The exact functionality you want is missing from GAP at the moment. However, there may be a work around.
The following example computation seems to be related to what you are looking for. Computations in R/I must be replaced by repeatedly using QuotientRemainder and PowerMod. gap> Z4:=ZmodnZ(4); (Integers mod 4) gap> R:=UnivariatePolynomialRing(Z4,1); PolynomialRing(..., [ x ]) gap> x:=IndeterminatesOfPolynomialRing(R)[1]; x gap> I:=TwoSidedIdealByGenerators( R,[x8-x0]); <two-sided ideal in PolynomialRing(..., [ x ]), (1 generators)> gap> gen:=x8-x0; x8-ZmodnZObj(1,4) gap> QuotientRemainder(R,x8,gen); [ ZmodnZObj(1,4), ZmodnZObj(1,4) ] gap> QuotientRemainder(R,x15,gen); [ x7, x7 ] gap> QuotientRemainder(R,x15+x8,gen); [ x7+ZmodnZObj(1,4), x7+ZmodnZObj(1,4) ] gap> PowerMod( R, x+x0, 15, gen ); ZmodnZObj(0,4) gap> PowerMod( R, x, 15, gen ); x7 Wish I could be more helpful. - David Joyner ++++++++++++++++++++++++++++++++++++++++++++ Larry Wilson wrote:
Perhaps this question has a very simple answer, but I have not been able to figure it out and would love to have some guidance. I would like to be able to do something like work in Z_4[x]/(x^8-1). I thought I was on the right track with: GAP4, Version: 4.4.2 of 18-Mar-2004, sparc-sun-solaris2.8-cc gap> A := FreeAlgebraWithOne(Integers, 1);; gap> x := GeneratorsOfAlgebra(A)[2]; (1)*x.1 gap> I := Ideal(A, [x^8-1*x^0, 4*x^0]); <two-sided ideal in <free left module over Integers, and ring-with-one, with 1 generators>, (2 generators)> gap> hom := NaturalHomomorphismByIdeal(A, I); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `GeneratorsOfLeftOperatorRingWithOne' on 1 arguments called from GeneratorsOfAlgebraWithOne( image ) called from <function>( <arguments> ) called from read-eval-loop Any help would be much appreciated, Larry _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
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