Dear Tsai, the Weyl algebra and the exterior algebra (including GB computations) are supported through the homalg project’s interface to Singular/Plural/SCA. The clifford algebra can also be supported easily:
gap> LoadPackage( "RingsForHomalg" ); true If this returns fail then probably because the package io fails to load; in this case please compile io, using ./configure and make gap> Q := HomalgFieldOfRationalsInSingular( ); Q gap> R := PolynomialRing( Q, "x,y,z" ); Q[x,y,z] gap> A := RingOfDerivations( R, "Dx,Dy,Dz" ); Q[x,y,z]<Dx,Dy,Dz> All this and more is documented: gap> ?RingsForHomalg:Singular AssignGeneratorVariables does not yet work properly for Weyl algebras. This will be fixed in the next GAP release. For the moment: gap> x := "x" / A; x gap> Dx := "Dx" / A; Dx gap> Dx * x; x*Dx+1 The homalg project has at the moment its own matrix interface: gap> ?HomalgMatrix We are planning to comply with the new matrix interface in GAP once it becomes widely used. gap> mat := HomalgMatrix( "[x*Dy, Dx*x, z*Dx, 1+Dy]", 2, 2, A ); <A 2 x 2 matrix over an external ring> gap> Display( mat ); x*Dy,x*Dx+1, z*Dx,Dy+1 See also: gap> ?MatricesForHomalg:Matrices Best wishes, Mohamed _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
