Quelle example01.xml Sprache: XML

This example was taken from Dr. Edward Green's paper ``Noncommutative
Grobner Bases, and Projective Resolutions'', and is referenced
as ``Example 2.7'' there; please see the manual for more information.

gap> LoadPackage("gbnp", false);
true
gap> A := FreeAssociativeAlgebraWithOne(Rationals,"a","b","c","d");
<algebra-with-one over Rationals, with 4 generators>
gap> a := A.a; b := A.b; c := A.c; d := A.d;
(1)*a
(1)*b
(1)*c
(1)*d
gap> polys := [c*d*a*b-c*b,b*c-d*a];
[ (-1)*c*b+(1)*c*d*a*b, (1)*b*c+(-1)*d*a ]
gap> reps := GP2NPList(polys);
[ [ [ [ 3, 4, 1, 2 ], [ 3, 2 ] ], [ 1, -1 ] ],
  [ [ [ 4, 1 ], [ 2, 3 ] ], [ -1, 1 ] ] ]
gap> gbreps := Grobner(reps);
[ [ [ [ 4, 1 ], [ 2, 3 ] ], [ 1, -1 ] ],
  [ [ [ 3, 2, 3, 2 ], [ 3, 2 ] ], [ 1, -1 ] ] ]
gap> gb := NP2GPList(gbreps,A);
[ (1)*d*a+(-1)*b*c, (1)*(c*b)^2+(-1)*c*b ]

gap> ml := NCMonomialLeftLengthLexOrdering(A);
NCMonomialLeftLengthLexicographicOrdering([ (1)*a, (1)*b, (1)*c, (1)*d ])
gap> PatchGBNP(ml);
LtNP patched.
GtNP patched.
gap> gbreps := Grobner(reps);;
gap> gb := NP2GPList(gbreps,A);
[ (1)*d*a+(-1)*b*c, (1)*(c*b)^2+(-1)*c*b ]

gap> ml2 := NCMonomialLeftLengthLexOrdering(A,[4,3,2,1]);
NCMonomialLeftLengthLexicographicOrdering([ (1)*d, (1)*c, (1)*b, (1)*a ])
gap> PatchGBNP(ml2);
LtNP patched.
GtNP patched.
gap> gbreps2 := SGrobner(reps);;
gap> gb2 := NP2GPList(gbreps2,A);
[ (1)*b*c+(-1)*d*a, (1)*c*d*a*b+(-1)*c*b, (1)*(d*a)^2*b+(-1)*d*a*b,
  (1)*c*(d*a)^2+(-1)*c*d*a, (1)*(d*a)^3+(-1)*(d*a)^2 ]

quality99%

¤ Dauer der Verarbeitung: 0.12 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.