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<h1>singular</h1>


<h2>A <strong class="pkg">GAP</strong> interface to Singular</h2>

<p>
    2025.08.26</p>

<p>
    26 August 2025
  </p>

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<p><b>
    Marco Costantini

  </b>
</p><p><b>
    Willem Adriaan de Graaf




  </b>
<br />Email: <span class="URL"><a href="mailto:degraaf@science.unitn.it">degraaf@science.unitn.it</a></span>
<br />Homepage: <span class="URL"><a href="https://www.science.unitn.it/~degraaf/">https://www.science.unitn.it/~degraaf/</a></span>
<br />Address: <br />Willem de Graaf<br /> Dipartimento di Matematica<br /> Università degli Studi di Trento<br /> I-38050 Povo (Trento)<br /> Italy<br />
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<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X861CFE957DD2453F">1 <span class="Heading"><strong class="pkg">singular</strong>: 
the <strong class="pkg">GAP</strong> interface to <strong class="pkg">Singular</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7DFB63A97E67C0A1">1.1 <span class="Heading">Introduction</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FE24D6E8258CC49">1.1-1 <span class="Heading">Package evolution</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83FD5A2A8047C857">1.1-2 <span class="Heading">The system <strong class="pkg">Singular</strong></span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X783E6C90833FAA5F">1.1-3 <span class="Heading">The system <strong class="pkg">GAP</strong></span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8360C04082558A12">1.2 <span class="Heading">Installation</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7909A9237804CDCE">1.2-1 <span class="Heading">Installing the system
<strong class="pkg">Singular</strong></span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8158504779874284">1.2-2 <span class="Heading">Installing the system <strong class="pkg">GAP</strong></span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AC4165B7843F037">1.2-3 <span class="Heading">Installing the package
<strong class="pkg">singular</strong></span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8229A3C4793932BA">1.2-4 sing_exec</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7E8229C88005E2EA">1.3 <span class="Heading">Interaction with
<strong class="pkg">Singular</strong></span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79C5E6F27C37DA10">1.3-1 StartSingular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81FDDDE47EBA9698">1.3-2 SingularHelp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86C329A285955655">1.3-3 <span class="Heading">Rings and orderings</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X840BA4C9839D3CF4">1.3-4 <span class="Heading">Supported coefficients fields</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X813A17AF85BFACB9">1.3-5 SetTermOrdering</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84A3CD498011A10C">1.3-6 SingularSetBaseRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X871A5AF87DAE21E6">1.3-7 SingularLibrary</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X876BA78F7CF049C3">1.3-8 SingularInterface</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79B84D5C7AC98756">1.3-9 SingularType</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X874F7C2F7CF4192E">1.4 <span class="Heading">Interaction with
<strong class="pkg">Singular</strong> at low level</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85EEFDDE8111A67B">1.4-1 SingularCommand</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B8471948055DD90">1.4-2 GapInterface</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X82726C947AFEC357">1.5 <span class="Heading">Other mathematical functions of the package</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A43611E876B7560">1.5-1 GroebnerBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A594BFA7B521F98">1.5-2 SINGULARGBASIS</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83668E317A047D24">1.5-3 HasTrivialGroebnerBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X877960128076E656">1.5-4 GcdUsingSingular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84AC005C837CE13C">1.5-5 FactorsUsingSingularNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87A0E69B81E52AA2">1.5-6 FactorsUsingSingular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EAC34C984599470">1.5-7 GeneratorsOfInvariantRing</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7E4CD3FF8230789C">1.6 <span class="Heading">Algebraic-geometric codes functions</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80553C51807FA705">1.6-1 AllPointsOnCurve</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78E2235083D9FDCC">1.6-2 AGCode</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8562222580239DA6">1.7 <span class="Heading">Troubleshooting and technical stuff</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C1724F780B84A6C">1.7-1 <span class="Heading">Supported platforms and underlying <strong class="pkg">GAP</strong> functions</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82CDC01B7AABF5F5">1.7-2 <span class="Heading">How different versions of <strong class="pkg">GAP</strong> display polynomial rings and polynomials</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DE6DC637A7FAC93">1.7-3 <span class="Heading">Test file</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82260C8E82090E87">1.7-4 <span class="Heading">Common problems</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D38248D79425B28">1.7-5 <span class="Heading">Errors on the <strong class="pkg">Singular</strong> side</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C8AE6BD787CD237">1.7-6 <span class="Heading">Sending a report</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78BE74C97BF4E287">1.7-7 SingularReportInformation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X843C50B18098609A">1.7-8 InfoSingular</a></span>
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<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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