Quelle example04.xml Sprache: XML

Many examples provided with {\GBNP} have been tested with the native
length left-lex ordering patched with the same ordering but a {\NMO}
version.  All such examples tested thus far work as intended, as
the following example shows.  It was taken from the book page 339 of
``Some Tapas of Computer Algebra'' by A.M. Cohen, H. Cuypers, H. Sterk,
\cite{CCS99}; it also appears as example 6 in the {\GBNP} example set.

gap> LoadPackage("gbnp", false);
true

gap> A4 := FreeAssociativeAlgebraWithOne(Rationals,"a","b","c","d","e","f");;
gap> a := A4.a;; b := A4.b;; c := A4.c;; d := A4.d;; e := A4.e;; f := A4.f;;

gap> polys4 := [ e*a, a^3 + f*a, a^9 + c*a^3, a^81 + c*a^9 + d*a^3,
>                a^27 + d*a^81 + e*a^9 + f*a^3, b + c*a^27 + e*a^81 + f*a^9,
>                c*b + d*a^27 + f*a^81, a + d*b + e*a^27, c*a + e*b + f*a^27,
>                d*a + f*b, b^3 - b, a*b - b*a, a*c - c*a, a*d - d*a,
>                a*e - e*a, a*f - f*a, b*c - c*b, b*d - d*b, b*e - e*b,
>                b*f - f*b, c*d - d*c, c*e - e*c, c*f - f*c, d*e - e*d,
>                d*f - f*d, e*f - f*e
> ];;
gap> reps4 := GP2NPList(polys4);;

gap> ml4 := NCMonomialLeftLengthLexOrdering(A4);
NCMonomialLeftLengthLexicographicOrdering([ (1)*a, (1)*b, (1)*c, (1)*d, (1)*e,\
(1)*f ])
gap> PatchGBNP(ml4);
LtNP patched.
GtNP patched.
gap> gb4 := Grobner(reps4);;
gap> NP2GPList(gb4,A4);
[ (1)*a, (1)*b, (1)*d*c+(-1)*c*d, (1)*e*c+(-1)*c*e, (1)*e*d+(-1)*d*e,
  (1)*f*c+(-1)*c*f, (1)*f*d+(-1)*d*f, (1)*f*e+(-1)*e*f ]

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