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features.html
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<!DOCTYPE html>
<html lang="en" data-content_root="./">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Features — FriCAS</title>
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
<link rel="stylesheet" type="text/css" href="_static/classic.css?v=514cf933" />
<link rel="stylesheet" href="_static/style.css" type="text/css" />
<script src="_static/documentation_options.js?v=a44cb687"></script>
<script src="_static/doctools.js?v=888ff710"></script>
<script src="_static/sphinx_highlight.js?v=dc90522c"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Download" href="download.html" />
<link rel="prev" title="ZeroDimensionalSolvePackage(R, ls, ls2)" href="api/ZeroDimensionalSolvePackage.html" />
</head><body>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="download.html" title="Download"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="api/ZeroDimensionalSolvePackage.html" title="ZeroDimensionalSolvePackage(R, ls, ls2)"
accesskey="P">previous</a> |</li>
<li class="nav-item nav-item-0"><a href="index.html">FriCAS</a> »</li>
<li class="nav-item nav-item-this"><a href="">Features</a></li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<section id="features">
<h1>Features<a class="headerlink" href="#features" title="Link to this heading">¶</a></h1>
<p>The capabilities of <a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a> cover areas such as</p>
<ul class="simple">
<li><p>linear, polynomial and differential system solving</p></li>
<li><p>integration (most complete implementation of the
<a class="reference external" href="https://en.wikipedia.org/wiki/Risch_algorithm">Risch algorithm</a>)</p></li>
<li><p>vector, matrix, and tensor calculus, eigenvalues, eigenvectors,</p></li>
<li><p>symbolic expression manipulation,</p></li>
<li><p>non-commutative polynomials</p></li>
<li><p>limit calculation,</p></li>
<li><p>arithmetic with Taylor, Laurent, and Puiseux series,</p></li>
<li><p>combinatorics, symmetric polynomials, special functions, number
theory,</p></li>
<li><p>arbitrary precision numerical computations,</p></li>
<li><p>modular arithmetic,</p></li>
<li><p>continued fractions, partial fraction decomposition,</p></li>
<li><p>integer factorization, polynomial factorization,</p></li>
<li><p>polynomial ideals, Gröbner bases, Gröbner factorization,
triangular sets, regular chains,</p></li>
<li><p>guessing of formulas for sequences,</p></li>
<li><p>computation with cardinal numbers.</p></li>
</ul>
<p>A distinguished feature of <a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a> is its type system. It
allows to create and compute with domains such as matrices of
polynomials over finite fields or polynomials having square matrices
with rational entries as their coefficient ring.</p>
<p>FriCAS provides structures such as</p>
<ul class="simple">
<li><p>complex numbers, quaternions, octonions,</p></li>
<li><p>groups, rings, fields, algebraic extension rings,</p></li>
<li><p>modules, (graded) algebras, finite fields,</p></li>
<li><p>non-commutative and non-associative algebras,</p></li>
<li><p>Clifford algebras, exterior algebras,</p></li>
</ul>
<p>The type system of <a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a> is based on its statically typed
programming language (<a class="reference external" href="http://wiki.fricas.org/ProgrammingSPAD">SPAD</a>).</p>
<p><a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a> can be extend by programs written in <a class="reference external" href="http://wiki.fricas.org/ProgrammingSPAD">SPAD</a> that are compiled
to machine code in the same way as the algebra library that comes with
<a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a>.</p>
<p>In a <a class="reference external" href="https://fricas.github.io/index.html">FriCAS</a> session the type system is somewhat relaxed.
Although underneath everything is computed with a specific type,
the interpreter tries to figure out in many cases what the best way is
to convert the user input into an appropriate type. Should the
interpreter fail to guess correctly, users can always specify the
types that they want.</p>
</section>
<div class="clearer"></div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="index.html">Table of Contents</a></h3>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="api/index.html">FriCAS API</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Features</a></li>
<li class="toctree-l1"><a class="reference internal" href="download.html">Download</a></li>
<li class="toctree-l1"><a class="reference internal" href="help.html">Help</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="development.html">Development</a></li>
<li class="toctree-l1"><a class="reference internal" href="citation.html">Citation</a></li>
<li class="toctree-l1"><a class="reference internal" href="history.html">History</a></li>
</ul>
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="_sources/features.rst.txt"
rel="nofollow">Show Source</a></li>
<li><a href="https://github.com/fricas/fricas/blob/master/src/doc/sphinx/source/features.rst"
rel="nofollow">Show on GitHub</a></li>
<li><a href="https://github.com/fricas/fricas/edit/master/src/doc/sphinx/source/features.rst"
rel="nofollow">Edit on GitHub</a></li>
</ul>
<div id="searchbox" style="display: none" role="search">
<h3 id="searchlabel">Quick search</h3>
<div class="searchformwrapper">
<form class="search" action="search.html" method="get">
<input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
<input type="submit" value="Go" />
</form>
</div>
</div>
<script>document.getElementById('searchbox').style.display = "block"</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="download.html" title="Download"
>next</a> |</li>
<li class="right" >
<a href="api/ZeroDimensionalSolvePackage.html" title="ZeroDimensionalSolvePackage(R, ls, ls2)"
>previous</a> |</li>
<li class="nav-item nav-item-0"><a href="index.html">FriCAS</a> »</li>
<li class="nav-item nav-item-this"><a href="">Features</a></li>
</ul>
</div>
<div class="footer" role="contentinfo">
© Copyright 2007-2024, FriCAS Team.
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</body>
</html>