Singular - an open source computer algebra system https://www.singular.uni-kl.de/index.php 2022-05-13T08:53:17Z Joomla! 1.5 - Open Source Content Management 2010-01-28T16:22:26Z 2010-01-28T16:22:26Z https://www.singular.uni-kl.de/index.php/component/content/article/about-singular/singular-an-open-source-computer-algebra-system.html Administrator ederc@mathematik.uni-kl.de

<!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. It is free and open-source under the <a href="http://www.gnu.org/copyleft/gpl.html" target="_blank">GNU General Public Licence</a>.</p> <!-- >>> Articles Anywhere >>> --><p><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> provides</p> <ul> <li>highly efficient core algorithms,</li> <li>a multitude of advanced algorithms in the above fields,</li> <li>an intuitive, C-like programming language, </li> <li>easy ways to make it user-extendible through libraries, and</li> <li>a comprehensive <a href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13690&amp;Itemid=18">online manual</a> and help function.</li> </ul> <p>Its main computational objects are ideals, modules and matrices over a large number of baserings. These include</p> <ul> <li>polynomial rings over various ground fields and some rings (including the integers),</li> <li>localizations of the above,</li> <li>a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra),</li> <li>quotient rings of the above,</li> <li>tensor products of the above.</li> </ul> <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< -->'s core algorithms handle</p> <ul> <li>Gröbner resp. standard bases and free resolutions, </li> <li>polynomial factorization, </li> <li>resultants, characteristic sets, and numerical root finding.</li> </ul> <ul> </ul> <p>Its advanced algorithms, contained in currently<a href="https://www.singular.uni-kl.de/Manual/4-3-0/sing_1011.htm"> more than 90 libraries</a>, address topics such as <strong>absolute factorization</strong>, <strong>algebraic D-modules</strong>, <strong>classification of singularities</strong>, <strong>deformation theory</strong>, <strong>Gauss-Manin systems</strong>, <strong>Hamburger-Noether (Puiseux) development</strong>, <strong>invariant theory</strong>, <strong>(non-) commutative homological algebra, </strong> <strong>normalization</strong>, <strong>primary decomposition</strong>, <strong>resolution of singularities</strong>, and <strong>sheaf cohomology</strong>.</p> <p>Further functionality is obtained by combining <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> with <a href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13692&amp;Itemid=14">third-party software linked to SINGULAR</a>. This includes tools for <strong>convex geometry</strong>, <strong>tropical geometry</strong>, and <strong>visualization</strong>.</p> <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> is developed under the direction of <a href="http://www.mathematik.uni-kl.de/~decker/" target="_blank">Wolfram Decker</a>, <a href="http://www.mathematik.uni-kl.de/~greuel/en/" target="_blank">Gert-Martin Greuel</a>, <a href="http://www.mathematik.uni-kl.de/~pfister/en/" target="_blank">Gerhard Pfister</a>, and <a href="http://www.mathematik.uni-kl.de/~hannes/en/" target="_blank">Hans Schönemann</a> who head  <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< -->'s core development team within the <a href="http://www.mathematik.uni-kl.de" target="_blank">Department of Mathematics</a> of the <a href="http://www.uni-kl.de" target="_blank">University of Kaiserslautern</a>.</p> <p> </p> <ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13688:funding&amp;Itemid=69">Funding</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13687:jenks-prize&amp;Itemid=69">Jenks Prize</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13681:history&amp;Itemid=69">History</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13730:acknowledgements&amp;Itemid=69">Acknowledgements</a></li> <br /></ol> <p> </p> <ol style="list-style-type: none;"> </ol>

<!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. It is free and open-source under the <a href="http://www.gnu.org/copyleft/gpl.html" target="_blank">GNU General Public Licence</a>.</p> <!-- >>> Articles Anywhere >>> --><p><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> provides</p> <ul> <li>highly efficient core algorithms,</li> <li>a multitude of advanced algorithms in the above fields,</li> <li>an intuitive, C-like programming language, </li> <li>easy ways to make it user-extendible through libraries, and</li> <li>a comprehensive <a href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13690&amp;Itemid=18">online manual</a> and help function.</li> </ul> <p>Its main computational objects are ideals, modules and matrices over a large number of baserings. These include</p> <ul> <li>polynomial rings over various ground fields and some rings (including the integers),</li> <li>localizations of the above,</li> <li>a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra),</li> <li>quotient rings of the above,</li> <li>tensor products of the above.</li> </ul> <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< -->'s core algorithms handle</p> <ul> <li>Gröbner resp. standard bases and free resolutions, </li> <li>polynomial factorization, </li> <li>resultants, characteristic sets, and numerical root finding.</li> </ul> <ul> </ul> <p>Its advanced algorithms, contained in currently<a href="https://www.singular.uni-kl.de/Manual/4-3-0/sing_1011.htm"> more than 90 libraries</a>, address topics such as <strong>absolute factorization</strong>, <strong>algebraic D-modules</strong>, <strong>classification of singularities</strong>, <strong>deformation theory</strong>, <strong>Gauss-Manin systems</strong>, <strong>Hamburger-Noether (Puiseux) development</strong>, <strong>invariant theory</strong>, <strong>(non-) commutative homological algebra, </strong> <strong>normalization</strong>, <strong>primary decomposition</strong>, <strong>resolution of singularities</strong>, and <strong>sheaf cohomology</strong>.</p> <p>Further functionality is obtained by combining <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> with <a href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13692&amp;Itemid=14">third-party software linked to SINGULAR</a>. This includes tools for <strong>convex geometry</strong>, <strong>tropical geometry</strong>, and <strong>visualization</strong>.</p> <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< --> is developed under the direction of <a href="http://www.mathematik.uni-kl.de/~decker/" target="_blank">Wolfram Decker</a>, <a href="http://www.mathematik.uni-kl.de/~greuel/en/" target="_blank">Gert-Martin Greuel</a>, <a href="http://www.mathematik.uni-kl.de/~pfister/en/" target="_blank">Gerhard Pfister</a>, and <a href="http://www.mathematik.uni-kl.de/~hannes/en/" target="_blank">Hans Schönemann</a> who head  <!-- >>> Articles Anywhere >>> --><span style="font-variant: small-caps; font-weight:bold;">Singular</span><!-- <<< Articles Anywhere <<< -->'s core development team within the <a href="http://www.mathematik.uni-kl.de" target="_blank">Department of Mathematics</a> of the <a href="http://www.uni-kl.de" target="_blank">University of Kaiserslautern</a>.</p> <p> </p> <ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13688:funding&amp;Itemid=69">Funding</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13687:jenks-prize&amp;Itemid=69">Jenks Prize</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13681:history&amp;Itemid=69">History</a></li> </ol><ol style="list-style-type: none;"> <li style="float:left;"><a class="wanted" href="https://www.singular.uni-kl.de/index.php?option=com_content&amp;view=article&amp;id=13730:acknowledgements&amp;Itemid=69">Acknowledgements</a></li> <br /></ol> <p> </p> <ol style="list-style-type: none;"> </ol>