SSL chap1.html

Interaktion und
PortierbarkeitHTML

products/Sources/formale Sprachen/GAP/pkg/ringsforhomalg/doc/chap1.html

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<title>GAP (RingsForHomalg) - Chapter 1: Introduction</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap1" onload="jscontent()">

<div class="chlinktop">Goto Chapter: <a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#contents">[Contents]</a> <a href="chap0.html">[Previous Chapter]</a> <a href="chap2.html">[Next Chapter]</a> </div>

<a href="chap1_mj.html">[MathJax on]</a>
<a id="X7DFB63A97E67C0A1" name="X7DFB63A97E67C0A1"></a>
<div class="ChapSects"><a href="chap1.html#X7DFB63A97E67C0A1">1 Introduction</a>
<div class="ContSect"> <a href="chap1.html#X7B818AF0834AE510">1.1 Ring Constructions for Supported External Computer Algebra Systems</a>

<div class="ContSSBlock">
 <a href="chap1.html#X827FA5FD7CBEE73C">1.1-1 external GAP</a>

 <a href="chap1.html#X840A7A5D7AE407F2">1.1-2 Singular</a>

 <a href="chap1.html#X839147CF813312D6">1.1-3 MAGMA</a>

 <a href="chap1.html#X83D66E0279CF39E6">1.1-4 Macaulay2</a>

 <a href="chap1.html#X7A9D29E187AA3F83">1.1-5 Sage</a>

 <a href="chap1.html#X83E0B3C584764593">1.1-6 Maple</a>

</div></div>
</div>

<h3>1 Introduction</h3>

This package is part of the homalg project <a href="chapBib.html#biBhomalg-project">[tpa22]</a>. The role of the package is described in the manual of the homalg package.

<a id="X7B818AF0834AE510" name="X7B818AF0834AE510"></a>

<h4>1.1 Ring Constructions for Supported External Computer Algebra Systems</h4>

Here are some of the supported ring constructions:

<a id="X827FA5FD7CBEE73C" name="X827FA5FD7CBEE73C"></a>

<h5>1.1-1 external GAP</h5>

<div class="example"><pre>
gap> zz := HomalgRingOfIntegersInExternalGAP( );
Z
gap> Display( zz );
<An external ring residing in the CAS GAP>
gap> F2 := HomalgRingOfIntegersInExternalGAP( 2, zz );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS GAP>
</pre></div>

<code class="code">F2 := HomalgRingOfIntegersInExternalGAP( 2 )</code> would launch another GAP.

<div class="example"><pre>
gap> Z4 := HomalgRingOfIntegersInExternalGAP( 4, zz );
Z/4Z
gap> Display( Z4 );
<An external ring residing in the CAS GAP>
gap> Z_4 := HomalgRingOfIntegersInExternalGAP( zz ) / 4;
Z/( 4 )
gap> Display( Z_4 );
<A residue class ring>
gap> Q := HomalgFieldOfRationalsInExternalGAP( zz );
Q
gap> Display( Q );
<An external ring residing in the CAS GAP>
</pre></div>

<a id="X840A7A5D7AE407F2" name="X840A7A5D7AE407F2"></a>

<h5>1.1-2 Singular</h5>

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Singular ).stdout )
gap> F2 := HomalgRingOfIntegersInSingular( 2 );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS Singular>
gap> F2s := HomalgRingOfIntegersInSingular( 2, "s" ,F2 );
GF(2)(s)
gap> Display( F2s );
<An external ring residing in the CAS Singular>
gap> zz := HomalgRingOfIntegersInSingular( F2 );
Z
gap> Display( zz );
<An external ring residing in the CAS Singular>
gap> Q := HomalgFieldOfRationalsInSingular( F2 );
Q
gap> Display( Q );
<An external ring residing in the CAS Singular>
gap> Qs := HomalgFieldOfRationalsInSingular( "s", F2 );
Q(s)
gap> Display( Qs );
<An external ring residing in the CAS Singular>
gap> Qi := HomalgFieldOfRationalsInSingular( "i", "i^2+1", Q );
Q[i]/(i^2+1)
gap> Display( Qi );
<An external ring residing in the CAS Singular>
#@fi
</pre></div>

<code class="code">Q := HomalgFieldOfRationalsInSingular( )</code> would launch another Singular.

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Singular ).stdout )
gap> F2xyz := F2 * "x,y,z";
GF(2)[x,y,z]
gap> Display( F2xyz );
<An external ring residing in the CAS Singular>
gap> F2sxyz := F2s * "x,y,z";
GF(2)(s)[x,y,z]
gap> Display( F2sxyz );
<An external ring residing in the CAS Singular>
gap> F2xyzw := F2xyz * "w";
GF(2)[x,y,z][w]
gap> Display( F2xyzw );
<An external ring residing in the CAS Singular>
gap> F2sxyzw := F2sxyz * "w";
GF(2)(s)[x,y,z][w]
gap> Display( F2sxyzw );
<An external ring residing in the CAS Singular>
gap> zzxyz := zz * "x,y,z";
Z[x,y,z]
gap> Display( zzxyz );
<An external ring residing in the CAS Singular>
gap> zzxyzw := zzxyz * "w";
Z[x,y,z][w]
gap> Display( zzxyzw );
<An external ring residing in the CAS Singular>
gap> Qxyz := Q * "x,y,z";
Q[x,y,z]
gap> Display( Qxyz );
<An external ring residing in the CAS Singular>
gap> Qsxyz := Qs * "x,y,z";
Q(s)[x,y,z]
gap> Display( Qsxyz );
<An external ring residing in the CAS Singular>
gap> Qixyz := Qi * "x,y,z";
(Q[i]/(i^2+1))[x,y,z]
gap> Display( Qixyz );
<An external ring residing in the CAS Singular>
gap> Qxyzw := Qxyz * "w";
Q[x,y,z][w]
gap> Display( Qxyzw );
<An external ring residing in the CAS Singular>
gap> Qsxyzw := Qsxyz * "w";
Q(s)[x,y,z][w]
gap> Display( Qsxyzw );
<An external ring residing in the CAS Singular>
gap> Dxyz := RingOfDerivations( Qxyz, "Dx,Dy,Dz" );
Q[x,y,z]<Dx,Dy,Dz>
gap> Display( Dxyz );
<An external ring residing in the CAS Singular>
gap> Exyz := ExteriorRing( Qxyz, "e,f,g" );
Q{e,f,g}
gap> Display( Exyz );
<An external ring residing in the CAS Singular>
gap> Dsxyz := RingOfDerivations( Qsxyz, "Dx,Dy,Dz" );
Q(s)[x,y,z]<Dx,Dy,Dz>
gap> Display( Dsxyz );
<An external ring residing in the CAS Singular>
gap> Esxyz := ExteriorRing( Qsxyz, "e,f,g" );
Q(s){e,f,g}
gap> Display( Esxyz );
<An external ring residing in the CAS Singular>
gap> Dixyz := RingOfDerivations( Qixyz, "Dx,Dy,Dz" );
(Q[i]/(i^2+1))[x,y,z]<Dx,Dy,Dz>
gap> Display( Dixyz );
<An external ring residing in the CAS Singular>
gap> Eixyz := ExteriorRing( Qixyz, "e,f,g" );
(Q[i]/(i^2+1)){e,f,g}
gap> Display( Eixyz );
<An external ring residing in the CAS Singular>
gap> qring := HomalgQRingInSingular( Qxyz, "x*y" );
Q[x,y,z]/( x*y )
gap> Display( qring );
<An external ring residing in the CAS Singular>
gap> "z + x*y" / qring = "z" / qring;
true
#@fi
</pre></div>

<a id="X839147CF813312D6" name="X839147CF813312D6"></a>

<h5>1.1-3 MAGMA</h5>

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_MAGMA ).stdout )
gap> zz := HomalgRingOfIntegersInMAGMA( );
Z
gap> Display( zz );
<An external ring residing in the CAS MAGMA>
gap> F2 := HomalgRingOfIntegersInMAGMA( 2, zz );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS MAGMA>
#@fi
</pre></div>

<code class="code">F2 := HomalgRingOfIntegersInMAGMA( 2 )</code> would launch another MAGMA.

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_MAGMA ).stdout )
gap> Z_4 := HomalgRingOfIntegersInMAGMA( zz ) / 4;
Z/( 4 )
gap> Display( Z_4 );
<A residue class ring>
gap> Q := HomalgFieldOfRationalsInMAGMA( zz );
Q
gap> Display( Q );
<An external ring residing in the CAS MAGMA>
gap> F2xyz := F2 * "x,y,z";
GF(2)[x,y,z]
gap> Display( F2xyz );
<An external ring residing in the CAS MAGMA>
gap> Qxyz := Q * "x,y,z";
Q[x,y,z]
gap> Display( Qxyz );
<An external ring residing in the CAS MAGMA>
gap> Exyz := ExteriorRing( Qxyz, "e,f,g" );
Q{e,f,g}
gap> Display( Exyz );
<An external ring residing in the CAS MAGMA>
#@fi
</pre></div>

<a id="X83D66E0279CF39E6" name="X83D66E0279CF39E6"></a>

<h5>1.1-4 Macaulay2</h5>

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Macaulay2 ).stdout )
gap> zz := HomalgRingOfIntegersInMacaulay2( );
Z
gap> Display( zz );
<An external ring residing in the CAS Macaulay2>
gap> F2 := HomalgRingOfIntegersInMacaulay2( 2, zz );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS Macaulay2>
#@fi
</pre></div>

<code class="code">F2 := HomalgRingOfIntegersInMacaulay2( 2 )</code> would launch another Macaulay2.

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Macaulay2 ).stdout )
gap> Z_4 := HomalgRingOfIntegersInMacaulay2( zz ) / 4;
Z/( 4 )
gap> Display( Z_4 );
<A residue class ring>
gap> Q := HomalgFieldOfRationalsInMacaulay2( zz );
Q
gap> Display( Q );
<An external ring residing in the CAS Macaulay2>
gap> F2xyz := F2 * "x,y,z";
GF(2)[x,y,z]
gap> Display( F2xyz );
<An external ring residing in the CAS Macaulay2>
gap> Qxyz := Q * "x,y,z";
Q[x,y,z]
gap> Display( Qxyz );
<An external ring residing in the CAS Macaulay2>
gap> Dxyz := RingOfDerivations( Qxyz, "Dx,Dy,Dz" );
Q[x,y,z]<Dx,Dy,Dz>
gap> Display( Dxyz );
<An external ring residing in the CAS Macaulay2>
gap> Exyz := ExteriorRing( Qxyz, "e,f,g" );
Q{e,f,g}
gap> Display( Exyz );
<An external ring residing in the CAS Macaulay2>
#@fi
</pre></div>

<a id="X7A9D29E187AA3F83" name="X7A9D29E187AA3F83"></a>

<h5>1.1-5 Sage</h5>

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Sage ).stdout )
gap> zz := HomalgRingOfIntegersInSage( );
Z
gap> Display( zz );
<An external ring residing in the CAS Sage>
gap> F2 := HomalgRingOfIntegersInSage( 2, zz );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS Sage>
#@fi
</pre></div>

<code class="code">F2 := HomalgRingOfIntegersInSage( 2 )</code> would launch another Sage.

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Sage ).stdout )
gap> Z_4 := HomalgRingOfIntegersInSage( zz ) / 4;
Z/( 4 )
gap> Display( Z_4 );
<A residue class ring>
gap> Q := HomalgFieldOfRationalsInSage( zz );
Q
gap> Display( Q );
<An external ring residing in the CAS Sage>
gap> F2x := F2 * "x";
GF(2)[x]
gap> Display( F2x );
<An external ring residing in the CAS Sage>
gap> Qx := Q * "x";
Q[x]
gap> Display( Qx );
<An external ring residing in the CAS Sage>
#@fi
</pre></div>

<a id="X83E0B3C584764593" name="X83E0B3C584764593"></a>

<h5>1.1-6 Maple</h5>

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Maple ).stdout )
gap> zz := HomalgRingOfIntegersInMaple( );
Z
gap> Display( zz );
<An external ring residing in the CAS Maple>
gap> F2 := HomalgRingOfIntegersInMaple( 2, zz );
GF(2)
gap> Display( F2 );
<An external ring residing in the CAS Maple>
#@fi
</pre></div>

<code class="code">F2 := HomalgRingOfIntegersInMaple( 2 )</code> would launch another Maple.

<div class="example"><pre>
#@if IsBound( TryLaunchCAS_IO_ForHomalg( HOMALG_IO_Maple ).stdout )
gap> Z4 := HomalgRingOfIntegersInMaple( 4, zz );
Z/4Z
gap> Display( Z4 );
<An external ring residing in the CAS Maple>
gap> Z_4 := HomalgRingOfIntegersInMaple( zz ) / 4;
Z/( 4 )
gap> Display( Z_4 );
<A residue class ring>
gap> Q := HomalgFieldOfRationalsInMaple( zz );
Q
gap> Display( Q );
<An external ring residing in the CAS Maple>
gap> F2xyz := F2 * "x,y,z";
GF(2)[x,y,z]
gap> Display( F2xyz );
<An external ring residing in the CAS Maple>
gap> Qxyz := Q * "x,y,z";
Q[x,y,z]
gap> Display( Qxyz );
<An external ring residing in the CAS Maple>
gap> Dxyz := RingOfDerivations( Qxyz, "Dx,Dy,Dz" );
Q[x,y,z]<Dx,Dy,Dz>
gap> Display( Dxyz );
<An external ring residing in the CAS Maple>
gap> Exyz := ExteriorRing( Qxyz, "e,f,g" );
Q{e,f,g}
gap> Display( Exyz );
<An external ring residing in the CAS Maple>
#@fi
</pre></div>

<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#contents">[Contents]</a> <a href="chap0.html">[Previous Chapter]</a> <a href="chap2.html">[Next Chapter]</a> </div>

<div class="chlinkbot">Goto Chapter: <a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div>

<hr />
generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a>
</body>
</html>

Messung V0.5 in Prozent

¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.20Angebot (Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können 2026-06-17) ¤

*Eine klare Vorstellung vom Zielzustand

Wurzel

Suchen

PVS Prover

Isabelle Prover

NIST Cobol Testsuite

Cephes Mathematical Library

Vienna Development Method

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.