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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Genius Manual</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><meta name="description" content="Manual for the Genius Math Tool."><link rel="home" href="index.html" title="Genius Manual"><link rel="next" href="ch01.html" title="Chapter 1. Introduction"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Genius Manual</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="ch01.html">Next</a></td></tr></table><hr></div><div lang="en" class="book"><div class="titlepage"><div><div><h1 class="title"><a name="index"></a>Genius Manual</h1></div><div><div class="authorgroup"><div class="author"><h3 class="author"><span class="firstname">Jiří</span> <span class="surname">Lebl</span></h3><div class="affiliation"><span class="orgname">Oklahoma State University<br></span><div class="address"><p> <code class="email">&lt;<a class="email" href="mailto:jiri.lebl@gmail.com">jiri.lebl@gmail.com</a>&gt;</code> </p></div></div></div><div class="author"><h3 class="author"><span class="firstname">Kai</span> <span class="surname">Willadsen</span></h3><div class="affiliation"><span class="orgname">University of Queensland, Australia<br></span><div class="address"><p> <code class="email">&lt;<a class="email" href="mailto:kaiw@itee.uq.edu.au">kaiw@itee.uq.edu.au</a>&gt;</code> </p></div></div></div></div></div><div><p class="releaseinfo">This manual describes version 1.0.27 of Genius.
    </p></div><div><p class="copyright">Copyright © 1997-2021 Jiří (George) Lebl</p></div><div><p class="copyright">Copyright © 2004 Kai Willadsen</p></div><div><div class="legalnotice"><a name="legalnotice"></a><p>
	  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 <a class="ulink" href="ghelp:fdl" target="_top">link</a> or in the file COPYING-DOCS
	  distributed with this manual.
         </p><p> 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.
	</p><p>
	  Many of the names used by companies to distinguish their
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	  the GNOME Documentation Project are made aware of those
	  trademarks, then the names are in capital letters or initial
	  capital letters.
	</p><p>
	  DOCUMENT AND MODIFIED VERSIONS OF THE DOCUMENT ARE PROVIDED
	  UNDER  THE TERMS OF THE GNU FREE DOCUMENTATION LICENSE
	  WITH THE FURTHER UNDERSTANDING THAT:

	  </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>DOCUMENT IS PROVIDED ON AN "AS IS" BASIS,
                    WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR
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	</p></div></div><div><div class="legalnotice"><a name="idm48"></a><p class="legalnotice-title"><b>Feedback</b></p><p>
	      To report a bug or make a suggestion regarding the <span class="application">Genius Mathematics Tool</span>
	      application or this manual, please visit the
	      <a class="ulink" href="http://www.jirka.org/genius.html" target="_top">Genius
		      Web page</a>
	      or email me at <code class="email">&lt;<a class="email" href="mailto:jiri.lebl@gmail.com">jiri.lebl@gmail.com</a>&gt;</code>.
      </p></div></div><div><div class="revhistory"><table style="border-style:solid; width:100%;" summary="Revision History"><tr><th align="left" valign="top" colspan="2"><b>Revision History</b></th></tr><tr><td align="left">Revision 0.2</td><td align="left">October 2021</td></tr><tr><td align="left" colspan="2"> 
	  		<p class="author">Jiri (George) Lebl
	    	<code class="email">&lt;<a class="email" href="mailto:jiri.lebl@gmail.com">jiri.lebl@gmail.com</a>&gt;</code>
	  		</p>
		</td></tr></table></div></div><div><div class="abstract"><p class="title"><b>Abstract</b></p><p>Manual for the Genius Math Tool.</p></div></div></div><hr></div><div class="toc"><p><b>Table of Contents</b></p><dl class="toc"><dt><span class="chapter"><a href="ch01.html">1. Introduction</a></span></dt><dt><span class="chapter"><a href="ch02.html">2. Getting Started</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch02.html#genius-to-start">To Start <span class="application">Genius Mathematics Tool</span></a></span></dt><dt><span class="sect1"><a href="ch02s02.html">When You Start Genius</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch03.html">3. Basic Usage</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch03.html#genius-usage-workarea">Using the Work Area</a></span></dt><dt><span class="sect1"><a href="ch03s02.html">To Create a New Program </a></span></dt><dt><span class="sect1"><a href="ch03s03.html">To Open and Run a Program </a></span></dt></dl></dd><dt><span class="chapter"><a href="ch04.html">4. Plotting</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch04.html#genius-line-plots">Line Plots</a></span></dt><dt><span class="sect1"><a href="ch04s02.html">Parametric Plots</a></span></dt><dt><span class="sect1"><a href="ch04s03.html">Slopefield Plots</a></span></dt><dt><span class="sect1"><a href="ch04s04.html">Vectorfield Plots</a></span></dt><dt><span class="sect1"><a href="ch04s05.html">Surface Plots</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch05.html">5. GEL Basics</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch05.html#genius-gel-values">Values</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05.html#genius-gel-values-numbers">Numbers</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-booleans">Booleans</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-strings">Strings</a></span></dt><dt><span class="sect2"><a href="ch05.html#genius-gel-values-null">Null</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s02.html">Using Variables</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-setting">Setting Variables</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-variables-built-in">Built-in Variables</a></span></dt><dt><span class="sect2"><a href="ch05s02.html#genius-gel-previous-result">Previous Result Variable</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s03.html">Using Functions</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-defining">Defining Functions</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-variable-argument-lists">Variable Argument Lists</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-passing-functions">Passing Functions to Functions</a></span></dt><dt><span class="sect2"><a href="ch05s03.html#genius-gel-functions-operations">Operations on Functions</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch05s04.html">Separator</a></span></dt><dt><span class="sect1"><a href="ch05s05.html">Comments</a></span></dt><dt><span class="sect1"><a href="ch05s06.html">Modular Evaluation</a></span></dt><dt><span class="sect1"><a href="ch05s07.html">List of GEL Operators</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch06.html">6. Programming with GEL</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch06.html#genius-gel-conditionals">Conditionals</a></span></dt><dt><span class="sect1"><a href="ch06s02.html">Loops</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch06s02.html#genius-gel-loops-while">While Loops</a></span></dt><dt><span class="sect2"><a href="ch06s02.html#genius-gel-loops-for">For Loops</a></span></dt><dt><span class="sect2"><a href="ch06s02.html#genius-gel-loops-foreach">Foreach Loops</a></span></dt><dt><span class="sect2"><a href="ch06s02.html#genius-gel-loops-break-continue">Break and Continue</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch06s03.html">Sums and Products</a></span></dt><dt><span class="sect1"><a href="ch06s04.html">Comparison Operators</a></span></dt><dt><span class="sect1"><a href="ch06s05.html">Global Variables and Scope of Variables</a></span></dt><dt><span class="sect1"><a href="ch06s06.html">Parameter variables</a></span></dt><dt><span class="sect1"><a href="ch06s07.html">Returning</a></span></dt><dt><span class="sect1"><a href="ch06s08.html">References</a></span></dt><dt><span class="sect1"><a href="ch06s09.html">Lvalues</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch07.html">7. Advanced Programming with GEL</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch07.html#genius-gel-error-handling">Error Handling</a></span></dt><dt><span class="sect1"><a href="ch07s02.html">Toplevel Syntax</a></span></dt><dt><span class="sect1"><a href="ch07s03.html">Returning Functions</a></span></dt><dt><span class="sect1"><a href="ch07s04.html">True Local Variables</a></span></dt><dt><span class="sect1"><a href="ch07s05.html">GEL Startup Procedure</a></span></dt><dt><span class="sect1"><a href="ch07s06.html">Loading Programs</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch08.html">8. Matrices in GEL</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch08.html#genius-gel-matrix-support">Entering Matrices</a></span></dt><dt><span class="sect1"><a href="ch08s02.html">Conjugate Transpose and Transpose Operator</a></span></dt><dt><span class="sect1"><a href="ch08s03.html">Linear Algebra</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch09.html">9. Polynomials in GEL</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch09.html#genius-gel-polynomials-using">Using Polynomials</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch10.html">10. Set Theory in GEL</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch10.html#genius-gel-sets-using">Using Sets</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch11.html">11. List of GEL functions</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch11.html#genius-gel-function-list-commands">Commands</a></span></dt><dt><span class="sect1"><a href="ch11s02.html">Basic</a></span></dt><dt><span class="sect1"><a href="ch11s03.html">Parameters</a></span></dt><dt><span class="sect1"><a href="ch11s04.html">Constants</a></span></dt><dt><span class="sect1"><a href="ch11s05.html">Numeric</a></span></dt><dt><span class="sect1"><a href="ch11s06.html">Trigonometry</a></span></dt><dt><span class="sect1"><a href="ch11s07.html">Number Theory</a></span></dt><dt><span class="sect1"><a href="ch11s08.html">Matrix Manipulation</a></span></dt><dt><span class="sect1"><a href="ch11s09.html">Linear Algebra</a></span></dt><dt><span class="sect1"><a href="ch11s10.html">Combinatorics</a></span></dt><dt><span class="sect1"><a href="ch11s11.html">Calculus</a></span></dt><dt><span class="sect1"><a href="ch11s12.html">Functions</a></span></dt><dt><span class="sect1"><a href="ch11s13.html">Equation Solving</a></span></dt><dt><span class="sect1"><a href="ch11s14.html">Statistics</a></span></dt><dt><span class="sect1"><a href="ch11s15.html">Polynomials</a></span></dt><dt><span class="sect1"><a href="ch11s16.html">Set Theory</a></span></dt><dt><span class="sect1"><a href="ch11s17.html">Commutative Algebra</a></span></dt><dt><span class="sect1"><a href="ch11s18.html">Miscellaneous</a></span></dt><dt><span class="sect1"><a href="ch11s19.html">Symbolic Operations</a></span></dt><dt><span class="sect1"><a href="ch11s20.html">Plotting</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch12.html">12. Example Programs in GEL</a></span></dt><dt><span class="chapter"><a href="ch13.html">13. Settings</a></span></dt><dd><dl><dt><span class="sect1"><a href="ch13.html#genius-prefs-output">Output</a></span></dt><dt><span class="sect1"><a href="ch13s02.html">Precision</a></span></dt><dt><span class="sect1"><a href="ch13s03.html">Terminal</a></span></dt><dt><span class="sect1"><a href="ch13s04.html">Memory</a></span></dt></dl></dd><dt><span class="chapter"><a href="ch14.html">14. About <span class="application">Genius Mathematics Tool</span></a></span></dt></dl></div><div class="list-of-figures"><p><b>List of Figures</b></p><dl><dt>2.1. <a href="ch02s02.html#mainwindow-fig"><span class="application">Genius Mathematics Tool</span> Window</a></dt><dt>4.1. <a href="ch04.html#lineplot-fig">Create Plot Window</a></dt><dt>4.2. <a href="ch04.html#lineplot2-fig">Plot Window</a></dt><dt>4.3. <a href="ch04s02.html#paramplot-fig">Parametric Plot Tab</a></dt><dt>4.4. <a href="ch04s02.html#paramplot2-fig">Parametric Plot</a></dt><dt>4.5. <a href="ch04s05.html#surfaceplot-fig">Surface Plot</a></dt></dl></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="ch01.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top"> </td><td width="20%" align="center"> </td><td width="40%" align="right" valign="top"> Chapter 1. Introduction</td></tr></table></div></body></html>