This package is part of the homalg project [ht09]. The role of the package is described in the manual of the homalg package.
Here are some of the supported ring constructions:
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 |
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] |
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] |
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] |
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] |
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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