Difference between revisions of "ApCoCoA-1:NC.LWIdeal"
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G := [F1,F2,F3,F4]; | G := [F1,F2,F3,F4]; | ||
GB:=NC.GB(G); | GB:=NC.GB(G); | ||
| − | [NC.LW(E) | E In GB]; -- the leading word ideal of <G> | + | [NC.LW(E) | E In GB]; -- the leading word ideal of <G> w.r.t. the length-lexicographic word ordering |
[[y, t], [x, t], [x, y], [x^2], [t, y^2], [y^2, x]] | [[y, t], [x, t], [x, y], [x^2], [t, y^2], [y^2, x]] | ||
Revision as of 17:38, 9 May 2013
NC.LTIdeal
Leading word ideal of a finitely generated two-sided ideal in a non-commutative polynomial ring.
Description
Proposition: Let I be a finitely generated two-sided ideal in a non-commutative polynomial ring K<x[1],...,x[n]>, and let Ordering be a word ordering on <x[1],...,x[n]>. If G is a Groebner basis of I with respect to Ordering. Then the leading word set LW{G}:={LW(g): g in G} is a generating system of the leading word ideal LW(I) with respect to Ordering.
Example
Use QQ[x,y,z,t];
NC.SetOrdering("LLEX");
F1 := [[x^2], [-y,x]];
F2 := [[x,y], [-t,y]];
F3 := [[x,t], [-t,x]];
F4 := [[y,t], [-t,y]];
G := [F1,F2,F3,F4];
GB:=NC.GB(G);
[NC.LW(E) | E In GB]; -- the leading word ideal of <G> w.r.t. the length-lexicographic word ordering
[[y, t], [x, t], [x, y], [x^2], [t, y^2], [y^2, x]]
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See also
