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1 Introduction
 1.1 Ring Constructions for Supported External Computer Algebra Systems
  1.1-1 external GAP

  1.1-2 Singular

  1.1-3 MAGMA

  1.1-4 Macaulay2

  1.1-5 Sage

  1.1-6 Maple

1 Introduction

This package is part of the homalg project [ht09]. The role of the package is described in the manual of the homalg package.

1.1 Ring Constructions for Supported External Computer Algebra Systems

Here are some of the supported ring constructions:

1.1-1 external GAP
gap> ZZ := HomalgRingOfIntegersInExternalGAP( );
<A homalg external ring residing in the CAS GAP>
 gap> Display( ZZ );
 Z
gap> F2 := HomalgRingOfIntegersInExternalGAP( 2, ZZ );
<A homalg external ring residing in the CAS GAP>
 gap> Display( F2 );
 GF(2)

F2 := HomalgRingOfIntegersInExternalGAP( 2 ) would launch another GAP.

gap> Z4 := HomalgRingOfIntegersInExternalGAP( 4, ZZ );
<A homalg external ring residing in the CAS GAP>
 gap> Display( Z4 );
 Z/4Z
gap> Z_4 := HomalgRingOfIntegersInExternalGAP( ZZ ) / 4;
<A homalg residue class ring>
gap> Display( Z_4 );
Z/( 4 )
gap> Q := HomalgFieldOfRationalsInExternalGAP( ZZ );
<A homalg external ring residing in the CAS GAP>
 gap> Display( Q );
 Q

1.1-2 Singular
gap> F2 := HomalgRingOfIntegersInSingular( 2 );
<A homalg external ring residing in the CAS Singular>
 gap> Display( F2 );
 GF(2)
gap> Q := HomalgFieldOfRationalsInSingular( F2 );
<A homalg external ring residing in the CAS Singular>
 gap> Display( Q );
 Q

Q := HomalgFieldOfRationalsInSingular( ) would launch another Singular.

gap> F2xyz := F2 * "x,y,z";
<A homalg external ring residing in the CAS Singular>
 gap> Display( F2xyz );
 GF(2)[x,y,z]
gap> Qxyz := Q * "x,y,z";
<A homalg external ring residing in the CAS Singular>
 gap> Display( Qxyz );
 Q[x,y,z]

1.1-3 MAGMA
gap> ZZ := HomalgRingOfIntegersInMAGMA( );
<A homalg external ring residing in the CAS MAGMA>
 gap> Display( ZZ );
 Z
gap> F2 := HomalgRingOfIntegersInMAGMA( 2, ZZ );
<A homalg external ring residing in the CAS MAGMA>
 gap> Display( F2 );
 GF(2)

F2 := HomalgRingOfIntegersInMAGMA( 2 ) would launch another MAGMA.

gap> Z_4 := HomalgRingOfIntegersInMAGMA( ZZ ) / 4;
<A homalg residue class ring>
gap> Display( Z_4 );
Z/( 4 )
gap> Q := HomalgFieldOfRationalsInMAGMA( ZZ );
<A homalg external ring residing in the CAS MAGMA>
 gap> Display( Q );
 Q
gap> F2xyz := F2 * "x,y,z";
<A homalg external ring residing in the CAS MAGMA>
 gap> Display( F2xyz );
 GF(2)[x,y,z]
gap> Qxyz := Q * "x,y,z";
<A homalg external ring residing in the CAS MAGMA>
 gap> Display( Qxyz );
 Q[x,y,z]

1.1-4 Macaulay2
gap> ZZ := HomalgRingOfIntegersInMacaulay2( );
<A homalg external ring residing in the CAS Macaulay2>
 gap> Display( ZZ );
 Z
gap> F2 := HomalgRingOfIntegersInMacaulay2( 2, ZZ );
<A homalg external ring residing in the CAS Macaulay2>
 gap> Display( F2 );
 GF(2)

F2 := HomalgRingOfIntegersInMacaulay2( 2 ) would launch another Macaulay2.

gap> Z_4 := HomalgRingOfIntegersInMacaulay2( ZZ ) / 4;
<A homalg residue class ring>
gap> Display( Z_4 );
Z/( 4 )
gap> Q := HomalgFieldOfRationalsInMacaulay2( ZZ );
<A homalg external ring residing in the CAS Macaulay2>
 gap> Display( Q );
 Q
gap> F2xyz := F2 * "x,y,z";
<A homalg external ring residing in the CAS Macaulay2>
 gap> Display( F2xyz );
 GF(2)[x,y,z]
gap> Qxyz := Q * "x,y,z";
<A homalg external ring residing in the CAS Macaulay2>
 gap> Display( Qxyz );
 Q[x,y,z]

1.1-5 Sage
gap> ZZ := HomalgRingOfIntegersInSage( );
<A homalg external ring residing in the CAS Sage>
 gap> Display( ZZ );
 Z
gap> F2 := HomalgRingOfIntegersInSage( 2, ZZ );
<A homalg external ring residing in the CAS Sage>
 gap> Display( F2 );
 GF(2)

F2 := HomalgRingOfIntegersInSage( 2 ) would launch another Sage.

gap> Z_4 := HomalgRingOfIntegersInSage( ZZ ) / 4;
<A homalg residue class ring>
gap> Display( Z_4 );
Z/( 4 )
gap> Q := HomalgFieldOfRationalsInSage( ZZ );
<A homalg external ring residing in the CAS Sage>
 gap> Display( Q );
 Q
gap> F2x := F2 * "x";
<A homalg external ring residing in the CAS Sage>
 gap> Display( F2x );
 GF(2)[x]
gap> Qx := Q * "x";
<A homalg external ring residing in the CAS Sage>
 gap> Display( Qx );
 Q[x]

1.1-6 Maple
gap> ZZ := HomalgRingOfIntegersInMaple( );
<A homalg external ring residing in the CAS Maple>
 gap> Display( ZZ );
 Z
gap> F2 := HomalgRingOfIntegersInMaple( 2, ZZ );
<A homalg external ring residing in the CAS Maple>
 gap> Display( F2 );
 GF(2)

F2 := HomalgRingOfIntegersInMaple( 2 ) would launch another Maple.

gap> Z4 := HomalgRingOfIntegersInMaple( 4, ZZ );
<A homalg external ring residing in the CAS Maple>
 gap> Display( Z4 );
 Z/4Z
gap> Z_4 := HomalgRingOfIntegersInMaple( ZZ ) / 4;
<A homalg residue class ring>
gap> Display( Z_4 );
Z/( 4 )
gap> Q := HomalgFieldOfRationalsInMaple( ZZ );
<A homalg external ring residing in the CAS Maple>
 gap> Display( Q );
 Q
gap> F2xyz := F2 * "x,y,z";
<A homalg external ring residing in the CAS Maple>
 gap> Display( F2xyz );
 GF(2)[x,y,z]
gap> Qxyz := Q * "x,y,z";
<A homalg external ring residing in the CAS Maple>
 gap> Display( Qxyz );
 Q[x,y,z]
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