "Returns the <varname>n</varname>th Lucas number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5090
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Lucas_number\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/LucasNumbers\">Planetmath</"
"ulink>, or <ulink url=\"http://mathworld.wolfram.com/"
"LucasNumber.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5100
msgid ""
"<anchor id=\"gel-function-MaximalPrimePowerFactors\"/"
">MaximalPrimePowerFactors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5102
#, no-wrap
msgid "MaximalPrimePowerFactors (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5103
msgid "Return all maximal prime power factors of a number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5108
msgid ""
"<anchor id=\"gel-function-MersennePrimeExponents\"/>MersennePrimeExponents"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5110
#, no-wrap
msgid "MersennePrimeExponents"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5111
msgid ""
"A vector of known Mersenne prime exponents, that is a list of positive "
"integers <varname>p</varname> such that 2<superscript>p</superscript>-1 is a "
"prime. See also <link linkend=\"gel-function-"
"IsMersennePrimeExponent\">IsMersennePrimeExponent</link> and <link "
"linkend=\"gel-function-LucasLehmer\">LucasLehmer</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5133
msgid "<anchor id=\"gel-function-MillerRabinTest\"/>MillerRabinTest"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5135
#, no-wrap
msgid "MillerRabinTest (n,reps)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5136
msgid ""
"Use the Miller-Rabin primality test on <varname>n</varname>, <varname>reps</"
"varname> number of times. The probability of false positive is "
"<userinput>(1/4)^reps</userinput>. It is probably usually better to use "
"<link linkend=\"gel-function-IsPrime\"> <function>IsPrime</function></link> "
"since that is faster and better on smaller integers."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5145
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Miller%E2%80%93Rabin_primality_test\">Wikipedia</ulink> or <ulink "
"url=\"http://planetmath.org/MillerRabinPrimeTest\">Planetmath</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/Rabin-"
"MillerStrongPseudoprimeTest.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5155
msgid "<anchor id=\"gel-function-MillerRabinTestSure\"/>MillerRabinTestSure"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5157
#, no-wrap
msgid "MillerRabinTestSure (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5158
msgid ""
"Use the Miller-Rabin primality test on <varname>n</varname> with enough "
"bases that assuming the Generalized Riemann Hypothesis the result is "
"deterministic."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5163
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Miller%E2%80%93Rabin_primality_test\">Wikipedia</ulink>, <ulink url=\"http://"
"planetmath.org/MillerRabinPrimeTest\">Planetmath</ulink>, or <ulink "
"url=\"http://mathworld.wolfram.com/Rabin-"
"MillerStrongPseudoprimeTest.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5173
msgid "<anchor id=\"gel-function-ModInvert\"/>ModInvert"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5175
#, no-wrap
msgid "ModInvert (n,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5176
msgid "Returns inverse of n mod m."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5177
msgid ""
"See <ulink url=\"http://mathworld.wolfram.com/"
"ModularInverse.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5185
msgid "<anchor id=\"gel-function-MoebiusMu\"/>MoebiusMu"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5187
#, no-wrap
msgid "MoebiusMu (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5188
msgid ""
"Return the Moebius mu function evaluated in <varname>n</varname>. That is, "
"it returns 0 if <varname>n</varname> is not a product of distinct primes and "
"<userinput>(-1)^k</userinput> if it is a product of <varname>k</varname> "
"distinct primes."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5194
msgid ""
"See <ulink url=\"http://planetmath.org/MoebiusFunction\">Planetmath</ulink> "
"or <ulink url=\"http://mathworld.wolfram.com/"
"MoebiusFunction.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5203
msgid "<anchor id=\"gel-function-NextPrime\"/>NextPrime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5205
#, no-wrap
msgid "NextPrime (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5206
msgid ""
"Returns the least prime greater than <varname>n</varname>. Negatives of "
"primes are considered prime and so to get the previous prime you can use "
"<userinput>-NextPrime(-n)</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5211
msgid ""
"This function uses the GMPs <function>mpz_nextprime</function>, which in "
"turn uses the probabilistic Miller-Rabin test (See also <link linkend=\"gel-"
"function-MillerRabinTest\"><function>MillerRabinTest</function></link>). The "
"probability of false positive is not tunable, but is low enough for all "
"practical purposes."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5228
msgid "<anchor id=\"gel-function-PadicValuation\"/>PadicValuation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5230
#, no-wrap
msgid "PadicValuation (n,p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5231
msgid ""
"Returns the p-adic valuation (number of trailing zeros in base <varname>p</"
"varname>)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5232
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/P-adic_order\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/PAdicValuation\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5241
msgid "<anchor id=\"gel-function-PowerMod\"/>PowerMod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5243
#, no-wrap
msgid "PowerMod (a,b,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5244
msgid ""
"Compute <userinput>a^b mod m</userinput>. The <varname>b</varname>'s power "
"of <varname>a</varname> modulo <varname>m</varname>. It is not necessary to "
"use this function as it is automatically used in modulo mode. Hence "
"<userinput>a^b mod m</userinput> is just as fast."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5255
msgid "<anchor id=\"gel-function-Prime\"/>Prime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5257
#, no-wrap
msgid "Prime (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5258
msgid "Aliases: <function>prime</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5259
msgid "Return the <varname>n</varname>th prime (up to a limit)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5269
msgid "<anchor id=\"gel-function-PrimeFactors\"/>PrimeFactors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5271
#, no-wrap
msgid "PrimeFactors (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5272
msgid "Return all prime factors of a number as a vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5273
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Prime_factor\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"PrimeFactor.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5282
msgid "<anchor id=\"gel-function-PseudoprimeTest\"/>PseudoprimeTest"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5284
#, no-wrap
msgid "PseudoprimeTest (n,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5285
msgid ""
"Pseudoprime test, returns <constant>true</constant> if and only if "
"<userinput>b^(n-1) == 1 mod n</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5287
msgid ""
"See <ulink url=\"http://planetmath.org/Pseudoprime\">Planetmath</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/Pseudoprime.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5296
msgid "<anchor id=\"gel-function-RemoveFactor\"/>RemoveFactor"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5298
#, no-wrap
msgid "RemoveFactor (n,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5299
msgid ""
"Removes all instances of the factor <varname>m</varname> from the number "
"<varname>n</varname>. That is divides by the largest power of <varname>m</"
"varname>, that divides <varname>n</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5300
msgid ""
"See <ulink url=\"http://planetmath.org/Divisibility\">Planetmath</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/Factor.html\">Mathworld</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5309
msgid ""
"<anchor id=\"gel-function-SilverPohligHellmanWithFactorization\"/"
">SilverPohligHellmanWithFactorization"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5311
#, no-wrap
msgid "SilverPohligHellmanWithFactorization (n,b,q,f)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5312
msgid ""
"Find discrete log of <varname>n</varname> base <varname>b</varname> in "
"F<subscript>q</subscript>, the finite group of order <varname>q</varname>, "
"where <varname>q</varname> is a prime using the Silver-Pohlig-Hellman "
"algorithm, given <varname>f</varname> being the factorization of <varname>q</"
"varname>-1."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5317
msgid "<anchor id=\"gel-function-SqrtModPrime\"/>SqrtModPrime"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5319
#, no-wrap
msgid "SqrtModPrime (n,p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5320
msgid ""
"Find square root of <varname>n</varname> modulo <varname>p</varname> (where "
"<varname>p</varname> is a prime). Null is returned if not a quadratic "
"residue."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5321
msgid ""
"See <ulink url=\"http://planetmath.org/QuadraticResidue\">Planetmath</ulink> "
"or <ulink url=\"http://mathworld.wolfram.com/"
"QuadraticResidue.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5330
msgid ""
"<anchor id=\"gel-function-StrongPseudoprimeTest\"/>StrongPseudoprimeTest"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5332
#, no-wrap
msgid "StrongPseudoprimeTest (n,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5333
msgid ""
"Run the strong pseudoprime test base <varname>b</varname> on <varname>n</"
"varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5334
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Strong_pseudoprime\">Wikipedia</ulink>, <ulink url=\"http://planetmath.org/"
"StrongPseudoprime\">Planetmath</ulink>, or <ulink url=\"http://"
"mathworld.wolfram.com/StrongPseudoprime.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5344
msgid "<anchor id=\"gel-function-gcd\"/>gcd"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5346
#, no-wrap
msgid "gcd (a,args...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5347
msgid "Aliases: <function>GCD</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5348
msgid ""
"Greatest common divisor of integers. You can enter as many integers as you "
"want in the argument list, or you can give a vector or a matrix of integers. "
"If you give more than one matrix of the same size then GCD is done element "
"by element."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5355
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Greatest_common_divisor\">Wikipedia</ulink>, <ulink url=\"http://"
"planetmath.org/GreatestCommonDivisor\">Planetmath</ulink>, or <ulink "
"url=\"http://mathworld.wolfram.com/GreatestCommonDivisor.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5365
msgid "<anchor id=\"gel-function-lcm\"/>lcm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5367
#, no-wrap
msgid "lcm (a,args...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5368
msgid "Aliases: <function>LCM</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5369
msgid ""
"Least common multiplier of integers. You can enter as many integers as you "
"want in the argument list, or you can give a vector or a matrix of integers. "
"If you give more than one matrix of the same size then LCM is done element "
"by element."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5375
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Least_common_multiple\">Wikipedia</ulink>, <ulink url=\"http://"
"planetmath.org/LeastCommonMultiple\">Planetmath</ulink>, or <ulink "
"url=\"http://mathworld.wolfram.com/LeastCommonMultiple.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:5388
msgid "Matrix Manipulation"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5391
msgid "<anchor id=\"gel-function-AppendElement\"/>AppendElement"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5393
#, no-wrap
msgid "AppendElement (v,elt)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5394
msgid ""
"Append an element to a vector and return the vector. No expansion is done. "
"Normally a row vector is built if starting from <constant>null</constant> or "
"a 1-by-1 matrix, but if given a column vector it will properly build a "
"column vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5401
msgid "<anchor id=\"gel-function-ApplyOverMatrix\"/>ApplyOverMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5403
#, no-wrap
msgid "ApplyOverMatrix (a,func)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5404
msgid ""
"Apply a function over all entries of a matrix and return a matrix of the "
"results."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5409
msgid "<anchor id=\"gel-function-ApplyOverMatrix2\"/>ApplyOverMatrix2"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5411
#, no-wrap
msgid "ApplyOverMatrix2 (a,b,func)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5412
msgid ""
"Apply a function over all entries of 2 matrices (or 1 value and 1 matrix) "
"and return a matrix of the results."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5417
msgid "<anchor id=\"gel-function-ColumnsOf\"/>ColumnsOf"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5419
#, no-wrap
msgid "ColumnsOf (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5420
msgid "Gets the columns of a matrix as a horizontal vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5425
msgid "<anchor id=\"gel-function-ComplementSubmatrix\"/>ComplementSubmatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5427
#, no-wrap
msgid "ComplementSubmatrix (m,r,c)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5428
msgid "Remove column(s) and row(s) from a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5433
msgid "<anchor id=\"gel-function-CompoundMatrix\"/>CompoundMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5435
#, no-wrap
msgid "CompoundMatrix (k,A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5436
msgid "Calculate the kth compound matrix of A."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5441
msgid "<anchor id=\"gel-function-CountZeroColumns\"/>CountZeroColumns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5443
#, no-wrap
msgid "CountZeroColumns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5444
msgid ""
"Count the number of zero columns in a matrix. For example, once you column-"
"reduce a matrix, you can use this to find the nullity. See <link "
"linkend=\"gel-function-cref\"><function>cref</function></link> and <link "
"linkend=\"gel-function-Nullity\"><function>Nullity</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5454
msgid "<anchor id=\"gel-function-DeleteColumn\"/>DeleteColumn"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5456
#, no-wrap
msgid "DeleteColumn (M,col)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5457
msgid "Delete a column of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5462
msgid "<anchor id=\"gel-function-DeleteRow\"/>DeleteRow"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5464
#, no-wrap
msgid "DeleteRow (M,row)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5465
msgid "Delete a row of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5470
msgid "<anchor id=\"gel-function-DiagonalOf\"/>DiagonalOf"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5472
#, no-wrap
msgid "DiagonalOf (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5473
msgid "Gets the diagonal entries of a matrix as a column vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5474
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Diagonal_of_a_matrix#Matrices\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5482
msgid "<anchor id=\"gel-function-DotProduct\"/>DotProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5484
#, no-wrap
msgid "DotProduct (u,v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5485
msgid ""
"Get the dot product of two vectors. The vectors must be of the same size. No "
"conjugates are taken so this is a bilinear form even if working over the "
"complex numbers; This is the bilinear scalar product not the sesquilinear "
"scalar product. See <link linkend=\"gel-function-"
"HermitianProduct\">HermitianProduct</link> for the standard sesquilinear "
"inner product."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5487
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Dot_product\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/DotProduct\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5496
msgid "<anchor id=\"gel-function-ExpandMatrix\"/>ExpandMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5498
#, no-wrap
msgid "ExpandMatrix (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5499
msgid ""
"Expands a matrix just like we do on unquoted matrix input. That is we expand "
"any internal matrices as blocks. This is a way to construct matrices out of "
"smaller ones and this is normally done automatically on input unless the "
"matrix is quoted."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5509
msgid "<anchor id=\"gel-function-HermitianProduct\"/>HermitianProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5511
#, no-wrap
msgid "HermitianProduct (u,v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5512
msgid "Aliases: <function>InnerProduct</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5513
msgid ""
"Get the Hermitian product of two vectors. The vectors must be of the same "
"size. This is a sesquilinear form using the identity matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5514
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Sesquilinear_form\">Wikipedia</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/HermitianInnerProduct.html\">Mathworld</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5523
msgid "<anchor id=\"gel-function-I\"/>I"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5525
#, no-wrap
msgid "I (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5526
msgid "Aliases: <function>eye</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5527
msgid ""
"Return an identity matrix of a given size, that is <varname>n</varname> by "
"<varname>n</varname>. If <varname>n</varname> is zero, returns "
"<constant>null</constant>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5528
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Identity_matrix\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/IdentityMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5537
msgid "<anchor id=\"gel-function-IndexComplement\"/>IndexComplement"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5539
#, no-wrap
msgid "IndexComplement (vec,msize)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5540
msgid ""
"Return the index complement of a vector of indexes. Everything is one based. "
"For example for vector <userinput>[2,3]</userinput> and size <userinput>5</"
"userinput>, we return <userinput>[1,4,5]</userinput>. If <varname>msize</"
"varname> is 0, we always return <constant>null</constant>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5547
msgid "<anchor id=\"gel-function-IsDiagonal\"/>IsDiagonal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5549
#, no-wrap
msgid "IsDiagonal (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5550
msgid "Is a matrix diagonal."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5551 C/genius.xml:5701
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Diagonal_matrix\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/DiagonalMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5560
msgid "<anchor id=\"gel-function-IsIdentity\"/>IsIdentity"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5562
#, no-wrap
msgid "IsIdentity (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5563
msgid ""
"Check if a matrix is the identity matrix. Automatically returns "
"<constant>false</constant> if the matrix is not square. Also works on "
"numbers, in which case it is equivalent to <userinput>x==1</userinput>. When "
"<varname>x</varname> is <constant>null</constant> (we could think of that as "
"a 0 by 0 matrix), no error is generated and <constant>false</constant> is "
"returned."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5572
msgid "<anchor id=\"gel-function-IsLowerTriangular\"/>IsLowerTriangular"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5574
#, no-wrap
msgid "IsLowerTriangular (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5575
msgid ""
"Is a matrix lower triangular. That is, are all the entries above the "
"diagonal zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5580
msgid "<anchor id=\"gel-function-IsMatrixInteger\"/>IsMatrixInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5582
#, no-wrap
msgid "IsMatrixInteger (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5583
msgid "Check if a matrix is a matrix of integers (non-complex)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5588
msgid "<anchor id=\"gel-function-IsMatrixNonnegative\"/>IsMatrixNonnegative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5590
#, no-wrap
msgid "IsMatrixNonnegative (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5591
msgid ""
"Check if a matrix is non-negative, that is if each element is non-negative. "
"Do not confuse positive matrices with positive semi-definite matrices."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5593 C/genius.xml:5607
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Positive_matrix\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5601
msgid "<anchor id=\"gel-function-IsMatrixPositive\"/>IsMatrixPositive"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5603
#, no-wrap
msgid "IsMatrixPositive (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5604
msgid ""
"Check if a matrix is positive, that is if each element is positive (and "
"hence real). In particular, no element is 0. Do not confuse positive "
"matrices with positive definite matrices."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5615
msgid "<anchor id=\"gel-function-IsMatrixRational\"/>IsMatrixRational"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5617
#, no-wrap
msgid "IsMatrixRational (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5618
msgid "Check if a matrix is a matrix of rational (non-complex) numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5624
msgid "<anchor id=\"gel-function-IsMatrixReal\"/>IsMatrixReal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5626
#, no-wrap
msgid "IsMatrixReal (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5627
msgid "Check if a matrix is a matrix of real (non-complex) numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5632
msgid "<anchor id=\"gel-function-IsMatrixSquare\"/>IsMatrixSquare"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5634
#, no-wrap
msgid "IsMatrixSquare (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5635
msgid "Check if a matrix is square, that is its width is equal to its height."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5643
msgid "<anchor id=\"gel-function-IsUpperTriangular\"/>IsUpperTriangular"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5645
#, no-wrap
msgid "IsUpperTriangular (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5646
msgid ""
"Is a matrix upper triangular? That is, a matrix is upper triangular if all "
"the entries below the diagonal are zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5651
msgid "<anchor id=\"gel-function-IsValueOnly\"/>IsValueOnly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5653
#, no-wrap
msgid "IsValueOnly (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5654
msgid ""
"Check if a matrix is a matrix of numbers only. Many internal functions make "
"this check. Values can be any number including complex numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5660
msgid "<anchor id=\"gel-function-IsVector\"/>IsVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5662
#, no-wrap
msgid "IsVector (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5663
msgid ""
"Is argument a horizontal or a vertical vector. Genius does not distinguish "
"between a matrix and a vector and a vector is just a 1 by <varname>n</"
"varname> or <varname>n</varname> by 1 matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5672
msgid "<anchor id=\"gel-function-IsZero\"/>IsZero"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5674
#, no-wrap
msgid "IsZero (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5675
msgid ""
"Check if a matrix is composed of all zeros. Also works on numbers, in which "
"case it is equivalent to <userinput>x==0</userinput>. When <varname>x</"
"varname> is <constant>null</constant> (we could think of that as a 0 by 0 "
"matrix), no error is generated and <constant>true</constant> is returned as "
"the condition is vacuous."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5685
msgid "<anchor id=\"gel-function-LowerTriangular\"/>LowerTriangular"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5687
#, no-wrap
msgid "LowerTriangular (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5688
msgid ""
"Returns a copy of the matrix <varname>M</varname> with all the entries above "
"the diagonal set to zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5693
msgid "<anchor id=\"gel-function-MakeDiagonal\"/>MakeDiagonal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5695
#, no-wrap
msgid "MakeDiagonal (v,arg...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5696
msgid "Aliases: <function>diag</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5697
msgid ""
"Make diagonal matrix from a vector. Alternatively you can pass in the values "
"to put on the diagonal as arguments. So <userinput>MakeDiagonal([1,2,3])</"
"userinput> is the same as <userinput>MakeDiagonal(1,2,3)</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5710
msgid "<anchor id=\"gel-function-MakeVector\"/>MakeVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5712
#, no-wrap
msgid "MakeVector (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5713
msgid "Alias: <function>MakeColumnVector</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5714
msgid ""
"Make column vector out of matrix by putting columns above each other. "
"Returns <constant>null</constant> when given <constant>null</constant>. Can "
"be used to ensure a vector is a column vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5721
msgid "<anchor id=\"gel-function-MakeRowVector\"/>MakeRowVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5723
#, no-wrap
msgid "MakeRowVector (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5724
msgid ""
"Make row vector out of matrix by putting rows one after another. Returns "
"<constant>null</constant> when given <constant>null</constant>. Can be used "
"to ensure a vector is a row vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5731
msgid "<anchor id=\"gel-function-MatrixProduct\"/>MatrixProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5733
#, no-wrap
msgid "MatrixProduct (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5734
msgid ""
"Calculate the product of all elements in a matrix or vector. That is we "
"multiply all the elements and return a number that is the product of all the "
"elements."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5743
msgid "<anchor id=\"gel-function-MatrixSum\"/>MatrixSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5745
#, no-wrap
msgid "MatrixSum (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5746
msgid ""
"Calculate the sum of all elements in a matrix or vector. That is we add all "
"the elements and return a number that is the sum of all the elements."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5755
msgid "<anchor id=\"gel-function-MatrixSumSquares\"/>MatrixSumSquares"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5757
#, no-wrap
msgid "MatrixSumSquares (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5758
msgid "Calculate the sum of squares of all elements in a matrix or vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5764
msgid "<anchor id=\"gel-function-NonzeroColumns\"/>NonzeroColumns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5766
#, no-wrap
msgid "NonzeroColumns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5767
msgid ""
"Returns a row vector of the indices of nonzero columns in the matrix "
"<varname>M</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5773
msgid "<anchor id=\"gel-function-NonzeroElements\"/>NonzeroElements"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5775
#, no-wrap
msgid "NonzeroElements (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5776
msgid ""
"Returns a row vector of the indices of nonzero elements in the vector "
"<varname>v</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5782
msgid "<anchor id=\"gel-function-OuterProduct\"/>OuterProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5784
#, no-wrap
msgid "OuterProduct (u,v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5785
msgid ""
"Get the outer product of two vectors. That is, suppose that <varname>u</"
"varname> and <varname>v</varname> are vertical vectors, then the outer "
"product is <userinput>v * u.'</userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5792
msgid "<anchor id=\"gel-function-ReverseVector\"/>ReverseVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5794
#, no-wrap
msgid "ReverseVector (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5795
msgid ""
"Reverse elements in a vector. Return <constant>null</constant> if given "
"<constant>null</constant>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5800
msgid "<anchor id=\"gel-function-RowSum\"/>RowSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5802
#, no-wrap
msgid "RowSum (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5803
msgid ""
"Calculate sum of each row in a matrix and return a vertical vector with the "
"result."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5809
msgid "<anchor id=\"gel-function-RowSumSquares\"/>RowSumSquares"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5811
#, no-wrap
msgid "RowSumSquares (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5812
msgid ""
"Calculate sum of squares of each row in a matrix and return a vertical "
"vector with the results."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5817
msgid "<anchor id=\"gel-function-RowsOf\"/>RowsOf"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5819
#, no-wrap
msgid "RowsOf (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5820
msgid ""
"Gets the rows of a matrix as a vertical vector. Each element of the vector "
"is a horizontal vector that is the corresponding row of <varname>M</"
"varname>. This function is useful if you wish to loop over the rows of a "
"matrix. For example, as <userinput>for r in RowsOf(M) do something(r)</"
"userinput>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5829
msgid "<anchor id=\"gel-function-SetMatrixSize\"/>SetMatrixSize"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5831
#, no-wrap
msgid "SetMatrixSize (M,rows,columns)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5832
msgid ""
"Make new matrix of given size from old one. That is, a new matrix will be "
"returned to which the old one is copied. Entries that don't fit are clipped "
"and extra space is filled with zeros. If <varname>rows</varname> or "
"<varname>columns</varname> are zero then <constant>null</constant> is "
"returned."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5842
msgid "<anchor id=\"gel-function-ShuffleVector\"/>ShuffleVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5844
#, no-wrap
msgid "ShuffleVector (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5845
msgid ""
"Shuffle elements in a vector. Return <constant>null</constant> if given "
"<constant>null</constant>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5846
msgid "Version 1.0.13 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5851
msgid "<anchor id=\"gel-function-SortVector\"/>SortVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5853
#, no-wrap
msgid "SortVector (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5854
msgid "Sort vector elements in an increasing order."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5859
msgid "<anchor id=\"gel-function-StripZeroColumns\"/>StripZeroColumns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5861
#, no-wrap
msgid "StripZeroColumns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5862
msgid "Removes any all-zero columns of <varname>M</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5867
msgid "<anchor id=\"gel-function-StripZeroRows\"/>StripZeroRows"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5869
#, no-wrap
msgid "StripZeroRows (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5870
msgid "Removes any all-zero rows of <varname>M</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5875
msgid "<anchor id=\"gel-function-Submatrix\"/>Submatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5877
#, no-wrap
msgid "Submatrix (m,r,c)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5878
msgid ""
"Return column(s) and row(s) from a matrix. This is just equivalent to "
"<userinput>m@(r,c)</userinput>. <varname>r</varname> and <varname>c</"
"varname> should be vectors of rows and columns (or single numbers if only "
"one row or column is needed)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5885
msgid "<anchor id=\"gel-function-SwapRows\"/>SwapRows"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5887
#, no-wrap
msgid "SwapRows (m,row1,row2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5888
msgid "Swap two rows in a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5893
msgid "<anchor id=\"gel-function-UpperTriangular\"/>UpperTriangular"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5895
#, no-wrap
msgid "UpperTriangular (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5896
msgid ""
"Returns a copy of the matrix <varname>M</varname> with all the entries below "
"the diagonal set to zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5901
msgid "<anchor id=\"gel-function-columns\"/>columns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5903
#, no-wrap
msgid "columns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5904
msgid "Get the number of columns of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5909
msgid "<anchor id=\"gel-function-elements\"/>elements"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5911
#, no-wrap
msgid "elements (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5912
msgid ""
"Get the total number of elements of a matrix. This is the number of columns "
"times the number of rows."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5918
msgid "<anchor id=\"gel-function-ones\"/>ones"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5920
#, no-wrap
msgid "ones (rows,columns...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5921
msgid ""
"Make an matrix of all ones (or a row vector if only one argument is given). "
"Returns <constant>null</constant> if either rows or columns are zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5926
msgid "<anchor id=\"gel-function-rows\"/>rows"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5928
#, no-wrap
msgid "rows (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5929
msgid "Get the number of rows of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5934
msgid "<anchor id=\"gel-function-zeros\"/>zeros"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5936
#, no-wrap
msgid "zeros (rows,columns...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5937
msgid ""
"Make a matrix of all zeros (or a row vector if only one argument is given). "
"Returns <constant>null</constant> if either rows or columns are zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5948
msgid "<anchor id=\"gel-function-AuxiliaryUnitMatrix\"/>AuxiliaryUnitMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5950
#, no-wrap
msgid "AuxiliaryUnitMatrix (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5951
msgid ""
"Get the auxiliary unit matrix of size <varname>n</varname>. This is a square "
"matrix with that is all zero except the superdiagonal being all ones. It is "
"the Jordan block matrix of one zero eigenvalue."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5953
msgid ""
"See <ulink url=\"http://planetmath.org/"
"JordanCanonicalFormTheorem\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/JordanBlock.html\">Mathworld</ulink> for more "
"information on Jordan Canonical Form."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5962
msgid "<anchor id=\"gel-function-BilinearForm\"/>BilinearForm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5964
#, no-wrap
msgid "BilinearForm (v,A,w)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5965
msgid "Evaluate (v,w) with respect to the bilinear form given by the matrix A."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5970
msgid "<anchor id=\"gel-function-BilinearFormFunction\"/>BilinearFormFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5972
#, no-wrap
msgid "BilinearFormFunction (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5973
msgid ""
"Return a function that evaluates two vectors with respect to the bilinear "
"form given by A."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5978
msgid ""
"<anchor id=\"gel-function-CharacteristicPolynomial\"/"
">CharacteristicPolynomial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5980
#, no-wrap
msgid "CharacteristicPolynomial (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5981
msgid "Aliases: <function>CharPoly</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5982
msgid ""
"Get the characteristic polynomial as a vector. That is, return the "
"coefficients of the polynomial starting with the constant term. This is the "
"polynomial defined by <userinput>det(M-xI)</userinput>. The roots of this "
"polynomial are the eigenvalues of <varname>M</varname>. See also <link "
"linkend=\"gel-function-"
"CharacteristicPolynomialFunction\">CharacteristicPolynomialFunction</link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:5988 C/genius.xml:6005
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Characteristic_polynomial\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/CharacteristicEquation\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:5997
msgid ""
"<anchor id=\"gel-function-CharacteristicPolynomialFunction\"/"
">CharacteristicPolynomialFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:5999
#, no-wrap
msgid "CharacteristicPolynomialFunction (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6000
msgid ""
"Get the characteristic polynomial as a function. This is the polynomial "
"defined by <userinput>det(M-xI)</userinput>. The roots of this polynomial "
"are the eigenvalues of <varname>M</varname>. See also <link linkend=\"gel-"
"function-CharacteristicPolynomial\">CharacteristicPolynomial</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6014
msgid "<anchor id=\"gel-function-ColumnSpace\"/>ColumnSpace"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6016
#, no-wrap
msgid "ColumnSpace (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6017
msgid ""
"Get a basis matrix for the columnspace of a matrix. That is, return a matrix "
"whose columns are the basis for the column space of <varname>M</varname>. "
"That is the space spanned by the columns of <varname>M</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6021 C/genius.xml:6211
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Row_and_column_spaces\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6029
msgid "<anchor id=\"gel-function-CommutationMatrix\"/>CommutationMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6031
#, no-wrap
msgid "CommutationMatrix (m, n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6032
msgid ""
"Return the commutation matrix <userinput>K(m,n)</userinput>, which is the "
"unique <userinput>m*n</userinput> by <userinput>m*n</userinput> matrix such "
"that <userinput>K(m,n) * MakeVector(A) = MakeVector(A.')</userinput> for all "
"<varname>m</varname> by <varname>n</varname> matrices <varname>A</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6039
msgid "<anchor id=\"gel-function-CompanionMatrix\"/>CompanionMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6041
#, no-wrap
msgid "CompanionMatrix (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6042
msgid "Companion matrix of a polynomial (as vector)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6047
msgid "<anchor id=\"gel-function-ConjugateTranspose\"/>ConjugateTranspose"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6049
#, no-wrap
msgid "ConjugateTranspose (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6050
msgid ""
"Conjugate transpose of a matrix (adjoint). This is the same as the "
"<userinput>'</userinput> operator."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6052
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Conjugate_transpose\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/ConjugateTranspose\">Planetmath</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6061
msgid "<anchor id=\"gel-function-Convolution\"/>Convolution"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6063
#, no-wrap
msgid "Convolution (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6064
msgid "Aliases: <function>convol</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6065
msgid "Calculate convolution of two horizontal vectors."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6070
msgid "<anchor id=\"gel-function-ConvolutionVector\"/>ConvolutionVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6072
#, no-wrap
msgid "ConvolutionVector (a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6073
msgid ""
"Calculate convolution of two horizontal vectors. Return result as a vector "
"and not added together."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6079
msgid "<anchor id=\"gel-function-CrossProduct\"/>CrossProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6081
#, no-wrap
msgid "CrossProduct (v,w)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6082
msgid ""
"CrossProduct of two vectors in R<superscript>3</superscript> as a column "
"vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6084
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Cross_product\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6092
msgid ""
"<anchor id=\"gel-function-DeterminantalDivisorsInteger\"/"
">DeterminantalDivisorsInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6094
#, no-wrap
msgid "DeterminantalDivisorsInteger (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6095
msgid "Get the determinantal divisors of an integer matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6100
msgid "<anchor id=\"gel-function-DirectSum\"/>DirectSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6102
#, no-wrap
msgid "DirectSum (M,N...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6103
msgid "Direct sum of matrices."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6104 C/genius.xml:6116
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Matrix_addition#directsum\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6112
msgid ""
"<anchor id=\"gel-function-DirectSumMatrixVector\"/>DirectSumMatrixVector"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6114
#, no-wrap
msgid "DirectSumMatrixVector (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6115
msgid "Direct sum of a vector of matrices."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6124
msgid "<anchor id=\"gel-function-Eigenvalues\"/>Eigenvalues"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6126
#, no-wrap
msgid "Eigenvalues (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6127
msgid "Aliases: <function>eig</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6128
msgid ""
"Get the eigenvalues of a square matrix. Currently only works for matrices of "
"size up to 4 by 4, or for triangular matrices (for which the eigenvalues are "
"on the diagonal)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6133
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Eigenvalue\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/Eigenvalue\">Planetmath</ulink>, "
"or <ulink url=\"http://mathworld.wolfram.com/Eigenvalue.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6143
msgid "<anchor id=\"gel-function-Eigenvectors\"/>Eigenvectors"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6145
#, no-wrap
msgid "Eigenvectors (M)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6146
#, no-wrap
msgid "Eigenvectors (M, &amp;eigenvalues)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6147
#, no-wrap
msgid "Eigenvectors (M, &amp;eigenvalues, &amp;multiplicities)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6148
msgid ""
"Get the eigenvectors of a square matrix. Optionally get also the eigenvalues "
"and their algebraic multiplicities. Currently only works for matrices of "
"size up to 2 by 2."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6152
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Eigenvector\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/Eigenvector\">Planetmath</ulink>, "
"or <ulink url=\"http://mathworld.wolfram.com/Eigenvector.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6162
msgid "<anchor id=\"gel-function-GramSchmidt\"/>GramSchmidt"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6164
#, no-wrap
msgid "GramSchmidt (v,B...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6165
msgid ""
"Apply the Gram-Schmidt process (to the columns) with respect to inner "
"product given by <varname>B</varname>. If <varname>B</varname> is not given "
"then the standard Hermitian product is used. <varname>B</varname> can either "
"be a sesquilinear function of two arguments or it can be a matrix giving a "
"sesquilinear form. The vectors will be made orthonormal with respect to "
"<varname>B</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6171
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Gram%E2%80%93Schmidt_process\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/GramSchmidtOrthogonalization\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6180
msgid "<anchor id=\"gel-function-HankelMatrix\"/>HankelMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6182
#, no-wrap
msgid "HankelMatrix (c,r)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6183
msgid ""
"Hankel matrix, a matrix whose skew-diagonals are constant. <varname>c</"
"varname> is the first row and <varname>r</varname> is the last column. It is "
"assumed that both arguments are vectors and the last element of <varname>c</"
"varname> is the same as the first element of <varname>r</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6186
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Hankel_matrix\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6194
msgid "<anchor id=\"gel-function-HilbertMatrix\"/>HilbertMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6196
#, no-wrap
msgid "HilbertMatrix (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6197
msgid "Hilbert matrix of order <varname>n</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6198 C/genius.xml:6239
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Hilbert_matrix\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/HilbertMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6207
msgid "<anchor id=\"gel-function-Image\"/>Image"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6209
#, no-wrap
msgid "Image (T)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6210
msgid "Get the image (columnspace) of a linear transform."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6219
msgid "<anchor id=\"gel-function-InfNorm\"/>InfNorm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6221
#, no-wrap
msgid "InfNorm (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6222
msgid ""
"Get the Inf Norm of a vector, sometimes called the sup norm or the max norm."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6227
msgid ""
"<anchor id=\"gel-function-InvariantFactorsInteger\"/>InvariantFactorsInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6229
#, no-wrap
msgid "InvariantFactorsInteger (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6230
msgid "Get the invariant factors of a square integer matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6235
msgid "<anchor id=\"gel-function-InverseHilbertMatrix\"/>InverseHilbertMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6237
#, no-wrap
msgid "InverseHilbertMatrix (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6238
msgid "Inverse Hilbert matrix of order <varname>n</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6248
msgid "<anchor id=\"gel-function-IsHermitian\"/>IsHermitian"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6250
#, no-wrap
msgid "IsHermitian (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6251
msgid "Is a matrix Hermitian. That is, is it equal to its conjugate transpose."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6252
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Hermitian_matrix\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/HermitianMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6261
msgid "<anchor id=\"gel-function-IsInSubspace\"/>IsInSubspace"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6263
#, no-wrap
msgid "IsInSubspace (v,W)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6264
msgid "Test if a vector is in a subspace."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6269
msgid "<anchor id=\"gel-function-IsInvertible\"/>IsInvertible"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6271
#, no-wrap
msgid "IsInvertible (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6272
msgid ""
"Is a matrix (or number) invertible (Integer matrix is invertible if and only "
"if it is invertible over the integers)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6277
msgid "<anchor id=\"gel-function-IsInvertibleField\"/>IsInvertibleField"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6279
#, no-wrap
msgid "IsInvertibleField (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6280
msgid "Is a matrix (or number) invertible over a field."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6285
msgid "<anchor id=\"gel-function-IsNormal\"/>IsNormal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6287
#, no-wrap
msgid "IsNormal (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6288
msgid ""
"Is <varname>M</varname> a normal matrix. That is, does <userinput>M*M' == "
"M'*M</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6290
msgid ""
"See <ulink url=\"http://planetmath.org/NormalMatrix\">Planetmath</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/NormalMatrix.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6299
msgid "<anchor id=\"gel-function-IsPositiveDefinite\"/>IsPositiveDefinite"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6301
#, no-wrap
msgid "IsPositiveDefinite (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6302
msgid ""
"Is <varname>M</varname> a Hermitian positive definite matrix. That is if "
"<userinput>HermitianProduct(M*v,v)</userinput> is always strictly positive "
"for any vector <varname>v</varname>. <varname>M</varname> must be square and "
"Hermitian to be positive definite. The check that is performed is that every "
"principal submatrix has a non-negative determinant. (See <link linkend=\"gel-"
"function-HermitianProduct\">HermitianProduct</link>)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6309
msgid ""
"Note that some authors (for example Mathworld) do not require that "
"<varname>M</varname> be Hermitian, and then the condition is on the real "
"part of the inner product, but we do not take this view. If you wish to "
"perform this check, just check the Hermitian part of the matrix <varname>M</"
"varname> as follows: <userinput>IsPositiveDefinite(M+M')</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6317
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Positive-"
"definite_matrix\">Wikipedia</ulink>, <ulink url=\"http://planetmath.org/"
"PositiveDefinite\">Planetmath</ulink>, or <ulink url=\"http://"
"mathworld.wolfram.com/PositiveDefiniteMatrix.html\">Mathworld</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6327
msgid ""
"<anchor id=\"gel-function-IsPositiveSemidefinite\"/>IsPositiveSemidefinite"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6329
#, no-wrap
msgid "IsPositiveSemidefinite (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6330
msgid ""
"Is <varname>M</varname> a Hermitian positive semidefinite matrix. That is if "
"<userinput>HermitianProduct(M*v,v)</userinput> is always non-negative for "
"any vector <varname>v</varname>. <varname>M</varname> must be square and "
"Hermitian to be positive semidefinite. The check that is performed is that "
"every principal submatrix has a non-negative determinant. (See <link "
"linkend=\"gel-function-HermitianProduct\">HermitianProduct</link>)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6337
msgid ""
"Note that some authors do not require that <varname>M</varname> be "
"Hermitian, and then the condition is on the real part of the inner product, "
"but we do not take this view. If you wish to perform this check, just check "
"the Hermitian part of the matrix <varname>M</varname> as follows: "
"<userinput>IsPositiveSemidefinite(M+M')</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6345
msgid ""
"See <ulink url=\"http://planetmath.org/PositiveSemidefinite\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"PositiveSemidefiniteMatrix.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6354
msgid "<anchor id=\"gel-function-IsSkewHermitian\"/>IsSkewHermitian"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6356
#, no-wrap
msgid "IsSkewHermitian (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6357
msgid ""
"Is a matrix skew-Hermitian. That is, is the conjugate transpose equal to "
"negative of the matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6358
msgid ""
"See <ulink url=\"http://planetmath.org/SkewHermitianMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6366
msgid "<anchor id=\"gel-function-IsUnitary\"/>IsUnitary"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6368
#, no-wrap
msgid "IsUnitary (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6369
msgid ""
"Is a matrix unitary? That is, does <userinput>M'*M</userinput> and "
"<userinput>M*M'</userinput> equal the identity."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6372
msgid ""
"See <ulink url=\"http://planetmath.org/UnitaryTransformation\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"UnitaryMatrix.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6381
msgid "<anchor id=\"gel-function-JordanBlock\"/>JordanBlock"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6383
#, no-wrap
msgid "JordanBlock (n,lambda)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6384
msgid "Aliases: <function>J</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6385
msgid ""
"Get the Jordan block corresponding to the eigenvalue <varname>lambda</"
"varname> with multiplicity <varname>n</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6388
msgid ""
"See <ulink url=\"http://planetmath.org/"
"JordanCanonicalFormTheorem\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/JordanBlock.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6397
msgid "<anchor id=\"gel-function-Kernel\"/>Kernel"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6399
#, no-wrap
msgid "Kernel (T)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6400
msgid "Get the kernel (nullspace) of a linear transform."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6401
msgid "(See <link linkend=\"gel-function-NullSpace\">NullSpace</link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6408
msgid "<anchor id=\"gel-function-KroneckerProduct\"/>KroneckerProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6410
#, no-wrap
msgid "KroneckerProduct (M, N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6411
msgid "Aliases: <function>TensorProduct</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6412
msgid ""
"Compute the Kronecker product (tensor product in standard basis) of two "
"matrices."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6416
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Kronecker_product\">Wikipedia</ulink>, <ulink url=\"http://planetmath.org/"
"KroneckerProduct\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/KroneckerProduct.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6428
msgid "<anchor id=\"gel-function-LUDecomposition\"/>LUDecomposition"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6430
#, no-wrap
msgid "LUDecomposition (A, L, U)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:6439
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>LUDecomposition(A,&amp;L,&amp;U)</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6431
msgid ""
"Get the LU decomposition of <varname>A</varname>, that is find a lower "
"triangular matrix and upper triangular matrix whose product is <varname>A</"
"varname>. Store the result in the <varname>L</varname> and <varname>U</"
"varname>, which should be references. It returns <constant>true</constant> "
"if successful. For example suppose that A is a square matrix, then after "
"running: <_:screen-1/> You will have the lower matrix stored in a variable "
"called <varname>L</varname> and the upper matrix in a variable called "
"<varname>U</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6445
msgid ""
"This is the LU decomposition of a matrix aka Crout and/or Cholesky "
"reduction. (ISBN 0-201-11577-8 pp.99-103) The upper triangular matrix "
"features a diagonal of values 1 (one). This is not Doolittle's Method, which "
"features the 1's diagonal on the lower matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6453
msgid ""
"Not all matrices have LU decompositions, for example <userinput>[0,1;1,0]</"
"userinput> does not and this function returns <constant>false</constant> in "
"this case and sets <varname>L</varname> and <varname>U</varname> to "
"<constant>null</constant>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6459
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/LU_decomposition\">Wikipedia</"
"ulink>, <ulink url=\"http://planetmath.org/LUDecomposition\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"LUDecomposition.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6469
msgid "<anchor id=\"gel-function-Minor\"/>Minor"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6471
#, no-wrap
msgid "Minor (M,i,j)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6472
msgid "Get the <varname>i</varname>-<varname>j</varname> minor of a matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6473
msgid ""
"See <ulink url=\"http://planetmath.org/Minor\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6481
msgid "<anchor id=\"gel-function-NonPivotColumns\"/>NonPivotColumns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6483
#, no-wrap
msgid "NonPivotColumns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6484
msgid "Return the columns that are not the pivot columns of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6489
msgid "<anchor id=\"gel-function-Norm\"/>Norm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6491
#, no-wrap
msgid "Norm (v,p...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6492
msgid "Aliases: <function>norm</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6493
msgid "Get the p Norm (or 2 Norm if no p is supplied) of a vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6498
msgid "<anchor id=\"gel-function-NullSpace\"/>NullSpace"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6500
#, no-wrap
msgid "NullSpace (T)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6501
msgid ""
"Get the nullspace of a matrix. That is the kernel of the linear mapping that "
"the matrix represents. This is returned as a matrix whose column space is "
"the nullspace of <varname>T</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6505
msgid ""
"See <ulink url=\"http://planetmath.org/Nullspace\">Planetmath</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6513
msgid "<anchor id=\"gel-function-Nullity\"/>Nullity"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6515
#, no-wrap
msgid "Nullity (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6516
msgid "Aliases: <function>nullity</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6517
msgid ""
"Get the nullity of a matrix. That is, return the dimension of the nullspace; "
"the dimension of the kernel of <varname>M</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6519
msgid ""
"See <ulink url=\"http://planetmath.org/Nullity\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6527
msgid "<anchor id=\"gel-function-OrthogonalComplement\"/>OrthogonalComplement"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6529
#, no-wrap
msgid "OrthogonalComplement (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6530
msgid "Get the orthogonal complement of the columnspace."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6535
msgid "<anchor id=\"gel-function-PivotColumns\"/>PivotColumns"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6537
#, no-wrap
msgid "PivotColumns (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6538
msgid ""
"Return pivot columns of a matrix, that is columns that have a leading 1 in "
"row reduced form. Also returns the row where they occur."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6543
msgid "<anchor id=\"gel-function-Projection\"/>Projection"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6545
#, no-wrap
msgid "Projection (v,W,B...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6546
msgid ""
"Projection of vector <varname>v</varname> onto subspace <varname>W</varname> "
"with respect to inner product given by <varname>B</varname>. If <varname>B</"
"varname> is not given then the standard Hermitian product is used. "
"<varname>B</varname> can either be a sesquilinear function of two arguments "
"or it can be a matrix giving a sesquilinear form."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6556
msgid "<anchor id=\"gel-function-QRDecomposition\"/>QRDecomposition"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6558
#, no-wrap
msgid "QRDecomposition (A, Q)"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:6566
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>R = QRDecomposition(A,&amp;Q)</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6559
msgid ""
"Get the QR decomposition of a square matrix <varname>A</varname>, returns "
"the upper triangular matrix <varname>R</varname> and sets <varname>Q</"
"varname> to the orthogonal (unitary) matrix. <varname>Q</varname> should be "
"a reference or <constant>null</constant> if you don't want any return. For "
"example: <_:screen-1/> You will have the upper triangular matrix stored in a "
"variable called <varname>R</varname> and the orthogonal (unitary) matrix "
"stored in <varname>Q</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6573
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/QR_decomposition\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/QRDecomposition\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"QRDecomposition.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6583
msgid "<anchor id=\"gel-function-RayleighQuotient\"/>RayleighQuotient"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6585
#, no-wrap
msgid "RayleighQuotient (A,x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6586
msgid ""
"Return the Rayleigh quotient (also called the Rayleigh-Ritz quotient or "
"ratio) of a matrix and a vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6587
msgid ""
"See <ulink url=\"http://planetmath.org/RayleighQuotient\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6595
msgid ""
"<anchor id=\"gel-function-RayleighQuotientIteration\"/"
">RayleighQuotientIteration"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6597
#, no-wrap
msgid "RayleighQuotientIteration (A,x,epsilon,maxiter,vecref)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6598
msgid ""
"Find eigenvalues of <varname>A</varname> using the Rayleigh quotient "
"iteration method. <varname>x</varname> is a guess at a eigenvector and could "
"be random. It should have nonzero imaginary part if it will have any chance "
"at finding complex eigenvalues. The code will run at most <varname>maxiter</"
"varname> iterations and return <constant>null</constant> if we cannot get "
"within an error of <varname>epsilon</varname>. <varname>vecref</varname> "
"should either be <constant>null</constant> or a reference to a variable "
"where the eigenvector should be stored."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6608
msgid ""
"See <ulink url=\"http://planetmath.org/RayleighQuotient\">Planetmath</ulink> "
"for more information on Rayleigh quotient."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6616
msgid "<anchor id=\"gel-function-Rank\"/>Rank"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6618
#, no-wrap
msgid "Rank (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6619
msgid "Aliases: <function>rank</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6620
msgid "Get the rank of a matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6621
msgid ""
"See <ulink url=\"http://planetmath.org/SylvestersLaw\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6629
msgid "<anchor id=\"gel-function-RosserMatrix\"/>RosserMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6631
#, no-wrap
msgid "RosserMatrix ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6632
msgid ""
"Returns the Rosser matrix, which is a classic symmetric eigenvalue test "
"problem."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6637
msgid "<anchor id=\"gel-function-Rotation2D\"/>Rotation2D"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6639
#, no-wrap
msgid "Rotation2D (angle)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6640
msgid "Aliases: <function>RotationMatrix</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6641
msgid ""
"Return the matrix corresponding to rotation around origin in "
"R<superscript>2</superscript>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6646
msgid "<anchor id=\"gel-function-Rotation3DX\"/>Rotation3DX"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6648
#, no-wrap
msgid "Rotation3DX (angle)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6649
msgid ""
"Return the matrix corresponding to rotation around origin in "
"R<superscript>3</superscript> about the x-axis."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6654
msgid "<anchor id=\"gel-function-Rotation3DY\"/>Rotation3DY"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6656
#, no-wrap
msgid "Rotation3DY (angle)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6657
msgid ""
"Return the matrix corresponding to rotation around origin in "
"R<superscript>3</superscript> about the y-axis."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6662
msgid "<anchor id=\"gel-function-Rotation3DZ\"/>Rotation3DZ"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6664
#, no-wrap
msgid "Rotation3DZ (angle)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6665
msgid ""
"Return the matrix corresponding to rotation around origin in "
"R<superscript>3</superscript> about the z-axis."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6670
msgid "<anchor id=\"gel-function-RowSpace\"/>RowSpace"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6672
#, no-wrap
msgid "RowSpace (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6673
msgid "Get a basis matrix for the rowspace of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6678
msgid "<anchor id=\"gel-function-SesquilinearForm\"/>SesquilinearForm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6680
#, no-wrap
msgid "SesquilinearForm (v,A,w)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6681
msgid ""
"Evaluate (v,w) with respect to the sesquilinear form given by the matrix A."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6686
msgid ""
"<anchor id=\"gel-function-SesquilinearFormFunction\"/"
">SesquilinearFormFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6688
#, no-wrap
msgid "SesquilinearFormFunction (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6689
msgid ""
"Return a function that evaluates two vectors with respect to the "
"sesquilinear form given by A."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6694
msgid "<anchor id=\"gel-function-SmithNormalFormField\"/>SmithNormalFormField"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6696
#, no-wrap
msgid "SmithNormalFormField (A)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6697
msgid ""
"Returns the Smith normal form of a matrix over fields (will end up with 1's "
"on the diagonal)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6698 C/genius.xml:6710
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Smith_normal_form\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6706
msgid ""
"<anchor id=\"gel-function-SmithNormalFormInteger\"/>SmithNormalFormInteger"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6708
#, no-wrap
msgid "SmithNormalFormInteger (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6709
msgid "Return the Smith normal form for square integer matrices over integers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6718
msgid "<anchor id=\"gel-function-SolveLinearSystem\"/>SolveLinearSystem"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6720
#, no-wrap
msgid "SolveLinearSystem (M,V,args...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6721
msgid ""
"Solve linear system Mx=V, return solution V if there is a unique solution, "
"<constant>null</constant> otherwise. Extra two reference parameters can "
"optionally be used to get the reduced M and V."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6726
msgid "<anchor id=\"gel-function-ToeplitzMatrix\"/>ToeplitzMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6728
#, no-wrap
msgid "ToeplitzMatrix (c, r...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6729
msgid ""
"Return the Toeplitz matrix constructed given the first column c and "
"(optionally) the first row r. If only the column c is given then it is "
"conjugated and the nonconjugated version is used for the first row to give a "
"Hermitian matrix (if the first element is real)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6733
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Toeplitz_matrix\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/ToeplitzMatrix\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6742
msgid "<anchor id=\"gel-function-Trace\"/>Trace"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6744
#, no-wrap
msgid "Trace (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6745
msgid "Aliases: <function>trace</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6746
msgid ""
"Calculate the trace of a matrix. That is the sum of the diagonal elements."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6747
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Trace_(linear_algebra)"
"\">Wikipedia</ulink> or <ulink url=\"http://planetmath.org/"
"Trace\">Planetmath</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6756
msgid "<anchor id=\"gel-function-Transpose\"/>Transpose"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6758
#, no-wrap
msgid "Transpose (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6759
msgid ""
"Transpose of a matrix. This is the same as the <userinput>.'</userinput> "
"operator."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6761
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Transpose\">Wikipedia</ulink> "
"or <ulink url=\"http://planetmath.org/Transpose\">Planetmath</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6770
msgid "<anchor id=\"gel-function-VandermondeMatrix\"/>VandermondeMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6772
#, no-wrap
msgid "VandermondeMatrix (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6773
msgid "Aliases: <function>vander</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6774
msgid "Return the Vandermonde matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6775
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Vandermonde_matrix\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6783
msgid "<anchor id=\"gel-function-VectorAngle\"/>VectorAngle"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6785
#, no-wrap
msgid "VectorAngle (v,w,B...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6786
msgid ""
"The angle of two vectors with respect to inner product given by <varname>B</"
"varname>. If <varname>B</varname> is not given then the standard Hermitian "
"product is used. <varname>B</varname> can either be a sesquilinear function "
"of two arguments or it can be a matrix giving a sesquilinear form."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6795
msgid "<anchor id=\"gel-function-VectorSpaceDirectSum\"/>VectorSpaceDirectSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6797
#, no-wrap
msgid "VectorSpaceDirectSum (M,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6798
msgid "The direct sum of the vector spaces M and N."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6803
msgid ""
"<anchor id=\"gel-function-VectorSubspaceIntersection\"/"
">VectorSubspaceIntersection"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6805
#, no-wrap
msgid "VectorSubspaceIntersection (M,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6806
msgid "Intersection of the subspaces given by M and N."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6811
msgid "<anchor id=\"gel-function-VectorSubspaceSum\"/>VectorSubspaceSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6813
#, no-wrap
msgid "VectorSubspaceSum (M,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6814
msgid ""
"The sum of the vector spaces M and N, that is {w | w=m+n, m in M, n in N}."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6819
msgid "<anchor id=\"gel-function-adj\"/>adj"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6821
#, no-wrap
msgid "adj (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6822
msgid "Aliases: <function>Adjugate</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6823
msgid "Get the classical adjoint (adjugate) of a matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6828
msgid "<anchor id=\"gel-function-cref\"/>cref"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6830
#, no-wrap
msgid "cref (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6831
msgid ""
"Aliases: <function>CREF</function> <function>ColumnReducedEchelonForm</"
"function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6832
msgid "Compute the Column Reduced Echelon Form."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6837
msgid "<anchor id=\"gel-function-det\"/>det"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6839
#, no-wrap
msgid "det (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6840
msgid "Aliases: <function>Determinant</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6841
msgid "Get the determinant of a matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6842
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Determinant\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/Determinant2\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6851
msgid "<anchor id=\"gel-function-ref\"/>ref"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6853
#, no-wrap
msgid "ref (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6854
msgid "Aliases: <function>REF</function> <function>RowEchelonForm</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6855
msgid ""
"Get the row echelon form of a matrix. That is, apply gaussian elimination "
"but not backaddition to <varname>M</varname>. The pivot rows are divided to "
"make all pivots 1."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6858
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Row_echelon_form\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/RowEchelonForm\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6867
msgid "<anchor id=\"gel-function-rref\"/>rref"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6869
#, no-wrap
msgid "rref (M)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6870
msgid ""
"Aliases: <function>RREF</function> <function>ReducedRowEchelonForm</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6871
msgid ""
"Get the reduced row echelon form of a matrix. That is, apply gaussian "
"elimination together with backaddition to <varname>M</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6872
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Reduced_row_echelon_form\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/ReducedRowEchelonForm\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:6884
msgid "Combinatorics"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6887
msgid "<anchor id=\"gel-function-Catalan\"/>Catalan"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6889
#, no-wrap
msgid "Catalan (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6890
msgid "Get <varname>n</varname>th Catalan number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6891
msgid ""
"See <ulink url=\"http://planetmath.org/CatalanNumbers\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6899
msgid "<anchor id=\"gel-function-Combinations\"/>Combinations"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6901
#, no-wrap
msgid "Combinations (k,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6902
msgid ""
"Get all combinations of k numbers from 1 to n as a vector of vectors. (See "
"also <link linkend=\"gel-function-NextCombination\">NextCombination</link>)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6905 C/genius.xml:7103
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Combination\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6913
msgid "<anchor id=\"gel-function-DoubleFactorial\"/>DoubleFactorial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6915
#, no-wrap
msgid "DoubleFactorial (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6916
msgid "Double factorial: <userinput>n(n-2)(n-4)...</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6917
msgid ""
"See <ulink url=\"http://planetmath.org/DoubleFactorial\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6925
msgid "<anchor id=\"gel-function-Factorial\"/>Factorial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6927
#, no-wrap
msgid "Factorial (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6928
msgid "Factorial: <userinput>n(n-1)(n-2)...</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6929
msgid ""
"See <ulink url=\"http://planetmath.org/Factorial\">Planetmath</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6937
msgid "<anchor id=\"gel-function-FallingFactorial\"/>FallingFactorial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6939
#, no-wrap
msgid "FallingFactorial (n,k)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6940
msgid "Falling factorial: <userinput>(n)_k = n(n-1)...(n-(k-1))</userinput>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6941
msgid ""
"See <ulink url=\"http://planetmath.org/FallingFactorial\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6949
msgid "<anchor id=\"gel-function-Fibonacci\"/>Fibonacci"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6951
#, no-wrap
msgid "Fibonacci (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6952
msgid "Aliases: <function>fib</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6953
msgid ""
"Calculate <varname>n</varname>th Fibonacci number. That is the number "
"defined recursively by <userinput>Fibonacci(n) = Fibonacci(n-1) + "
"Fibonacci(n-2)</userinput> and <userinput>Fibonacci(1) = Fibonacci(2) = 1</"
"userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6960
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Fibonacci_number\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/FibonacciSequence\">Planetmath</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"FibonacciNumber.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6970
msgid "<anchor id=\"gel-function-FrobeniusNumber\"/>FrobeniusNumber"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6972
#, no-wrap
msgid "FrobeniusNumber (v,arg...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6973
msgid ""
"Calculate the Frobenius number. That is calculate largest number that cannot "
"be given as a non-negative integer linear combination of a given vector of "
"non-negative integers. The vector can be given as separate numbers or a "
"single vector. All the numbers given should have GCD of 1."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6980
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Coin_problem\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"FrobeniusNumber.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6989
msgid "<anchor id=\"gel-function-GaloisMatrix\"/>GaloisMatrix"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6991
#, no-wrap
msgid "GaloisMatrix (combining_rule)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:6992
msgid ""
"Galois matrix given a linear combining rule (a_1*x_1+...+a_n*x_n=x_(n+1))."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:6997
msgid "<anchor id=\"gel-function-GreedyAlgorithm\"/>GreedyAlgorithm"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:6999
#, no-wrap
msgid "GreedyAlgorithm (n,v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7000
msgid ""
"Find the vector <varname>c</varname> of non-negative integers such that "
"taking the dot product with <varname>v</varname> is equal to n. If not "
"possible returns <constant>null</constant>. <varname>v</varname> should be "
"given sorted in increasing order and should consist of non-negative integers."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7007
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Greedy_algorithm\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"GreedyAlgorithm.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7016
msgid "<anchor id=\"gel-function-HarmonicNumber\"/>HarmonicNumber"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7018
#, no-wrap
msgid "HarmonicNumber (n,r)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7019
msgid "Aliases: <function>HarmonicH</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7020
msgid ""
"Harmonic Number, the <varname>n</varname>th harmonic number of order "
"<varname>r</varname>. That is, it is the sum of <userinput>1/k^r</userinput> "
"for <varname>k</varname> from 1 to n. Equivalent to <userinput>sum k = 1 to "
"n do 1/k^r</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7023
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Harmonic_number\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7031
msgid "<anchor id=\"gel-function-Hofstadter\"/>Hofstadter"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7033
#, no-wrap
msgid "Hofstadter (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7034
msgid ""
"Hofstadter's function q(n) defined by q(1)=1, q(2)=1, q(n)=q(n-q(n-1))+q(n-"
"q(n-2))."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7035
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Hofstadter_sequence\">Wikipedia</ulink> for more information. The sequence "
"is <ulink url=\"https://oeis.org/A005185\">A005185 in OEIS</ulink>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7044
msgid ""
"<anchor id=\"gel-function-LinearRecursiveSequence\"/>LinearRecursiveSequence"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7046
#, no-wrap
msgid "LinearRecursiveSequence (seed_values,combining_rule,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7047
msgid "Compute linear recursive sequence using Galois stepping."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7052
msgid "<anchor id=\"gel-function-Multinomial\"/>Multinomial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7054
#, no-wrap
msgid "Multinomial (v,arg...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7055
msgid ""
"Calculate multinomial coefficients. Takes a vector of <varname>k</varname> "
"non-negative integers and computes the multinomial coefficient. This "
"corresponds to the coefficient in the homogeneous polynomial in <varname>k</"
"varname> variables with the corresponding powers."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:7064
#, no-wrap
msgid "(a+b+c)! / (a!b!c!)\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7061
msgid ""
"The formula for <userinput>Multinomial(a,b,c)</userinput> can be written as: "
"<_:programlisting-1/> In other words, if we would have only two elements, "
"then <userinput>Multinomial(a,b)</userinput> is the same thing as "
"<userinput>Binomial(a+b,a)</userinput> or <userinput>Binomial(a+b,b)</"
"userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7071
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Multinomial_theorem\">Wikipedia</ulink>, <ulink url=\"http://planetmath.org/"
"MultinomialTheorem\">Planetmath</ulink>, or <ulink url=\"http://"
"mathworld.wolfram.com/MultinomialCoefficient.html\">Mathworld</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7081
msgid "<anchor id=\"gel-function-NextCombination\"/>NextCombination"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7083
#, no-wrap
msgid "NextCombination (v,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7084
msgid ""
"Get combination that would come after v in call to combinations, first "
"combination should be <userinput>[1:k]</userinput>. This function is useful "
"if you have many combinations to go through and you don't want to waste "
"memory to store them all."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:7091
#, no-wrap
msgid ""
"<userinput>for n in Combinations (4,6) do (\n"
"  SomeFunction (n)\n"
");</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:7096
#, no-wrap
msgid ""
"<userinput>n:=[1:4];\n"
"do (\n"
"  SomeFunction (n)\n"
") while not IsNull(n:=NextCombination(n,6));</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7089
msgid ""
"For example with Combinations you would normally write a loop like: "
"<_:screen-1/> But with NextCombination you would write something like: "
"<_:screen-2/> See also <link linkend=\"gel-function-"
"Combinations\">Combinations</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7111
msgid "<anchor id=\"gel-function-Pascal\"/>Pascal"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7113
#, no-wrap
msgid "Pascal (i)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7114
msgid ""
"Get the Pascal's triangle as a matrix. This will return an <varname>i</"
"varname>+1 by <varname>i</varname>+1 lower diagonal matrix that is the "
"Pascal's triangle after <varname>i</varname> iterations."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7118
msgid ""
"See <ulink url=\"http://planetmath.org/PascalsTriangle\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7126
msgid "<anchor id=\"gel-function-Permutations\"/>Permutations"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7128
#, no-wrap
msgid "Permutations (k,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7129
msgid ""
"Get all permutations of <varname>k</varname> numbers from 1 to <varname>n</"
"varname> as a vector of vectors."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7130 C/genius.xml:7219
msgid ""
"See <ulink url=\"http://mathworld.wolfram.com/Permutation.html\">Mathworld</"
"ulink> or <ulink url=\"https://en.wikipedia.org/wiki/"
"Permutation\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7139
msgid "<anchor id=\"gel-function-RisingFactorial\"/>RisingFactorial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7141
#, no-wrap
msgid "RisingFactorial (n,k)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7142
msgid "Aliases: <function>Pochhammer</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7143
msgid "(Pochhammer) Rising factorial: (n)_k = n(n+1)...(n+(k-1))."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7144
msgid ""
"See <ulink url=\"http://planetmath.org/RisingFactorial\">Planetmath</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7152
msgid "<anchor id=\"gel-function-StirlingNumberFirst\"/>StirlingNumberFirst"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7154
#, no-wrap
msgid "StirlingNumberFirst (n,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7155
msgid "Aliases: <function>StirlingS1</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7156
msgid "Stirling number of the first kind."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7157
msgid ""
"See <ulink url=\"http://planetmath.org/"
"StirlingNumbersOfTheFirstKind\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/StirlingNumberoftheFirstKind.html\">Mathworld</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7166
msgid "<anchor id=\"gel-function-StirlingNumberSecond\"/>StirlingNumberSecond"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7168
#, no-wrap
msgid "StirlingNumberSecond (n,m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7169
msgid "Aliases: <function>StirlingS2</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7170
msgid "Stirling number of the second kind."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7171
msgid ""
"See <ulink url=\"http://planetmath.org/"
"StirlingNumbersSecondKind\">Planetmath</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/StirlingNumberoftheSecondKind.html\">Mathworld</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7180
msgid "<anchor id=\"gel-function-Subfactorial\"/>Subfactorial"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7182
#, no-wrap
msgid "Subfactorial (n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7183
msgid "Subfactorial: n! times sum_{k=0}^n (-1)^k/k!."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7188
msgid "<anchor id=\"gel-function-Triangular\"/>Triangular"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7190
#, no-wrap
msgid "Triangular (nth)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7191
msgid "Calculate the <varname>n</varname>th triangular number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7192
msgid ""
"See <ulink url=\"http://planetmath.org/TriangularNumbers\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7200
msgid "<anchor id=\"gel-function-nCr\"/>nCr"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7202
#, no-wrap
msgid "nCr (n,r)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7203
msgid "Aliases: <function>Binomial</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7204
msgid ""
"Calculate combinations, that is, the binomial coefficient. <varname>n</"
"varname> can be any real number."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7206
msgid ""
"See <ulink url=\"http://planetmath.org/Choose\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7214
msgid "<anchor id=\"gel-function-nPr\"/>nPr"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7216
#, no-wrap
msgid "nPr (n,r)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7217
msgid ""
"Calculate the number of permutations of size <varname>r</varname> of numbers "
"from 1 to <varname>n</varname>."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:7231
msgid "Calculus"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7234
msgid ""
"<anchor id=\"gel-function-CompositeSimpsonsRule\"/>CompositeSimpsonsRule"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7236
#, no-wrap
msgid "CompositeSimpsonsRule (f,a,b,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7237
msgid ""
"Integration of f by Composite Simpson's Rule on the interval [a,b] with n "
"subintervals with error of max(f'''')*h^4*(b-a)/180, note that n should be "
"even."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7238 C/genius.xml:7250
msgid ""
"See <ulink url=\"http://planetmath.org/SimpsonsRule\">Planetmath</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7246
msgid ""
"<anchor id=\"gel-function-CompositeSimpsonsRuleTolerance\"/"
">CompositeSimpsonsRuleTolerance"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7248
#, no-wrap
msgid "CompositeSimpsonsRuleTolerance (f,a,b,FourthDerivativeBound,Tolerance)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7249
msgid ""
"Integration of f by Composite Simpson's Rule on the interval [a,b] with the "
"number of steps calculated by the fourth derivative bound and the desired "
"tolerance."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7258
msgid "<anchor id=\"gel-function-Derivative\"/>Derivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7260
#, no-wrap
msgid "Derivative (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7261
msgid ""
"Attempt to calculate derivative by trying first symbolically and then "
"numerically."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7262 C/genius.xml:7394 C/genius.xml:8808 C/genius.xml:8822
#: C/genius.xml:8836 C/genius.xml:8850
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Derivative\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7270
msgid ""
"<anchor id=\"gel-function-EvenPeriodicExtension\"/>EvenPeriodicExtension"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7272
#, no-wrap
msgid "EvenPeriodicExtension (f,L)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7273
msgid ""
"Return a function that is the even periodic extension of <function>f</"
"function> with half period <varname>L</varname>. That is a function defined "
"on the interval <userinput>[0,L]</userinput> extended to be even on "
"<userinput>[-L,L]</userinput> and then extended to be periodic with period "
"<userinput>2*L</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7278
msgid ""
"See also <link linkend=\"gel-function-"
"OddPeriodicExtension\">OddPeriodicExtension</link> and <link linkend=\"gel-"
"function-PeriodicExtension\">PeriodicExtension</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7289
msgid ""
"<anchor id=\"gel-function-FourierSeriesFunction\"/>FourierSeriesFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7291
#, no-wrap
msgid "FourierSeriesFunction (a,b,L)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7292
msgid ""
"Return a function that is a Fourier series with the coefficients given by "
"the vectors <varname>a</varname> (sines) and <varname>b</varname> (cosines). "
"Note that <userinput>a@(1)</userinput> is the constant coefficient! That is, "
"<userinput>a@(n)</userinput> refers to the term <userinput>cos(x*(n-1)*pi/"
"L)</userinput>, while <userinput>b@(n)</userinput> refers to the term "
"<userinput>sin(x*n*pi/L)</userinput>. Either <varname>a</varname> or "
"<varname>b</varname> can be <constant>null</constant>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7300 C/genius.xml:7414 C/genius.xml:7434
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"FourierSeries.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7309
msgid "<anchor id=\"gel-function-InfiniteProduct\"/>InfiniteProduct"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7311
#, no-wrap
msgid "InfiniteProduct (func,start,inc)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7312
msgid "Try to calculate an infinite product for a single parameter function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7317
msgid "<anchor id=\"gel-function-InfiniteProduct2\"/>InfiniteProduct2"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7319
#, no-wrap
msgid "InfiniteProduct2 (func,arg,start,inc)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7320
msgid ""
"Try to calculate an infinite product for a double parameter function with "
"func(arg,n)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7325
msgid "<anchor id=\"gel-function-InfiniteSum\"/>InfiniteSum"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7327
#, no-wrap
msgid "InfiniteSum (func,start,inc)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7328
msgid "Try to calculate an infinite sum for a single parameter function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7333
msgid "<anchor id=\"gel-function-InfiniteSum2\"/>InfiniteSum2"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7335
#, no-wrap
msgid "InfiniteSum2 (func,arg,start,inc)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7336
msgid ""
"Try to calculate an infinite sum for a double parameter function with "
"func(arg,n)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7341
msgid "<anchor id=\"gel-function-IsContinuous\"/>IsContinuous"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7343
#, no-wrap
msgid "IsContinuous (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7344
msgid ""
"Try and see if a real-valued function is continuous at x0 by calculating the "
"limit there."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7349
msgid "<anchor id=\"gel-function-IsDifferentiable\"/>IsDifferentiable"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7351
#, no-wrap
msgid "IsDifferentiable (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7352
msgid ""
"Test for differentiability by approximating the left and right limits and "
"comparing."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7357
msgid "<anchor id=\"gel-function-LeftHandRule\"/>LeftHandRule"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7359
#, no-wrap
msgid "LeftHandRule (f,a,b,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7360
msgid ""
"Integration by left hand rule on the interval [a,b] with n subintervals."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7365
msgid "<anchor id=\"gel-function-LeftLimit\"/>LeftLimit"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7367
#, no-wrap
msgid "LeftLimit (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7368
msgid "Calculate the left limit of a real-valued function at x0."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7373
msgid "<anchor id=\"gel-function-Limit\"/>Limit"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7375
#, no-wrap
msgid "Limit (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7376
msgid ""
"Calculate the limit of a real-valued function at x0. Tries to calculate both "
"left and right limits."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7381
msgid "<anchor id=\"gel-function-MidpointRule\"/>MidpointRule"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7383
#, no-wrap
msgid "MidpointRule (f,a,b,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7384
msgid "Integration by midpoint rule on the interval [a,b] with n subintervals."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7389
msgid "<anchor id=\"gel-function-NumericalDerivative\"/>NumericalDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7391
#, no-wrap
msgid "NumericalDerivative (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7392
msgid "Aliases: <function>NDerivative</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7393
msgid "Attempt to calculate numerical derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7402
msgid ""
"<anchor id=\"gel-function-NumericalFourierSeriesCoefficients\"/"
">NumericalFourierSeriesCoefficients"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7404
#, no-wrap
msgid "NumericalFourierSeriesCoefficients (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7405
msgid ""
"Return a vector of vectors <userinput>[a,b]</userinput> where <varname>a</"
"varname> are the cosine coefficients and <varname>b</varname> are the sine "
"coefficients of the Fourier series of <function>f</function> with half-"
"period <varname>L</varname> (that is defined on <userinput>[-L,L]</"
"userinput> and extended periodically) with coefficients up to <varname>N</"
"varname>th harmonic computed numerically. The coefficients are computed by "
"numerical integration using <link linkend=\"gel-function-"
"NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7424
msgid ""
"<anchor id=\"gel-function-NumericalFourierSeriesFunction\"/"
">NumericalFourierSeriesFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7426
#, no-wrap
msgid "NumericalFourierSeriesFunction (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7427
msgid ""
"Return a function that is the Fourier series of <function>f</function> with "
"half-period <varname>L</varname> (that is defined on <userinput>[-L,L]</"
"userinput> and extended periodically) with coefficients up to <varname>N</"
"varname>th harmonic computed numerically. This is the trigonometric real "
"series composed of sines and cosines. The coefficients are computed by "
"numerical integration using <link linkend=\"gel-function-"
"NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7444
msgid ""
"<anchor id=\"gel-function-NumericalFourierCosineSeriesCoefficients\"/"
">NumericalFourierCosineSeriesCoefficients"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7446
#, no-wrap
msgid "NumericalFourierCosineSeriesCoefficients (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7447
msgid ""
"Return a vector of coefficients of the cosine Fourier series of <function>f</"
"function> with half-period <varname>L</varname>. That is, we take "
"<function>f</function> defined on <userinput>[0,L]</userinput> take the even "
"periodic extension and compute the Fourier series, which only has cosine "
"terms. The series is computed up to the <varname>N</varname>th harmonic. The "
"coefficients are computed by numerical integration using <link linkend=\"gel-"
"function-NumericalIntegral\"><function>NumericalIntegral</function></link>. "
"Note that <userinput>a@(1)</userinput> is the constant coefficient! That is, "
"<userinput>a@(n)</userinput> refers to the term <userinput>cos(x*(n-1)*pi/"
"L)</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7459 C/genius.xml:7480
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"FourierCosineSeries.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7469
msgid ""
"<anchor id=\"gel-function-NumericalFourierCosineSeriesFunction\"/"
">NumericalFourierCosineSeriesFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7471
#, no-wrap
msgid "NumericalFourierCosineSeriesFunction (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7472
msgid ""
"Return a function that is the cosine Fourier series of <function>f</"
"function> with half-period <varname>L</varname>. That is, we take "
"<function>f</function> defined on <userinput>[0,L]</userinput> take the even "
"periodic extension and compute the Fourier series, which only has cosine "
"terms. The series is computed up to the <varname>N</varname>th harmonic. The "
"coefficients are computed by numerical integration using <link linkend=\"gel-"
"function-NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7490
msgid ""
"<anchor id=\"gel-function-NumericalFourierSineSeriesCoefficients\"/"
">NumericalFourierSineSeriesCoefficients"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7492
#, no-wrap
msgid "NumericalFourierSineSeriesCoefficients (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7493
msgid ""
"Return a vector of coefficients of the sine Fourier series of <function>f</"
"function> with half-period <varname>L</varname>. That is, we take "
"<function>f</function> defined on <userinput>[0,L]</userinput> take the odd "
"periodic extension and compute the Fourier series, which only has sine "
"terms. The series is computed up to the <varname>N</varname>th harmonic. The "
"coefficients are computed by numerical integration using <link linkend=\"gel-"
"function-NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7502 C/genius.xml:7523
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Fourier_series\">Wikipedia</"
"ulink> or <ulink url=\"http://mathworld.wolfram.com/"
"FourierSineSeries.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7512
msgid ""
"<anchor id=\"gel-function-NumericalFourierSineSeriesFunction\"/"
">NumericalFourierSineSeriesFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7514
#, no-wrap
msgid "NumericalFourierSineSeriesFunction (f,L,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7515
msgid ""
"Return a function that is the sine Fourier series of <function>f</function> "
"with half-period <varname>L</varname>. That is, we take <function>f</"
"function> defined on <userinput>[0,L]</userinput> take the odd periodic "
"extension and compute the Fourier series, which only has sine terms. The "
"series is computed up to the <varname>N</varname>th harmonic. The "
"coefficients are computed by numerical integration using <link linkend=\"gel-"
"function-NumericalIntegral\"><function>NumericalIntegral</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7533
msgid "<anchor id=\"gel-function-NumericalIntegral\"/>NumericalIntegral"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7535
#, no-wrap
msgid "NumericalIntegral (f,a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7536
msgid ""
"Integration by rule set in NumericalIntegralFunction of f from a to b using "
"NumericalIntegralSteps steps. By default NumericalIntegralFunction is the "
"CompositeSimpsonsRule."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7542
msgid ""
"<anchor id=\"gel-function-NumericalLeftDerivative\"/>NumericalLeftDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7544
#, no-wrap
msgid "NumericalLeftDerivative (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7545
msgid "Attempt to calculate numerical left derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7550
msgid ""
"<anchor id=\"gel-function-NumericalLimitAtInfinity\"/"
">NumericalLimitAtInfinity"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7552
#, no-wrap
msgid "NumericalLimitAtInfinity (_f,step_fun,tolerance,successive_for_success,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7553
msgid "Attempt to calculate the limit of f(step_fun(i)) as i goes from 1 to N."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7558
msgid ""
"<anchor id=\"gel-function-NumericalRightDerivative\"/"
">NumericalRightDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7560
#, no-wrap
msgid "NumericalRightDerivative (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7561
msgid "Attempt to calculate numerical right derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7566
msgid "<anchor id=\"gel-function-OddPeriodicExtension\"/>OddPeriodicExtension"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7568
#, no-wrap
msgid "OddPeriodicExtension (f,L)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7569
msgid ""
"Return a function that is the odd periodic extension of <function>f</"
"function> with half period <varname>L</varname>. That is a function defined "
"on the interval <userinput>[0,L]</userinput> extended to be odd on "
"<userinput>[-L,L]</userinput> and then extended to be periodic with period "
"<userinput>2*L</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7574
msgid ""
"See also <link linkend=\"gel-function-"
"EvenPeriodicExtension\">EvenPeriodicExtension</link> and <link linkend=\"gel-"
"function-PeriodicExtension\">PeriodicExtension</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7585
msgid ""
"<anchor id=\"gel-function-OneSidedFivePointFormula\"/"
">OneSidedFivePointFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7587
#, no-wrap
msgid "OneSidedFivePointFormula (f,x0,h)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7588
msgid "Compute one-sided derivative using five point formula."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7593
msgid ""
"<anchor id=\"gel-function-OneSidedThreePointFormula\"/"
">OneSidedThreePointFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7595
#, no-wrap
msgid "OneSidedThreePointFormula (f,x0,h)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7596
msgid "Compute one-sided derivative using three-point formula."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7601
msgid "<anchor id=\"gel-function-PeriodicExtension\"/>PeriodicExtension"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7603
#, no-wrap
msgid "PeriodicExtension (f,a,b)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7604
msgid ""
"Return a function that is the periodic extension of <function>f</function> "
"defined on the interval <userinput>[a,b]</userinput> and has period "
"<userinput>b-a</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7607
msgid ""
"See also <link linkend=\"gel-function-"
"OddPeriodicExtension\">OddPeriodicExtension</link> and <link linkend=\"gel-"
"function-EvenPeriodicExtension\">EvenPeriodicExtension</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7618
msgid "<anchor id=\"gel-function-RightHandRule\"/>RightHandRule"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7620
#, no-wrap
msgid "RightHandRule (f,a,b,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7621
msgid ""
"Integration by right hand rule on the interval [a,b] with n subintervals."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7626
msgid "<anchor id=\"gel-function-RightLimit\"/>RightLimit"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7628
#, no-wrap
msgid "RightLimit (f,x0)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7629
msgid "Calculate the right limit of a real-valued function at x0."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7634
msgid "<anchor id=\"gel-function-TrapezoidRule\"/>TrapezoidRule"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7636
#, no-wrap
msgid "TrapezoidRule (f,a,b,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7637
msgid ""
"Integration by trapezoid rule on the interval [a,b] with n subintervals."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7642
msgid ""
"<anchor id=\"gel-function-TwoSidedFivePointFormula\"/"
">TwoSidedFivePointFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7644
#, no-wrap
msgid "TwoSidedFivePointFormula (f,x0,h)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7645
msgid "Compute two-sided derivative using five-point formula."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7650
msgid ""
"<anchor id=\"gel-function-TwoSidedThreePointFormula\"/"
">TwoSidedThreePointFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7652
#, no-wrap
msgid "TwoSidedThreePointFormula (f,x0,h)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7653
msgid "Compute two-sided derivative using three-point formula."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:7661
msgid "Functions"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7664
msgid "<anchor id=\"gel-function-Argument\"/>Argument"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7666
#, no-wrap
msgid "Argument (z)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7667
msgid "Aliases: <function>Arg</function> <function>arg</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7668
msgid "argument (angle) of complex number."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7673
msgid "<anchor id=\"gel-function-BesselJ0\"/>BesselJ0"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7675
#, no-wrap
msgid "BesselJ0 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7676
msgid ""
"Bessel function of the first kind of order 0. Only implemented for real "
"numbers."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7677 C/genius.xml:7690 C/genius.xml:7703 C/genius.xml:7716
#: C/genius.xml:7729 C/genius.xml:7742
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Bessel_functions\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7686
msgid "<anchor id=\"gel-function-BesselJ1\"/>BesselJ1"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7688
#, no-wrap
msgid "BesselJ1 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7689
msgid ""
"Bessel function of the first kind of order 1. Only implemented for real "
"numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7699
msgid "<anchor id=\"gel-function-BesselJn\"/>BesselJn"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7701
#, no-wrap
msgid "BesselJn (n,x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7702
msgid ""
"Bessel function of the first kind of order <varname>n</varname>. Only "
"implemented for real numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7712
msgid "<anchor id=\"gel-function-BesselY0\"/>BesselY0"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7714
#, no-wrap
msgid "BesselY0 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7715
msgid ""
"Bessel function of the second kind of order 0. Only implemented for real "
"numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7725
msgid "<anchor id=\"gel-function-BesselY1\"/>BesselY1"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7727
#, no-wrap
msgid "BesselY1 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7728
msgid ""
"Bessel function of the second kind of order 1. Only implemented for real "
"numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7738
msgid "<anchor id=\"gel-function-BesselYn\"/>BesselYn"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7740
#, no-wrap
msgid "BesselYn (n,x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7741
msgid ""
"Bessel function of the second kind of order <varname>n</varname>. Only "
"implemented for real numbers."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7751
msgid "<anchor id=\"gel-function-DirichletKernel\"/>DirichletKernel"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7753
#, no-wrap
msgid "DirichletKernel (n,t)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7754
msgid "Dirichlet kernel of order <varname>n</varname>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7759
msgid "<anchor id=\"gel-function-DiscreteDelta\"/>DiscreteDelta"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7761
#, no-wrap
msgid "DiscreteDelta (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7762
msgid "Returns 1 if and only if all elements are zero."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7767
msgid "<anchor id=\"gel-function-ErrorFunction\"/>ErrorFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7769
#, no-wrap
msgid "ErrorFunction (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7770
msgid "Aliases: <function>erf</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7771
msgid "The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7772
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Error_function\">Wikipedia</"
"ulink> or <ulink url=\"http://planetmath.org/ErrorFunction\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7781
msgid "<anchor id=\"gel-function-FejerKernel\"/>FejerKernel"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7783
#, no-wrap
msgid "FejerKernel (n,t)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7784
msgid ""
"Fejer kernel of order <varname>n</varname> evaluated at <varname>t</varname>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7786
msgid ""
"See <ulink url=\"http://planetmath.org/FejerKernel\">Planetmath</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7794
msgid "<anchor id=\"gel-function-GammaFunction\"/>GammaFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7796
#, no-wrap
msgid "GammaFunction (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7797
msgid "Aliases: <function>Gamma</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7798
msgid "The Gamma function. Currently only implemented for real values."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7799
msgid ""
"See <ulink url=\"http://planetmath.org/GammaFunction\">Planetmath</ulink> or "
"<ulink url=\"https://en.wikipedia.org/wiki/Gamma_function\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7808
msgid "<anchor id=\"gel-function-KroneckerDelta\"/>KroneckerDelta"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7810
#, no-wrap
msgid "KroneckerDelta (v)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7811
msgid "Returns 1 if and only if all elements are equal."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7816
msgid "<anchor id=\"gel-function-LambertW\"/>LambertW"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7818
#, no-wrap
msgid "LambertW (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7819
msgid ""
"The principal branch of Lambert W function computed for only real values "
"greater than or equal to <userinput>-1/e</userinput>. That is, "
"<function>LambertW</function> is the inverse of the expression "
"<userinput>x*e^x</userinput>. Even for real <varname>x</varname> this "
"expression is not one to one and therefore has two branches over "
"<userinput>[-1/e,0)</userinput>. See <link linkend=\"gel-function-"
"LambertWm1\"><function>LambertWm1</function></link> for the other real "
"branch."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7828 C/genius.xml:7848
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Lambert_W_function\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7837
msgid "<anchor id=\"gel-function-LambertWm1\"/>LambertWm1"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7839
#, no-wrap
msgid "LambertWm1 (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7840
msgid ""
"The minus-one branch of Lambert W function computed for only real values "
"greater than or equal to <userinput>-1/e</userinput> and less than 0. That "
"is, <function>LambertWm1</function> is the second branch of the inverse of "
"<userinput>x*e^x</userinput>. See <link linkend=\"gel-function-"
"LambertW\"><function>LambertW</function></link> for the principal branch."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7856
msgid "<anchor id=\"gel-function-MinimizeFunction\"/>MinimizeFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7858
#, no-wrap
msgid "MinimizeFunction (func,x,incr)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7859
msgid "Find the first value where f(x)=0."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7864
msgid "<anchor id=\"gel-function-MoebiusDiskMapping\"/>MoebiusDiskMapping"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7866
#, no-wrap
msgid "MoebiusDiskMapping (a,z)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7867
msgid "Moebius mapping of the disk to itself mapping a to 0."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7868 C/genius.xml:7881 C/genius.xml:7894 C/genius.xml:7907
#: C/genius.xml:7920
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"M%C3%B6bius_transformation\">Wikipedia</ulink> or <ulink url=\"http://"
"planetmath.org/MobiusTransformation\">Planetmath</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7877
msgid "<anchor id=\"gel-function-MoebiusMapping\"/>MoebiusMapping"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7879
#, no-wrap
msgid "MoebiusMapping (z,z2,z3,z4)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7880
msgid ""
"Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity "
"respectively."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7890
msgid ""
"<anchor id=\"gel-function-MoebiusMappingInftyToInfty\"/"
">MoebiusMappingInftyToInfty"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7892
#, no-wrap
msgid "MoebiusMappingInftyToInfty (z,z2,z3)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7893
msgid ""
"Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 "
"to 1 and 0 respectively."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7903
msgid ""
"<anchor id=\"gel-function-MoebiusMappingInftyToOne\"/"
">MoebiusMappingInftyToOne"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7905
#, no-wrap
msgid "MoebiusMappingInftyToOne (z,z3,z4)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7906
msgid ""
"Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 "
"and infinity respectively."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7916
msgid ""
"<anchor id=\"gel-function-MoebiusMappingInftyToZero\"/"
">MoebiusMappingInftyToZero"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7918
#, no-wrap
msgid "MoebiusMappingInftyToZero (z,z2,z4)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7919
msgid ""
"Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 "
"and infinity respectively."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7929
msgid "<anchor id=\"gel-function-PoissonKernel\"/>PoissonKernel"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7931
#, no-wrap
msgid "PoissonKernel (r,sigma)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7932
msgid ""
"Poisson kernel on D(0,1) (not normalized to 1, that is integral of this is "
"2pi)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7937
msgid "<anchor id=\"gel-function-PoissonKernelRadius\"/>PoissonKernelRadius"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7939
#, no-wrap
msgid "PoissonKernelRadius (r,sigma)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7940
msgid "Poisson kernel on D(0,R) (not normalized to 1)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7945
msgid "<anchor id=\"gel-function-RiemannZeta\"/>RiemannZeta"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7947
#, no-wrap
msgid "RiemannZeta (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7948
msgid "Aliases: <function>zeta</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7949
msgid "The Riemann zeta function. Currently only implemented for real values."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7950
msgid ""
"See <ulink url=\"http://planetmath.org/RiemannZetaFunction\">Planetmath</"
"ulink> or <ulink url=\"https://en.wikipedia.org/wiki/"
"Riemann_zeta_function\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7959
msgid "<anchor id=\"gel-function-UnitStep\"/>UnitStep"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7961
#, no-wrap
msgid "UnitStep (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7962
msgid ""
"The unit step function is 0 for x&lt;0, 1 otherwise. This is the integral of "
"the Dirac Delta function. Also called the Heaviside function."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7963
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Unit_step\">Wikipedia</ulink> "
"for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7971
msgid "<anchor id=\"gel-function-cis\"/>cis"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7973
#, no-wrap
msgid "cis (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7974
msgid ""
"The <function>cis</function> function, that is the same as <userinput>cos(x)"
"+1i*sin(x)</userinput>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7982
msgid "<anchor id=\"gel-function-deg2rad\"/>deg2rad"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7984
#, no-wrap
msgid "deg2rad (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7985
msgid "Convert degrees to radians."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7990
msgid "<anchor id=\"gel-function-rad2deg\"/>rad2deg"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:7992
#, no-wrap
msgid "rad2deg (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:7993
msgid "Convert radians to degrees."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:7998
msgid "<anchor id=\"gel-function-sinc\"/>sinc"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8000
#, no-wrap
msgid "sinc (x)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8001
msgid ""
"Calculates the unnormalized sinc function, that is <userinput>sin(x)/x</"
"userinput>. If you want the normalized function call <userinput>sinc(pi*x)</"
"userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8004
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Sinc\">Wikipedia</ulink> for "
"more information."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8016
msgid "Equation Solving"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8020
msgid "<anchor id=\"gel-function-CubicFormula\"/>CubicFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8022
#, no-wrap
msgid "CubicFormula (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8023
msgid ""
"Compute roots of a cubic (degree 3) polynomial using the cubic formula. The "
"polynomial should be given as a vector of coefficients. That is "
"<userinput>4*x^3 + 2*x + 1</userinput> corresponds to the vector "
"<userinput>[1,2,0,4]</userinput>. Returns a column vector of the three "
"solutions. The first solution is always the real one as a cubic always has "
"one real solution."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8032
msgid ""
"See <ulink url=\"http://planetmath.org/CubicFormula\">Planetmath</ulink>, "
"<ulink url=\"http://mathworld.wolfram.com/CubicFormula.html\">Mathworld</"
"ulink>, or <ulink url=\"https://en.wikipedia.org/wiki/"
"Cubic_equation\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8042
msgid "<anchor id=\"gel-function-EulersMethod\"/>EulersMethod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8044
#, no-wrap
msgid "EulersMethod (f,x0,y0,x1,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8045
msgid ""
"Use classical Euler's method to numerically solve y'=f(x,y) for initial "
"<varname>x0</varname>, <varname>y0</varname> going to <varname>x1</varname> "
"with <varname>n</varname> increments, returns <varname>y</varname> at "
"<varname>x1</varname>. Unless you explicitly want to use Euler's method, you "
"should really think about using <link linkend=\"gel-function-"
"RungeKutta\">RungeKutta</link> for solving ODE."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8055 C/genius.xml:8096 C/genius.xml:8301 C/genius.xml:8339
msgid ""
"Systems can be solved by just having <varname>y</varname> be a (column) "
"vector everywhere. That is, <varname>y0</varname> can be a vector in which "
"case <varname>f</varname> should take a number <varname>x</varname> and a "
"vector of the same size for the second argument and should return a vector "
"of the same size."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8062 C/genius.xml:8118
msgid ""
"See <ulink url=\"http://mathworld.wolfram.com/"
"EulerForwardMethod.html\">Mathworld</ulink> or <ulink url=\"https://"
"en.wikipedia.org/wiki/Eulers_method\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8071
msgid "<anchor id=\"gel-function-EulersMethodFull\"/>EulersMethodFull"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8073
#, no-wrap
msgid "EulersMethodFull (f,x0,y0,x1,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8074
msgid ""
"Use classical Euler's method to numerically solve y'=f(x,y) for initial "
"<varname>x0</varname>, <varname>y0</varname> going to <varname>x1</varname> "
"with <varname>n</varname> increments, returns an <userinput>n+1</userinput> "
"by 2 matrix with the <varname>x</varname> and <varname>y</varname> values. "
"Unless you explicitly want to use Euler's method, you should really think "
"about using <link linkend=\"gel-function-RungeKuttaFull\">RungeKuttaFull</"
"link> for solving ODE. Suitable for plugging into <link linkend=\"gel-"
"function-LinePlotDrawLine\">LinePlotDrawLine</link> or <link linkend=\"gel-"
"function-LinePlotDrawPoints\">LinePlotDrawPoints</link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8091
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotClear();</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>line = EulersMethodFull(`(x,y)=y,0,1.0,3.0,50);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(line,\"window\",\"fit\",\"color\",\"blue\",\"legend\",\"Exponential growth\");</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8089 C/genius.xml:8332 C/genius.xml:8715 C/genius.xml:8755
msgid "Example: <_:screen-1/>"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8108
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotClear();</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>lines = EulersMethodFull(`(x,y)=[y@(2),-y@(1)],0,[1.0,1.0],10.0,500);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>lines = ExpandMatrix(lines);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>firstline = lines@(,[1,2]);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>secondline = lines@(,[1,3]);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotWindow = [0,10,-2,2];</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(firstline,\"color\",\"blue\",\"legend\",\"First\");</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints(secondline,\"color\",\"red\",\"thickness\",3,\"legend\",\"Second\");</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8103 C/genius.xml:8346
msgid ""
"The output for a system is still a n by 2 matrix with the second entry being "
"a vector. If you wish to plot the line, make sure to use row vectors, and "
"then flatten the matrix with <link linkend=\"gel-function-"
"ExpandMatrix\">ExpandMatrix</link>, and pick out the right columns. Example: "
"<_:screen-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8128
msgid "<anchor id=\"gel-function-FindRootBisection\"/>FindRootBisection"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8130
#, no-wrap
msgid "FindRootBisection (f,a,b,TOL,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8131
msgid ""
"Find root of a function using the bisection method. <varname>a</varname> and "
"<varname>b</varname> are the initial guess interval, <userinput>f(a)</"
"userinput> and <userinput>f(b)</userinput> should have opposite signs. "
"<varname>TOL</varname> is the desired tolerance and <varname>N</varname> is "
"the limit on the number of iterations to run, 0 means no limit. The function "
"returns a vector <userinput>[success,value,iteration]</userinput>, where "
"<varname>success</varname> is a boolean indicating success, <varname>value</"
"varname> is the last value computed, and <varname>iteration</varname> is the "
"number of iterations done."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8140
msgid ""
"<anchor id=\"gel-function-FindRootFalsePosition\"/>FindRootFalsePosition"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8142
#, no-wrap
msgid "FindRootFalsePosition (f,a,b,TOL,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8143
msgid ""
"Find root of a function using the method of false position. <varname>a</"
"varname> and <varname>b</varname> are the initial guess interval, "
"<userinput>f(a)</userinput> and <userinput>f(b)</userinput> should have "
"opposite signs. <varname>TOL</varname> is the desired tolerance and "
"<varname>N</varname> is the limit on the number of iterations to run, 0 "
"means no limit. The function returns a vector "
"<userinput>[success,value,iteration]</userinput>, where <varname>success</"
"varname> is a boolean indicating success, <varname>value</varname> is the "
"last value computed, and <varname>iteration</varname> is the number of "
"iterations done."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8152
msgid ""
"<anchor id=\"gel-function-FindRootMullersMethod\"/>FindRootMullersMethod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8154
#, no-wrap
msgid "FindRootMullersMethod (f,x0,x1,x2,TOL,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8155
msgid ""
"Find root of a function using the Muller's method. <varname>TOL</varname> is "
"the desired tolerance and <varname>N</varname> is the limit on the number of "
"iterations to run, 0 means no limit. The function returns a vector "
"<userinput>[success,value,iteration]</userinput>, where <varname>success</"
"varname> is a boolean indicating success, <varname>value</varname> is the "
"last value computed, and <varname>iteration</varname> is the number of "
"iterations done."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8162
msgid "<anchor id=\"gel-function-FindRootSecant\"/>FindRootSecant"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8164
#, no-wrap
msgid "FindRootSecant (f,a,b,TOL,N)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8165
msgid ""
"Find root of a function using the secant method. <varname>a</varname> and "
"<varname>b</varname> are the initial guess interval, <userinput>f(a)</"
"userinput> and <userinput>f(b)</userinput> should have opposite signs. "
"<varname>TOL</varname> is the desired tolerance and <varname>N</varname> is "
"the limit on the number of iterations to run, 0 means no limit. The function "
"returns a vector <userinput>[success,value,iteration]</userinput>, where "
"<varname>success</varname> is a boolean indicating success, <varname>value</"
"varname> is the last value computed, and <varname>iteration</varname> is the "
"number of iterations done."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8174
msgid "<anchor id=\"gel-function-HalleysMethod\"/>HalleysMethod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8176
#, no-wrap
msgid "HalleysMethod (f,df,ddf,guess,epsilon,maxn)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8177
msgid ""
"Find zeros using Halley's method. <varname>f</varname> is the function, "
"<varname>df</varname> is the derivative of <varname>f</varname>, and "
"<varname>ddf</varname> is the second derivative of <varname>f</varname>. "
"<varname>guess</varname> is the initial guess. The function returns after "
"two successive values are within <varname>epsilon</varname> of each other, "
"or after <varname>maxn</varname> tries, in which case the function returns "
"<constant>null</constant> indicating failure."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8184
msgid ""
"See also <link linkend=\"gel-function-"
"NewtonsMethod\"><function>NewtonsMethod</function></link> and <link "
"linkend=\"gel-function-SymbolicDerivative\"><function>SymbolicDerivative</"
"function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8189
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>HalleysMethod(`(x)=x^2-10,`(x)=2*x,`(x)=2,3,10^-10,100)</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8187 C/genius.xml:8213 C/genius.xml:8555
msgid "Example to find the square root of 10: <_:screen-1/>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8192
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Halley%27s_method\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8201
msgid "<anchor id=\"gel-function-NewtonsMethod\"/>NewtonsMethod"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8203
#, no-wrap
msgid "NewtonsMethod (f,df,guess,epsilon,maxn)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8204
msgid ""
"Find zeros using Newton's method. <varname>f</varname> is the function and "
"<varname>df</varname> is the derivative of <varname>f</varname>. "
"<varname>guess</varname> is the initial guess. The function returns after "
"two successive values are within <varname>epsilon</varname> of each other, "
"or after <varname>maxn</varname> tries, in which case the function returns "
"<constant>null</constant> indicating failure."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8210
msgid ""
"See also <link linkend=\"gel-function-"
"NewtonsMethodPoly\"><function>NewtonsMethodPoly</function></link> and <link "
"linkend=\"gel-function-SymbolicDerivative\"><function>SymbolicDerivative</"
"function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8215
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>NewtonsMethod(`(x)=x^2-10,`(x)=2*x,3,10^-10,100)</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8218 C/genius.xml:8560
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Newtons_method\">Wikipedia</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8227
msgid "<anchor id=\"gel-function-PolynomialRoots\"/>PolynomialRoots"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8229
#, no-wrap
msgid "PolynomialRoots (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8230
msgid ""
"Compute roots of a polynomial (degrees 1 through 4) using one of the "
"formulas for such polynomials. The polynomial should be given as a vector of "
"coefficients. That is <userinput>4*x^3 + 2*x + 1</userinput> corresponds to "
"the vector <userinput>[1,2,0,4]</userinput>. Returns a column vector of the "
"solutions."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8239
msgid ""
"The function calls <link linkend=\"gel-function-"
"QuadraticFormula\">QuadraticFormula</link>, <link linkend=\"gel-function-"
"CubicFormula\">CubicFormula</link>, and <link linkend=\"gel-function-"
"QuarticFormula\">QuarticFormula</link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8249
msgid "<anchor id=\"gel-function-QuadraticFormula\"/>QuadraticFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8251
#, no-wrap
msgid "QuadraticFormula (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8252
msgid ""
"Compute roots of a quadratic (degree 2) polynomial using the quadratic "
"formula. The polynomial should be given as a vector of coefficients. That is "
"<userinput>3*x^2 + 2*x + 1</userinput> corresponds to the vector "
"<userinput>[1,2,3]</userinput>. Returns a column vector of the two solutions."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8260
msgid ""
"See <ulink url=\"http://planetmath.org/QuadraticFormula\">Planetmath</"
"ulink>, or <ulink url=\"http://mathworld.wolfram.com/"
"QuadraticFormula.html\">Mathworld</ulink>, or <ulink url=\"https://"
"en.wikipedia.org/wiki/Quadratic_formula\">Wikipedia</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8270
msgid "<anchor id=\"gel-function-QuarticFormula\"/>QuarticFormula"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8272
#, no-wrap
msgid "QuarticFormula (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8273
msgid ""
"Compute roots of a quartic (degree 4) polynomial using the quartic formula. "
"The polynomial should be given as a vector of coefficients. That is "
"<userinput>5*x^4 + 2*x + 1</userinput> corresponds to the vector "
"<userinput>[1,2,0,0,5]</userinput>. Returns a column vector of the four "
"solutions."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8281
msgid ""
"See <ulink url=\"http://planetmath.org/QuarticFormula\">Planetmath</ulink>, "
"<ulink url=\"http://mathworld.wolfram.com/QuarticEquation.html\">Mathworld</"
"ulink>, or <ulink url=\"https://en.wikipedia.org/wiki/"
"Quartic_equation\">Wikipedia</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8291
msgid "<anchor id=\"gel-function-RungeKutta\"/>RungeKutta"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8293
#, no-wrap
msgid "RungeKutta (f,x0,y0,x1,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8294
msgid ""
"Use classical non-adaptive fourth order Runge-Kutta method to numerically "
"solve y'=f(x,y) for initial <varname>x0</varname>, <varname>y0</varname> "
"going to <varname>x1</varname> with <varname>n</varname> increments, returns "
"<varname>y</varname> at <varname>x1</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8308 C/genius.xml:8361
msgid ""
"See <ulink url=\"http://mathworld.wolfram.com/Runge-"
"KuttaMethod.html\">Mathworld</ulink> or <ulink url=\"https://"
"en.wikipedia.org/wiki/Runge-Kutta_methods\">Wikipedia</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8317
msgid "<anchor id=\"gel-function-RungeKuttaFull\"/>RungeKuttaFull"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8319
#, no-wrap
msgid "RungeKuttaFull (f,x0,y0,x1,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8320
msgid ""
"Use classical non-adaptive fourth order Runge-Kutta method to numerically "
"solve y'=f(x,y) for initial <varname>x0</varname>, <varname>y0</varname> "
"going to <varname>x1</varname> with <varname>n</varname> increments, returns "
"an <userinput>n+1</userinput> by 2 matrix with the <varname>x</varname> and "
"<varname>y</varname> values. Suitable for plugging into <link linkend=\"gel-"
"function-LinePlotDrawLine\">LinePlotDrawLine</link> or <link linkend=\"gel-"
"function-LinePlotDrawPoints\">LinePlotDrawPoints</link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8334
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotClear();</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>line = RungeKuttaFull(`(x,y)=y,0,1.0,3.0,50);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(line,\"window\",\"fit\",\"color\",\"blue\",\"legend\",\"Exponential growth\");</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8351
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotClear();</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>lines = RungeKuttaFull(`(x,y)=[y@(2),-y@(1)],0,[1.0,1.0],10.0,100);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>lines = ExpandMatrix(lines);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>firstline = lines@(,[1,2]);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>secondline = lines@(,[1,3]);</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotWindow = [0,10,-2,2];</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(firstline,\"color\",\"blue\",\"legend\",\"First\");</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints(secondline,\"color\",\"red\",\"thickness\",3,\"legend\",\"Second\");</userinput>\n"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8375
msgid "Statistics"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8378
msgid "<anchor id=\"gel-function-Average\"/>Average"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8380
#, no-wrap
msgid "Average (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8381
msgid ""
"Aliases: <function>average</function> <function>Mean</function> "
"<function>mean</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8382
msgid "Calculate average (the arithmetic mean) of an entire matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8383 C/genius.xml:8448
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Mean\">Wikipedia</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/ArithmeticMean.html\">Mathworld</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8392
msgid "<anchor id=\"gel-function-GaussDistribution\"/>GaussDistribution"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8394
#, no-wrap
msgid "GaussDistribution (x,sigma)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8395
msgid ""
"Integral of the GaussFunction from 0 to <varname>x</varname> (area under the "
"normal curve)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8396 C/genius.xml:8409
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/"
"Normal_distribution\">Wikipedia</ulink> or <ulink url=\"http://"
"mathworld.wolfram.com/NormalDistribution.html\">Mathworld</ulink> for more "
"information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8405
msgid "<anchor id=\"gel-function-GaussFunction\"/>GaussFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8407
#, no-wrap
msgid "GaussFunction (x,sigma)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8408
msgid "The normalized Gauss distribution function (the normal curve)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8419
msgid "<anchor id=\"gel-function-Median\"/>Median"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8421
#, no-wrap
msgid "Median (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8422
msgid "Aliases: <function>median</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8423
msgid "Calculate median of an entire matrix."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8424 C/genius.xml:8462
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/Median\">Wikipedia</ulink> or "
"<ulink url=\"http://mathworld.wolfram.com/"
"StatisticalMedian.html\">Mathworld</ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8433
msgid ""
"<anchor id=\"gel-function-PopulationStandardDeviation\"/"
">PopulationStandardDeviation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8435
#, no-wrap
msgid "PopulationStandardDeviation (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8436
msgid "Aliases: <function>stdevp</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8437
msgid "Calculate the population standard deviation of a whole matrix."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8442
msgid "<anchor id=\"gel-function-RowAverage\"/>RowAverage"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8444
#, no-wrap
msgid "RowAverage (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8445
msgid "Aliases: <function>RowMean</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8446
msgid ""
"Calculate average of each row in a matrix. That is, compute the arithmetic "
"mean."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8457
msgid "<anchor id=\"gel-function-RowMedian\"/>RowMedian"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8459
#, no-wrap
msgid "RowMedian (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8460
msgid ""
"Calculate median of each row in a matrix and return a column vector of the "
"medians."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8471
msgid ""
"<anchor id=\"gel-function-RowPopulationStandardDeviation\"/"
">RowPopulationStandardDeviation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8473
#, no-wrap
msgid "RowPopulationStandardDeviation (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8474
msgid "Aliases: <function>rowstdevp</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8475
msgid ""
"Calculate the population standard deviations of rows of a matrix and return "
"a vertical vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8480
msgid "<anchor id=\"gel-function-RowStandardDeviation\"/>RowStandardDeviation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8482
#, no-wrap
msgid "RowStandardDeviation (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8483
msgid "Aliases: <function>rowstdev</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8484
msgid ""
"Calculate the standard deviations of rows of a matrix and return a vertical "
"vector."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8489
msgid "<anchor id=\"gel-function-StandardDeviation\"/>StandardDeviation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8491
#, no-wrap
msgid "StandardDeviation (m)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8492
msgid "Aliases: <function>stdev</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8493
msgid "Calculate the standard deviation of a whole matrix."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8501
msgid "Polynomials"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8504
msgid "<anchor id=\"gel-function-AddPoly\"/>AddPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8506
#, no-wrap
msgid "AddPoly (p1,p2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8507
msgid "Add two polynomials (vectors)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8512
msgid "<anchor id=\"gel-function-DividePoly\"/>DividePoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8514
#, no-wrap
msgid "DividePoly (p,q,&amp;r)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8515
msgid ""
"Divide two polynomials (as vectors) using long division. Returns the "
"quotient of the two polynomials. The optional argument <varname>r</varname> "
"is used to return the remainder. The remainder will have lower degree than "
"<varname>q</varname>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8520
msgid ""
"See <ulink url=\"http://planetmath.org/PolynomialLongDivision\">Planetmath</"
"ulink> for more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8528
msgid "<anchor id=\"gel-function-IsPoly\"/>IsPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8530
#, no-wrap
msgid "IsPoly (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8531
msgid "Check if a vector is usable as a polynomial."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8536
msgid "<anchor id=\"gel-function-MultiplyPoly\"/>MultiplyPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8538
#, no-wrap
msgid "MultiplyPoly (p1,p2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8539
msgid "Multiply two polynomials (as vectors)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8544
msgid "<anchor id=\"gel-function-NewtonsMethodPoly\"/>NewtonsMethodPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8546
#, no-wrap
msgid "NewtonsMethodPoly (poly,guess,epsilon,maxn)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8547
msgid ""
"Find a root of a polynomial using Newton's method. <varname>poly</varname> "
"is the polynomial as a vector and <varname>guess</varname> is the initial "
"guess. The function returns after two successive values are within "
"<varname>epsilon</varname> of each other, or after <varname>maxn</varname> "
"tries, in which case the function returns <constant>null</constant> "
"indicating failure."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8552
msgid ""
"See also <link linkend=\"gel-function-"
"NewtonsMethod\"><function>NewtonsMethod</function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8557
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>NewtonsMethodPoly([-10,0,1],3,10^-10,100)</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8568
msgid "<anchor id=\"gel-function-Poly2ndDerivative\"/>Poly2ndDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8570
#, no-wrap
msgid "Poly2ndDerivative (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8571
msgid "Take second polynomial (as vector) derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8576
msgid "<anchor id=\"gel-function-PolyDerivative\"/>PolyDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8578
#, no-wrap
msgid "PolyDerivative (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8579
msgid "Take polynomial (as vector) derivative."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8584
msgid "<anchor id=\"gel-function-PolyToFunction\"/>PolyToFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8586
#, no-wrap
msgid "PolyToFunction (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8587
msgid "Make function out of a polynomial (as vector)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8592
msgid "<anchor id=\"gel-function-PolyToString\"/>PolyToString"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8594
#, no-wrap
msgid "PolyToString (p,var...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8595
msgid "Make string out of a polynomial (as vector)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8600
msgid "<anchor id=\"gel-function-SubtractPoly\"/>SubtractPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8602
#, no-wrap
msgid "SubtractPoly (p1,p2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8603
msgid "Subtract two polynomials (as vectors)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8608
msgid "<anchor id=\"gel-function-TrimPoly\"/>TrimPoly"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8610
#, no-wrap
msgid "TrimPoly (p)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8611
msgid "Trim zeros from a polynomial (as vector)."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8619
msgid "Set Theory"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8622
msgid "<anchor id=\"gel-function-Intersection\"/>Intersection"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8624
#, no-wrap
msgid "Intersection (X,Y)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8625
msgid ""
"Returns a set theoretic intersection of X and Y (X and Y are vectors "
"pretending to be sets)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8630
msgid "<anchor id=\"gel-function-IsIn\"/>IsIn"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8632
#, no-wrap
msgid "IsIn (x,X)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8633
msgid ""
"Returns <constant>true</constant> if the element x is in the set X (where X "
"is a vector pretending to be a set)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8638
msgid "<anchor id=\"gel-function-IsSubset\"/>IsSubset"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8640
#, no-wrap
msgid "IsSubset (X, Y)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8641
msgid ""
"Returns <constant>true</constant> if X is a subset of Y (X and Y are vectors "
"pretending to be sets)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8646
msgid "<anchor id=\"gel-function-MakeSet\"/>MakeSet"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8648
#, no-wrap
msgid "MakeSet (X)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8649
msgid "Returns a vector where every element of X appears only once."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8654
msgid "<anchor id=\"gel-function-SetMinus\"/>SetMinus"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8656
#, no-wrap
msgid "SetMinus (X,Y)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8657
msgid ""
"Returns a set theoretic difference X-Y (X and Y are vectors pretending to be "
"sets)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8662
msgid "<anchor id=\"gel-function-Union\"/>Union"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8664
#, no-wrap
msgid "Union (X,Y)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8665
msgid ""
"Returns a set theoretic union of X and Y (X and Y are vectors pretending to "
"be sets)."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8673
msgid "Commutative Algebra"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8676
msgid "<anchor id=\"gel-function-MacaulayBound\"/>MacaulayBound"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8678
#, no-wrap
msgid "MacaulayBound (c,d)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8679
msgid ""
"For a Hilbert function that is c for degree d, given the Macaulay bound for "
"the Hilbert function of degree d+1 (The c^&lt;d&gt; operator from Green's "
"proof)."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8685
msgid ""
"<anchor id=\"gel-function-MacaulayLowerOperator\"/>MacaulayLowerOperator"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8687
#, no-wrap
msgid "MacaulayLowerOperator (c,d)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8688
msgid "The c_&lt;d&gt; operator from Green's proof of Macaulay's Theorem."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8694
msgid "<anchor id=\"gel-function-MacaulayRep\"/>MacaulayRep"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8696
#, no-wrap
msgid "MacaulayRep (c,d)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8697
msgid "Return the dth Macaulay representation of a positive integer c."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8705
msgid "Miscellaneous"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8708
msgid "<anchor id=\"gel-function-ASCIIToString\"/>ASCIIToString"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8710
#, no-wrap
msgid "ASCIIToString (vec)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8711
msgid ""
"Convert a vector of ASCII values to a string. See also <link linkend=\"gel-"
"function-StringToASCII\"><function>StringToASCII</function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8717
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>ASCIIToString([97,98,99])</userinput>\n"
"= \"abc\"\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8721 C/genius.xml:8761
msgid ""
"See <ulink url=\"https://en.wikipedia.org/wiki/ASCII\">Wikipedia</ulink> for "
"more information."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8729
msgid "<anchor id=\"gel-function-AlphabetToString\"/>AlphabetToString"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8731
#, no-wrap
msgid "AlphabetToString (vec,alphabet)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8732
msgid ""
"Convert a vector of 0-based alphabet values (positions in the alphabet "
"string) to a string. A <constant>null</constant> vector results in an empty "
"string. See also <link linkend=\"gel-function-"
"StringToAlphabet\"><function>StringToAlphabet</function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8738
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>AlphabetToString([1,2,3,0,0],\"abcd\")</userinput>\n"
"= \"bcdaa\"\n"
"<prompt>genius&gt;</prompt> <userinput>AlphabetToString(null,\"abcd\")</userinput>\n"
"= \"\"\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8736 C/genius.xml:8778 C/genius.xml:8800 C/genius.xml:8891
#: C/genius.xml:8925 C/genius.xml:9031 C/genius.xml:9099 C/genius.xml:9286
#: C/genius.xml:9313 C/genius.xml:9360 C/genius.xml:9405 C/genius.xml:9461
#: C/genius.xml:9515 C/genius.xml:9589
msgid "Examples: <_:screen-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8748
msgid "<anchor id=\"gel-function-StringToASCII\"/>StringToASCII"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8750
#, no-wrap
msgid "StringToASCII (str)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8751
msgid ""
"Convert a string to a (row) vector of ASCII values. See also <link "
"linkend=\"gel-function-ASCIIToString\"><function>ASCIIToString</function></"
"link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8757
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>StringToASCII(\"abc\")</userinput>\n"
"= [97, 98, 99]\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8769
msgid "<anchor id=\"gel-function-StringToAlphabet\"/>StringToAlphabet"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8771
#, no-wrap
msgid "StringToAlphabet (str,alphabet)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8772
msgid ""
"Convert a string to a (row) vector of 0-based alphabet values (positions in "
"the alphabet string), -1's for unknown letters. An empty string results in a "
"<constant>null</constant>. See also <link linkend=\"gel-function-"
"AlphabetToString\"><function>AlphabetToString</function></link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8780
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>StringToAlphabet(\"cca\",\"abcd\")</userinput>\n"
"= [2, 2, 0]\n"
"<prompt>genius&gt;</prompt> <userinput>StringToAlphabet(\"ccag\",\"abcd\")</userinput>\n"
"= [2, 2, 0, -1]\n"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:8793
msgid "Symbolic Operations"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8796
msgid "<anchor id=\"gel-function-SymbolicDerivative\"/>SymbolicDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8798
#, no-wrap
msgid "SymbolicDerivative (f)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8799
msgid ""
"Attempt to symbolically differentiate the function f, where f is a function "
"of one variable."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8802
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SymbolicDerivative(sin)</userinput>\n"
"= (`(x)=cos(x))\n"
"<prompt>genius&gt;</prompt> <userinput>SymbolicDerivative(`(x)=7*x^2)</userinput>\n"
"= (`(x)=(7*(2*x)))\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8816
msgid ""
"<anchor id=\"gel-function-SymbolicDerivativeTry\"/>SymbolicDerivativeTry"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8818
#, no-wrap
msgid "SymbolicDerivativeTry (f)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8819
msgid ""
"Attempt to symbolically differentiate the function f, where f is a function "
"of one variable, returns <constant>null</constant> if unsuccessful but is "
"silent. (See <link linkend=\"gel-function-"
"SymbolicDerivative\"><function>SymbolicDerivative</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8830
msgid ""
"<anchor id=\"gel-function-SymbolicNthDerivative\"/>SymbolicNthDerivative"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8832
#, no-wrap
msgid "SymbolicNthDerivative (f,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8833
msgid ""
"Attempt to symbolically differentiate a function n times. (See <link "
"linkend=\"gel-function-SymbolicDerivative\"><function>SymbolicDerivative</"
"function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8844
msgid ""
"<anchor id=\"gel-function-SymbolicNthDerivativeTry\"/"
">SymbolicNthDerivativeTry"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8846
#, no-wrap
msgid "SymbolicNthDerivativeTry (f,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8847
msgid ""
"Attempt to symbolically differentiate a function n times quietly and return "
"<constant>null</constant> on failure (See <link linkend=\"gel-function-"
"SymbolicNthDerivative\"><function>SymbolicNthDerivative</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8858
msgid ""
"<anchor id=\"gel-function-SymbolicTaylorApproximationFunction\"/"
">SymbolicTaylorApproximationFunction"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8860
#, no-wrap
msgid "SymbolicTaylorApproximationFunction (f,x0,n)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8861
msgid ""
"Attempt to construct the Taylor approximation function around x0 to the nth "
"degree. (See <link linkend=\"gel-function-"
"SymbolicDerivative\"><function>SymbolicDerivative</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8873
msgid "<anchor id=\"gel-function-ExportPlot\"/>ExportPlot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8875
#, no-wrap
msgid "ExportPlot (file,type)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8876
#, no-wrap
msgid "ExportPlot (file)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8877
msgid ""
"Export the contents of the plotting window to a file. The type is a string "
"that specifies the file type to use, \"png\", \"eps\", or \"ps\". If the "
"type is not specified, then it is taken to be the extension, in which case "
"the extension must be \".png\", \".eps\", or \".ps\"."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8884
msgid "Note that files are overwritten without asking."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8887
msgid ""
"On successful export, true is returned. Otherwise error is printed and "
"exception is raised."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8893
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>ExportPlot(\"file.png\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>ExportPlot(\"/directory/file\",\"eps\")</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8902
msgid "<anchor id=\"gel-function-LinePlot\"/>LinePlot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8904
#, no-wrap
msgid "LinePlot (func1,func2,func3,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8905
#, no-wrap
msgid "LinePlot (func1,func2,func3,x1,x2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8906
#, no-wrap
msgid "LinePlot (func1,func2,func3,x1,x2,y1,y2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8907
#, no-wrap
msgid "LinePlot (func1,func2,func3,[x1,x2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8908
#, no-wrap
msgid "LinePlot (func1,func2,func3,[x1,x2,y1,y2])"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8909
msgid ""
"Plot a function (or several functions) with a line. First (up to 10) "
"arguments are functions, then optionally you can specify the limits of the "
"plotting window as <varname>x1</varname>, <varname>x2</varname>, "
"<varname>y1</varname>, <varname>y2</varname>. If limits are not specified, "
"then the currently set limits apply (See <link linkend=\"gel-function-"
"LinePlotWindow\"><function>LinePlotWindow</function></link>) If the y limits "
"are not specified, then the functions are computed and then the maxima and "
"minima are used."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8920 C/genius.xml:8964 C/genius.xml:9162 C/genius.xml:9281
#: C/genius.xml:9584
msgid ""
"The parameter <link linkend=\"gel-function-"
"LinePlotDrawLegends\"><function>LinePlotDrawLegends</function></link> "
"controls the drawing of the legend."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:8927
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlot(sin,cos)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlot(`(x)=x^2,-1,1,0,1)</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8935
msgid "<anchor id=\"gel-function-LinePlotClear\"/>LinePlotClear"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8937
#, no-wrap
msgid "LinePlotClear ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8938
msgid ""
"Show the line plot window and clear out functions and any other lines that "
"were drawn."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8946
msgid "<anchor id=\"gel-function-LinePlotCParametric\"/>LinePlotCParametric"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8948
#, no-wrap
msgid "LinePlotCParametric (func,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8949
#, no-wrap
msgid "LinePlotCParametric (func,t1,t2,tinc)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8950
#, no-wrap
msgid "LinePlotCParametric (func,t1,t2,tinc,x1,x2,y1,y2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8951
msgid ""
"Plot a parametric complex valued function with a line. First comes the "
"function that returns <computeroutput>x+iy</computeroutput>, then optionally "
"the <varname>t</varname> limits as <userinput>t1,t2,tinc</userinput>, then "
"optionally the limits as <userinput>x1,x2,y1,y2</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8957
msgid ""
"If limits are not specified, then the currently set limits apply (See <link "
"linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</function></"
"link>). If instead the string \"fit\" is given for the x and y limits, then "
"the limits are the maximum extent of the graph"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:8974
msgid "<anchor id=\"gel-function-LinePlotDrawLine\"/>LinePlotDrawLine"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8976
#, no-wrap
msgid "LinePlotDrawLine (x1,y1,x2,y2,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:8977
#, no-wrap
msgid "LinePlotDrawLine (v,...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8978
msgid ""
"Draw a line from <varname>x1</varname>,<varname>y1</varname> to <varname>x2</"
"varname>,<varname>y2</varname>. <varname>x1</varname>,<varname>y1</varname>, "
"<varname>x2</varname>,<varname>y2</varname> can be replaced by an "
"<varname>n</varname> by 2 matrix for a longer polyline. Alternatively the "
"vector <varname>v</varname> may be a column vector of complex numbers, that "
"is an <varname>n</varname> by 1 matrix and each complex number is then "
"considered a point in the plane."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8988
msgid ""
"Extra parameters can be added to specify line color, thickness, arrows, the "
"plotting window, or legend. You can do this by adding an argument string "
"<userinput>\"color\"</userinput>, <userinput>\"thickness\"</userinput>, "
"<userinput>\"window\"</userinput>, <userinput>\"arrow\"</userinput>, or "
"<userinput>\"legend\"</userinput>, and after it specify the color, the "
"thickness, the window as 4-vector, type of arrow, or the legend. (Arrow and "
"window are from version 1.0.6 onwards.)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:8998
msgid ""
"If the line is to be treated as a filled polygon, filled with the given "
"color, you can specify the argument <userinput>\"filled\"</userinput>. Since "
"version 1.0.22 onwards."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9002 C/genius.xml:9439
msgid ""
"The color should be either a string indicating the common English word for "
"the color that GTK will recognize such as <userinput>\"red\"</userinput>, "
"<userinput>\"blue\"</userinput>, <userinput>\"yellow\"</userinput>, etc... "
"Alternatively the color can be specified in RGB format as "
"<userinput>\"#rgb\"</userinput>, <userinput>\"#rrggbb\"</userinput>, or "
"<userinput>\"#rrrrggggbbbb\"</userinput>, where the r, g, or b are hex "
"digits of the red, green, and blue components of the color. Finally, since "
"version 1.0.18, the color can also be specified as a real vector specifying "
"the red green and blue components where the components are between 0 and 1, "
"e.g. <userinput>[1.0,0.5,0.1]</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9013 C/genius.xml:9088
msgid ""
"The window should be given as usual as <userinput>[x1,x2,y1,y2]</userinput>, "
"or alternatively can be given as a string <userinput>\"fit\"</userinput> in "
"which case, the x range will be set precisely and the y range will be set "
"with five percent borders around the line."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9020
msgid ""
"Arrow specification should be <userinput>\"origin\"</userinput>, "
"<userinput>\"end\"</userinput>, <userinput>\"both\"</userinput>, or "
"<userinput>\"none\"</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9027 C/genius.xml:9095 C/genius.xml:9457 C/genius.xml:9511
msgid ""
"Finally, legend should be a string that can be used as the legend in the "
"graph. That is, if legends are being printed."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9033
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(0,0,1,1,\"color\",\"blue\",\"thickness\",3)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine([0,0;1,-1;-1,-1])</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine([0,0;1,1],\"arrow\",\"end\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine(RungeKuttaFull(`(x,y)=y,0,0.001,10,100),\"color\",\"blue\",\"legend\",\"The Solution\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>for r=0.0 to 1.0 by 0.1 do LinePlotDrawLine([0,0;1,r],\"color\",[r,(1-r),0.5],\"window\",[0,1,0,1])</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawLine([0,0;10,0;10,10;0,10],\"filled\",\"color\",\"green\")</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9041
msgid ""
"Unlike many other functions that do not care if they take a column or a row "
"vector, if specifying points as a vector of complex values, due to possible "
"ambiguities, it must always be given as a column vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9047
msgid ""
"Specifying <varname>v</varname> as a column vector of complex numbers is "
"implemented from version 1.0.22 and onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9055
msgid "<anchor id=\"gel-function-LinePlotDrawPoints\"/>LinePlotDrawPoints"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9057
#, no-wrap
msgid "LinePlotDrawPoints (x,y,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9058
#, no-wrap
msgid "LinePlotDrawPoints (v,...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9059
msgid ""
"Draw a point at <varname>x</varname>,<varname>y</varname>. The input can be "
"an <varname>n</varname> by 2 matrix for <varname>n</varname> different "
"points. This function has essentially the same input as <link linkend=\"gel-"
"function-LinePlotDrawLine\">LinePlotDrawLine</link>. Alternatively the "
"vector <varname>v</varname> may be a column vector of complex numbers, that "
"is an <varname>n</varname> by 1 matrix and each complex number is then "
"considered a point in the plane."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9068
msgid ""
"Extra parameters can be added to specify color, thickness, the plotting "
"window, or legend. You can do this by adding an argument string "
"<userinput>\"color\"</userinput>, <userinput>\"thickness\"</userinput>, "
"<userinput>\"window\"</userinput>, or <userinput>\"legend\"</userinput>, and "
"after it specify the color, the thickness, the window as 4-vector, or the "
"legend."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9078 C/genius.xml:9494
msgid ""
"The color should be either a string indicating the common English word for "
"the color that GTK will recognize such as <userinput>\"red\"</userinput>, "
"<userinput>\"blue\"</userinput>, <userinput>\"yellow\"</userinput>, etc... "
"Alternatively the color can be specified in RGB format as "
"<userinput>\"#rgb\"</userinput>, <userinput>\"#rrggbb\"</userinput>, or "
"<userinput>\"#rrrrggggbbbb\"</userinput>, where the r, g, or b are hex "
"digits of the red, green, and blue components of the color. Finally the "
"color can also be specified as a real vector specifying the red green and "
"blue components where the components are between 0 and 1."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9101
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints(0,0,\"color\",\"blue\",\"thickness\",3)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints([0,0;1,-1;-1,-1])</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints(RungeKuttaFull(`(x,y)=y,0,0.001,10,100),\"color\",\"blue\",\"legend\",\"The Solution\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints([1;1+1i;1i;0],\"thickness\",5)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>LinePlotDrawPoints(ApplyOverMatrix((0:6)',`(k)=exp(k*2*pi*1i/7)),\"thickness\",3,\"legend\",\"The 7th roots of unity\")</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9108
msgid ""
"Unlike many other functions that do not care if they take a column or a row "
"vector, if specifying points as a vector of complex values, due to possible "
"ambiguities, it must always be given as a column vector. Therefore, notice "
"in the last example the transpose of the vector <userinput>0:6</userinput> "
"to make it into a column vector."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9116
msgid ""
"Available from version 1.0.18 onwards. Specifying <varname>v</varname> as a "
"column vector of complex numbers is implemented from version 1.0.22 and "
"onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9125
msgid ""
"<anchor id=\"gel-function-LinePlotMouseLocation\"/>LinePlotMouseLocation"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9127
#, no-wrap
msgid "LinePlotMouseLocation ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9128
msgid ""
"Returns a row vector of a point on the line plot corresponding to the "
"current mouse location. If the line plot is not visible, then prints an "
"error and returns <constant>null</constant>. In this case you should run "
"<link linkend=\"gel-function-LinePlot\"><function>LinePlot</function></link> "
"or <link linkend=\"gel-function-LinePlotClear\"><function>LinePlotClear</"
"function></link> to put the graphing window into the line plot mode. See "
"also <link linkend=\"gel-function-"
"LinePlotWaitForClick\"><function>LinePlotWaitForClick</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9143
msgid "<anchor id=\"gel-function-LinePlotParametric\"/>LinePlotParametric"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9145
#, no-wrap
msgid "LinePlotParametric (xfunc,yfunc,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9146
#, no-wrap
msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9147
#, no-wrap
msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,x1,x2,y1,y2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9148
#, no-wrap
msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,[x1,x2,y1,y2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9149
#, no-wrap
msgid "LinePlotParametric (xfunc,yfunc,t1,t2,tinc,\"fit\")"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9150
msgid ""
"Plot a parametric function with a line. First come the functions for "
"<varname>x</varname> and <varname>y</varname> then optionally the "
"<varname>t</varname> limits as <userinput>t1,t2,tinc</userinput>, then "
"optionally the limits as <userinput>x1,x2,y1,y2</userinput>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9155
msgid ""
"If x and y limits are not specified, then the currently set limits apply "
"(See <link linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</"
"function></link>). If instead the string \"fit\" is given for the x and y "
"limits, then the limits are the maximum extent of the graph"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9171
msgid "<anchor id=\"gel-function-LinePlotWaitForClick\"/>LinePlotWaitForClick"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9173
#, no-wrap
msgid "LinePlotWaitForClick ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9174
msgid ""
"If in line plot mode, waits for a click on the line plot window and returns "
"the location of the click as a row vector. If the window is closed the "
"function returns immediately with <constant>null</constant>. If the window "
"is not in line plot mode, it is put in it and shown if not shown. See also "
"<link linkend=\"gel-function-"
"LinePlotMouseLocation\"><function>LinePlotMouseLocation</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9188
msgid "<anchor id=\"gel-function-PlotCanvasFreeze\"/>PlotCanvasFreeze"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9190
#, no-wrap
msgid "PlotCanvasFreeze ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9191
msgid ""
"Freeze drawing of the canvas plot temporarily. Useful if you need to draw a "
"bunch of elements and want to delay drawing everything to avoid flicker in "
"an animation. After everything has been drawn you should call <link "
"linkend=\"gel-function-PlotCanvasThaw\"><function>PlotCanvasThaw</function></"
"link>."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9196
msgid ""
"The canvas is always thawed after end of any execution, so it will never "
"remain frozen. The moment a new command line is shown for example the plot "
"canvas is thawed automatically. Also note that calls to freeze and thaw may "
"be safely nested."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9206
msgid "<anchor id=\"gel-function-PlotCanvasThaw\"/>PlotCanvasThaw"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9208
#, no-wrap
msgid "PlotCanvasThaw ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9209
msgid ""
"Thaw the plot canvas frozen by <link linkend=\"gel-function-"
"PlotCanvasFreeze\"><function>PlotCanvasFreeze</function></link> and redraw "
"the canvas immediately. The canvas is also always thawed after end of "
"execution of any program."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9220
msgid "<anchor id=\"gel-function-PlotWindowPresent\"/>PlotWindowPresent"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9222
#, no-wrap
msgid "PlotWindowPresent ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9223
msgid ""
"Show and raise the plot window, creating it if necessary. Normally the "
"window is created when one of the plotting functions is called, but it is "
"not always raised if it happens to be below other windows. So this function "
"is good to call in scripts where the plot window might have been created "
"before, and by now is hidden behind the console or other windows."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9232
msgid "Version 1.0.19 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9237
msgid ""
"<anchor id=\"gel-function-SlopefieldClearSolutions\"/"
">SlopefieldClearSolutions"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9239
#, no-wrap
msgid "SlopefieldClearSolutions ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9240
msgid ""
"Clears the solutions drawn by the <link linkend=\"gel-function-"
"SlopefieldDrawSolution\"><function>SlopefieldDrawSolution</function></link> "
"function."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9249
msgid ""
"<anchor id=\"gel-function-SlopefieldDrawSolution\"/>SlopefieldDrawSolution"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9251
#, no-wrap
msgid "SlopefieldDrawSolution (x, y, dx)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9252
msgid ""
"When a slope field plot is active, draw a solution with the specified "
"initial condition. The standard Runge-Kutta method is used with increment "
"<varname>dx</varname>. Solutions stay on the graph until a different plot is "
"shown or until you call <link linkend=\"gel-function-"
"SlopefieldClearSolutions\"><function>SlopefieldClearSolutions</function></"
"link>. You can also use the graphical interface to draw solutions and "
"specify initial conditions with the mouse."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9266
msgid "<anchor id=\"gel-function-SlopefieldPlot\"/>SlopefieldPlot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9268
#, no-wrap
msgid "SlopefieldPlot (func)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9269
#, no-wrap
msgid "SlopefieldPlot (func,x1,x2,y1,y2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9270
msgid ""
"Plot a slope field. The function <varname>func</varname> should take two "
"real numbers <varname>x</varname> and <varname>y</varname>, or a single "
"complex number. Optionally you can specify the limits of the plotting window "
"as <varname>x1</varname>, <varname>x2</varname>, <varname>y1</varname>, "
"<varname>y2</varname>. If limits are not specified, then the currently set "
"limits apply (See <link linkend=\"gel-function-"
"LinePlotWindow\"><function>LinePlotWindow</function></link>)."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9288
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>SlopefieldPlot(`(x,y)=sin(x-y),-5,5,-5,5)</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9295
msgid "<anchor id=\"gel-function-SurfacePlot\"/>SurfacePlot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9297
#, no-wrap
msgid "SurfacePlot (func)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9298
#, no-wrap
msgid "SurfacePlot (func,x1,x2,y1,y2,z1,z2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9299
#, no-wrap
msgid "SurfacePlot (func,x1,x2,y1,y2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9300
#, no-wrap
msgid "SurfacePlot (func,[x1,x2,y1,y2,z1,z2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9301
#, no-wrap
msgid "SurfacePlot (func,[x1,x2,y1,y2])"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9302
msgid ""
"Plot a surface function that takes either two arguments or a complex number. "
"First comes the function then optionally limits as <varname>x1</varname>, "
"<varname>x2</varname>, <varname>y1</varname>, <varname>y2</varname>, "
"<varname>z1</varname>, <varname>z2</varname>. If limits are not specified, "
"then the currently set limits apply (See <link linkend=\"gel-function-"
"SurfacePlotWindow\"><function>SurfacePlotWindow</function></link>). Genius "
"can only plot a single surface function at this time."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9310
msgid ""
"If the z limits are not specified then the maxima and minima of the function "
"are used."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9315
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SurfacePlot(|sin|,-1,1,-1,1,0,1.5)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlot(`(x,y)=x^2+y,-1,1,-1,1,-2,2)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlot(`(z)=|z|^2,-1,1,-1,1,0,2)</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9324
msgid "<anchor id=\"gel-function-SurfacePlotClear\"/>SurfacePlotClear"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9326
#, no-wrap
msgid "SurfacePlotClear ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9327
msgid ""
"Show the surface plot window and clear out functions and any other lines "
"that were drawn."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9331
msgid "Available in version 1.0.19 and onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9338
msgid "<anchor id=\"gel-function-SurfacePlotData\"/>SurfacePlotData"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9340
#, no-wrap
msgid "SurfacePlotData (data)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9341
#, no-wrap
msgid "SurfacePlotData (data,label)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9342
#, no-wrap
msgid "SurfacePlotData (data,x1,x2,y1,y2,z1,z2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9343
#, no-wrap
msgid "SurfacePlotData (data,label,x1,x2,y1,y2,z1,z2)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9344
#, no-wrap
msgid "SurfacePlotData (data,[x1,x2,y1,y2,z1,z2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9345
#, no-wrap
msgid "SurfacePlotData (data,label,[x1,x2,y1,y2,z1,z2])"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9346
msgid ""
"Plot a surface from data. The data is an n by 3 matrix whose rows are the x, "
"y and z coordinates. The data can also be simply a vector whose length is a "
"multiple of 3 and so contains the triples of x, y, z. The data should "
"contain at least 3 points."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9353
msgid ""
"Optionally we can give the label and also optionally the limits. If limits "
"are not given, they are computed from the data, <link linkend=\"gel-function-"
"SurfacePlotWindow\"><function>SurfacePlotWindow</function></link> is not "
"used, if you want to use it, pass it in explicitly. If label is not given "
"then empty label is used."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9362
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotData([0,0,0;1,0,1;0,1,1;1,1,3])</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotData(data,\"My data\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotData(data,-1,1,-1,1,0,10)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotData(data,SurfacePlotWindow)</userinput>\n"
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9372
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>d:=null; for r=0 to 1 by 0.1 do for theta=0 to 2*pi by pi/5 do d=[d;[r*cos(theta),r*sin(theta),-r^2*theta]];</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotData(d)</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9368
msgid ""
"Here's an example of how to plot in polar coordinates, in particular how to "
"plot the function <userinput>-r^2 * theta</userinput>: <_:screen-1/>"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9381
msgid "<anchor id=\"gel-function-SurfacePlotDataGrid\"/>SurfacePlotDataGrid"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9383
#, no-wrap
msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9384
#, no-wrap
msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2,z1,z2])"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9385
#, no-wrap
msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2],label)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9386
#, no-wrap
msgid "SurfacePlotDataGrid (data,[x1,x2,y1,y2,z1,z2],label)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9387
msgid ""
"Plot a surface from regular rectangular data. The data is given in a n by m "
"matrix where the rows are the x coordinate and the columns are the y "
"coordinate. The x coordinate is divided into equal n-1 subintervals and y "
"coordinate is divided into equal m-1 subintervals. The limits <varname>x1</"
"varname> and <varname>x2</varname> give the interval on the x-axis that we "
"use, and the limits <varname>y1</varname> and <varname>y2</varname> give the "
"interval on the y-axis that we use. If the limits <varname>z1</varname> and "
"<varname>z2</varname> are not given they are computed from the data (to be "
"the extreme values from the data)."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9401
msgid ""
"Optionally we can give the label, if label is not given then empty label is "
"used."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9407
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDataGrid([1,2;3,4],[0,1,0,1])</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDataGrid(data,[-1,1,-1,1],\"My data\")</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>d:=null; for i=1 to 20 do for j=1 to 10 do d@(i,j) = (0.1*i-1)^2-(0.1*j)^2;</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDataGrid(d,[-1,1,0,1],\"half a saddle\")</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9418
msgid "<anchor id=\"gel-function-SurfacePlotDrawLine\"/>SurfacePlotDrawLine"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9420
#, no-wrap
msgid "SurfacePlotDrawLine (x1,y1,z1,x2,y2,z2,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9421
#, no-wrap
msgid "SurfacePlotDrawLine (v,...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9422
msgid ""
"Draw a line from <varname>x1</varname>,<varname>y1</varname>,<varname>z1</"
"varname> to <varname>x2</varname>,<varname>y2</varname>,<varname>z2</"
"varname>. <varname>x1</varname>,<varname>y1</varname>,<varname>z1</varname>, "
"<varname>x2</varname>,<varname>y2</varname>,<varname>z2</varname> can be "
"replaced by an <varname>n</varname> by 3 matrix for a longer polyline."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9429 C/genius.xml:9484
msgid ""
"Extra parameters can be added to specify line color, thickness, the plotting "
"window, or legend. You can do this by adding an argument string "
"<userinput>\"color\"</userinput>, <userinput>\"thickness\"</userinput>, "
"<userinput>\"window\"</userinput>, or <userinput>\"legend\"</userinput>, and "
"after it specify the color, the thickness, the window as 6-vector, or the "
"legend."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9450 C/genius.xml:9504
msgid ""
"The window should be given as usual as <userinput>[x1,x2,y1,y2,z1,z2]</"
"userinput>, or alternatively can be given as a string <userinput>\"fit\"</"
"userinput> in which case, the x range will be set precisely and the y range "
"will be set with five percent borders around the line."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9463
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDrawLine(0,0,0,1,1,1,\"color\",\"blue\",\"thickness\",3)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDrawLine([0,0,0;1,-1,2;-1,-1,-3])</userinput>\n"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9467 C/genius.xml:9521
msgid "Available from version 1.0.19 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9474
msgid ""
"<anchor id=\"gel-function-SurfacePlotDrawPoints\"/>SurfacePlotDrawPoints"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9476
#, no-wrap
msgid "SurfacePlotDrawPoints (x,y,z,...)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9477
#, no-wrap
msgid "SurfacePlotDrawPoints (v,...)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9478
msgid ""
"Draw a point at <varname>x</varname>,<varname>y</varname>,<varname>z</"
"varname>. The input can be an <varname>n</varname> by 3 matrix for "
"<varname>n</varname> different points. This function has essentially the "
"same input as <link linkend=\"gel-function-"
"SurfacePlotDrawLine\">SurfacePlotDrawLine</link>."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9517
#, no-wrap
msgid ""
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDrawPoints(0,0,0,\"color\",\"blue\",\"thickness\",3)</userinput>\n"
"<prompt>genius&gt;</prompt> <userinput>SurfacePlotDrawPoints([0,0,0;1,-1,2;-1,-1,1])</userinput>\n"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9528
msgid ""
"<anchor id=\"gel-function-VectorfieldClearSolutions\"/"
">VectorfieldClearSolutions"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9530
#, no-wrap
msgid "VectorfieldClearSolutions ()"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9531
msgid ""
"Clears the solutions drawn by the <link linkend=\"gel-function-"
"VectorfieldDrawSolution\"><function>VectorfieldDrawSolution</function></"
"link> function."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9536 C/genius.xml:9555
msgid "Version 1.0.6 onwards."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9541
msgid ""
"<anchor id=\"gel-function-VectorfieldDrawSolution\"/>VectorfieldDrawSolution"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9543
#, no-wrap
msgid "VectorfieldDrawSolution (x, y, dt, tlen)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9544
msgid ""
"When a vector field plot is active, draw a solution with the specified "
"initial condition. The standard Runge-Kutta method is used with increment "
"<varname>dt</varname> for an interval of length <varname>tlen</varname>. "
"Solutions stay on the graph until a different plot is shown or until you "
"call <link linkend=\"gel-function-"
"VectorfieldClearSolutions\"><function>VectorfieldClearSolutions</function></"
"link>. You can also use the graphical interface to draw solutions and "
"specify initial conditions with the mouse."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9560
msgid "<anchor id=\"gel-function-VectorfieldPlot\"/>VectorfieldPlot"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9562
#, no-wrap
msgid "VectorfieldPlot (funcx, funcy)"
msgstr ""

#. (itstool) path: listitem/synopsis
#: C/genius.xml:9563
#, no-wrap
msgid "VectorfieldPlot (funcx, funcy, x1, x2, y1, y2)"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9564
msgid ""
"Plot a two dimensional vector field. The function <varname>funcx</varname> "
"should be the dx/dt of the vectorfield and the function <varname>funcy</"
"varname> should be the dy/dt of the vectorfield. The functions should take "
"two real numbers <varname>x</varname> and <varname>y</varname>, or a single "
"complex number. When the parameter <link linkend=\"gel-function-"
"VectorfieldNormalized\"><function>VectorfieldNormalized</function></link> is "
"<constant>true</constant>, then the magnitude of the vectors is normalized. "
"That is, only the direction and not the magnitude is shown."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9577
msgid ""
"Optionally you can specify the limits of the plotting window as <varname>x1</"
"varname>, <varname>x2</varname>, <varname>y1</varname>, <varname>y2</"
"varname>. If limits are not specified, then the currently set limits apply "
"(See <link linkend=\"gel-function-LinePlotWindow\"><function>LinePlotWindow</"
"function></link>)."
msgstr ""

#. (itstool) path: para/screen
#: C/genius.xml:9591
#, no-wrap
msgid "<prompt>genius&gt;</prompt> <userinput>VectorfieldPlot(`(x,y)=x^2-y, `(x,y)=y^2-x, -1, 1, -1, 1)</userinput>\n"
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:9604
msgid "Example Programs in GEL"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9608
#, no-wrap
msgid "function f(x) = if x &lt;= 1 then 1 else (f(x-1)*x)\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9606
msgid "Here is a function that calculates factorials: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9613
#, no-wrap
msgid ""
"function f(x) = (\n"
"  if x &lt;= 1 then\n"
"    1\n"
"  else\n"
"    (f(x-1)*x)\n"
")\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9611
msgid "With indentation it becomes: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9623
#, no-wrap
msgid ""
"function f(x) = (\n"
"  if (x &lt;= 1) then return (1);\n"
"  return (f(x-1) * x)\n"
")\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9621
msgid ""
"This is a direct port of the factorial function from the <application>bc</"
"application> manpage. The syntax seems similar to <application>bc</"
"application>, but different in that in GEL, the last expression is the one "
"that is returned. Using the <literal>return</literal> function instead, it "
"would be: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9634
#, no-wrap
msgid "function f(x) = prod k=1 to x do k\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9630
msgid ""
"By far the easiest way to define a factorial function would be using the "
"product loop as follows. This is not only the shortest and fastest, but also "
"probably the most readable version. <_:programlisting-1/>"
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9643
#, no-wrap
msgid ""
"# Calculate the row-echelon form of a matrix\n"
"function MyOwnREF(m) = (\n"
"  if not IsMatrix(m) or not IsValueOnly(m) then\n"
"    (error(\"MyOwnREF: argument not a value only matrix\");bailout);\n"
"  s := min(rows(m), columns(m));\n"
"  i := 1;\n"
"  d := 1;\n"
"  while d &lt;= s and i &lt;= columns(m) do (\n"
"\n"
"    # This just makes the anchor element non-zero if at\n"
"    # all possible\n"
"    if m@(d,i) == 0 then (\n"
"      j := d+1;\n"
"      while j &lt;= rows(m) do (\n"
"        if m@(j,i) == 0 then\n"
"          (j=j+1;continue);\n"
"        a := m@(j,);\n"
"        m@(j,) := m@(d,);\n"
"        m@(d,) := a;\n"
"        j := j+1;\n"
"        break\n"
"      )\n"
"    );\n"
"    if m@(d,i) == 0 then\n"
"      (i:=i+1;continue);\n"
"    \n"
"    # Here comes the actual zeroing of all but the anchor\n"
"    # element rows\n"
"    j := d+1;\n"
"    while j &lt;= rows(m)) do (\n"
"      if m@(j,i) != 0 then (\n"
"        m@(j,) := m@(j,)-(m@(j,i)/m@(d,i))*m@(d,)\n"
"      );\n"
"      j := j+1\n"
"    );\n"
"    m@(d,) := m@(d,) * (1/m@(d,i));\n"
"    d := d+1;\n"
"    i := i+1\n"
"  );\n"
"  m\n"
")\n"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9638
msgid ""
"Here is a larger example, this basically redefines the internal <link "
"linkend=\"gel-function-ref\"><function>ref</function></link> function to "
"calculate the row echelon form of a matrix. The function <function>ref</"
"function> is built in and much faster, but this example demonstrates some of "
"the more complex features of GEL. <_:programlisting-1/>"
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:9691
msgid "Settings"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9693
msgid ""
"To configure <application>Genius Mathematics Tool</application>, choose "
"<menuchoice><guimenu>Settings</guimenu> <guimenuitem>Preferences</"
"guimenuitem></menuchoice>. There are several basic parameters provided by "
"the calculator in addition to the ones provided by the standard library. "
"These control how the calculator behaves."
msgstr ""

#. (itstool) path: note/title
#: C/genius.xml:9703
msgid "Changing Settings with GEL"
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:9704
msgid ""
"Many of the settings in Genius are simply global variables, and can be "
"evaluated and assigned to in the same way as normal variables. See <xref "
"linkend=\"genius-gel-variables\"/> about evaluating and assigning to "
"variables, and <xref linkend=\"genius-gel-function-parameters\"/> for a list "
"of settings that can be modified in this way."
msgstr ""

#. (itstool) path: para/programlisting
#: C/genius.xml:9713
#, no-wrap
msgid "MaxDigits = 12\n"
msgstr ""

#. (itstool) path: note/para
#: C/genius.xml:9711
msgid ""
"As an example, you can set the maximum number of digits in a result to 12 by "
"typing: <_:programlisting-1/>"
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:9719
msgid "Output"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9722
msgid "<guilabel>Maximum digits to output</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9726
msgid ""
"The maximum digits in a result (<link linkend=\"gel-function-"
"MaxDigits\"><function>MaxDigits</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9730
msgid "<guilabel>Results as floats</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9734
msgid ""
"If the results should be always printed as floats (<link linkend=\"gel-"
"function-ResultsAsFloats\"><function>ResultsAsFloats</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9738
msgid "<guilabel>Floats in scientific notation</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9742
msgid ""
"If floats should be in scientific notation (<link linkend=\"gel-function-"
"ScientificNotation\"><function>ScientificNotation</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9746
msgid "<guilabel>Always print full expressions</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9750
msgid ""
"Should we print out full expressions for non-numeric return values (longer "
"than a line) (<link linkend=\"gel-function-"
"FullExpressions\"><function>FullExpressions</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9755
msgid "<guilabel>Use mixed fractions</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9759
msgid ""
"If fractions should be printed as mixed fractions such as \"1 1/3\" rather "
"than \"4/3\". (<link linkend=\"gel-function-"
"MixedFractions\"><function>MixedFractions</function></link>)"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9764
msgid ""
"<guilabel>Display 0.0 when floating point number is less than 10^-x (0=never "
"chop)</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9768
msgid ""
"How to chop output. But only when other numbers nearby are large. See the "
"documentation of the parameter <link linkend=\"gel-function-"
"OutputChopExponent\"><function>OutputChopExponent</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9775
msgid ""
"<guilabel>Only chop numbers when another number is greater than 10^-x</"
"guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9779
msgid ""
"When to chop output. This is set by the parameter <link linkend=\"gel-"
"function-OutputChopWhenExponent\"><function>OutputChopWhenExponent</"
"function></link>. See the documentation of the parameter <link linkend=\"gel-"
"function-OutputChopExponent\"><function>OutputChopExponent</function></link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9786
msgid "<guilabel>Remember output settings across sessions</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9790
msgid ""
"Should the output settings in the <guilabel>Number/Expression output "
"options</guilabel> frame be remembered for next session. Does not apply to "
"the <guilabel>Error/Info output options</guilabel> frame."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9792
msgid ""
"If unchecked, either the default or any previously saved settings are used "
"each time Genius starts up. Note that settings are saved at the end of the "
"session, so if you wish to change the defaults check this box, restart "
"<application>Genius Mathematics Tool</application> and then uncheck it again."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9803
msgid "<guilabel>Display errors in a dialog</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9807
msgid ""
"If set the errors will be displayed in a separate dialog, if unset the "
"errors will be printed on the console."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9813
msgid "<guilabel>Display information messages in a dialog</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9817
msgid ""
"If set the information messages will be displayed in a separate dialog, if "
"unset the information messages will be printed on the console."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9824
msgid "<guilabel>Maximum errors to display</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9828
msgid ""
"The maximum number of errors to return on one evaluation (<link "
"linkend=\"gel-function-MaxErrors\"><function>MaxErrors</function></link>). "
"If you set this to 0 then all errors are always returned. Usually if some "
"loop causes many errors, then it is unlikely that you will be able to make "
"sense out of more than a few of these, so seeing a long list of errors is "
"usually not helpful."
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:9840
msgid ""
"In addition to these preferences, there are some preferences that can only "
"be changed by setting them in the workspace console. For others that may "
"affect the output see <xref linkend=\"genius-gel-function-parameters\"/>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9849
msgid "<function>IntegerOutputBase</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9853
msgid "The base that will be used to output integers"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9858
msgid "<function>OutputStyle</function>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9862
msgid ""
"A string, can be <literal>\"normal\"</literal>, <literal>\"latex\"</"
"literal>, <literal>\"mathml\"</literal> or <literal>\"troff\"</literal> and "
"it will affect how matrices (and perhaps other stuff) is printed, useful for "
"pasting into documents. Normal style is the default human readable printing "
"style of <application>Genius Mathematics Tool</application>. The other "
"styles are for typesetting in LaTeX, MathML (XML), or in Troff."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:9874
msgid "Precision"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9877
msgid "<guilabel>Floating point precision</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9881
msgid ""
"The floating point precision in bits (<link linkend=\"gel-function-"
"FloatPrecision\"><function>FloatPrecision</function></link>). Note that "
"changing this only affects newly computed quantities. Old values stored in "
"variables are obviously still in the old precision and if you want to have "
"them more precise you will have to recompute them. Exceptions to this are "
"the system constants such as <link linkend=\"gel-function-pi\"><function>pi</"
"function></link> or <link linkend=\"gel-function-e\"><function>e</function></"
"link>."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9895
msgid "<guilabel>Remember precision setting across sessions</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9899
msgid ""
"Should the precision setting be remembered for the next session. If "
"unchecked, either the default or any previously saved setting is used each "
"time Genius starts up. Note that settings are saved at the end of the "
"session, so if you wish to change the default check this box, restart genius "
"and then uncheck it again."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:9912
msgid "Terminal"
msgstr ""

#. (itstool) path: sect1/para
#: C/genius.xml:9914
msgid "Terminal refers to the console in the work area."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9920
msgid "<guilabel>Scrollback lines</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9924
msgid "Lines of scrollback in the terminal."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9928
msgid "<guilabel>Font</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9932
msgid "The font to use on the terminal."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9936
msgid "<guilabel>Black on white</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9940
msgid "If to use black on white on the terminal."
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9944
msgid "<guilabel>Blinking cursor</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9948
msgid ""
"If the cursor in the terminal should blink when the terminal is in focus. "
"This can sometimes be annoying and it generates idle traffic if you are "
"using Genius remotely."
msgstr ""

#. (itstool) path: sect1/title
#: C/genius.xml:9955
msgid "Memory"
msgstr ""

#. (itstool) path: varlistentry/term
#: C/genius.xml:9958
msgid "<guilabel>Maximum number of nodes to allocate</guilabel>"
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9962
msgid ""
"Internally all data is put onto small nodes in memory. This gives a limit on "
"the maximum number of nodes to allocate for computations. This limit avoids "
"the problem of running out of memory if you do something by mistake that "
"uses too much memory, such as a recursion without end. This could slow your "
"computer and make it hard to even interrupt the program."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9970
msgid ""
"Once the limit is reached, <application>Genius Mathematics Tool</"
"application> asks if you wish to interrupt the computation or if you wish to "
"continue. If you continue, no limit is applied and it will be possible to "
"run your computer out of memory. The limit will be applied again next time "
"you execute a program or an expression on the Console regardless of how you "
"answered the question."
msgstr ""

#. (itstool) path: listitem/para
#: C/genius.xml:9978
msgid ""
"Setting the limit to zero means there is no limit to the amount of memory "
"that genius uses."
msgstr ""

#. (itstool) path: chapter/title
#: C/genius.xml:9992
msgid "About <application>Genius Mathematics Tool</application>"
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:9994
msgid ""
"<application>Genius Mathematics Tool</application> was written by Jiří "
"(George) Lebl (<email>jirka@5z.com</email>). The history of "
"<application>Genius Mathematics Tool</application> goes back to late 1997. "
"It was the first calculator program for GNOME, but it then grew beyond being "
"just a desktop calculator. To find more information about "
"<application>Genius Mathematics Tool</application>, please visit the <ulink "
"url=\"http://www.jirka.org/genius.html\" type=\"http\">Genius Web page</"
"ulink>."
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:10001
msgid ""
"To report a bug or make a suggestion regarding this application or this "
"manual, send email to me (the author) or post to the mailing list (see the "
"web page)."
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:10007
msgid ""
"This program is distributed under the terms of the GNU General Public "
"license as published by the Free Software Foundation; either version 3 of "
"the License, or (at your option) any later version. A copy of this license "
"can be found at this <ulink url=\"http://www.gnu.org/copyleft/gpl.html\" "
"type=\"http\">link</ulink>, or in the file COPYING included with the source "
"code of this program."
msgstr ""

#. (itstool) path: chapter/para
#: C/genius.xml:10014
msgid ""
"Jiří Lebl was during various parts of the development partially supported "
"for the work by NSF grants DMS 0900885, DMS 1362337, the University of "
"Illinois at Urbana-Champaign, the University of California at San Diego, the "
"University of Wisconsin-Madison, and Oklahoma State University. The software "
"has been used for both teaching and research."
msgstr ""