msgid ""
msgstr ""
"Project-Id-Version: PACKAGE VERSION\n"
"POT-Creation-Date: 2024-02-20 21:27+0000\n"
"PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n"
"Last-Translator: FULL NAME <EMAIL@ADDRESS>\n"
"Language-Team: LANGUAGE <LL@li.org>\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\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 ""