Difference between revisions of "ApCoCoA-1:NCo.LWIdeal"
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| − | <see>NCo.LW</see> | + | <see>ApCoCoA-1:NCo.LW|NCo.LW</see> |
| − | <see>NCo.SetOrdering</see> | + | <see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see> |
| − | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
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Revision as of 08:30, 7 October 2020
NCo.LWIdeal
Leading word ideal of a finitely generated two-sided ideal in a free monoid ring.
Syntax
Description
Proposition: Let I be a finitely generated two-sided ideal in a free monoid ring K<X>, and let Ordering be a word ordering on <X>. 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
NCo.SetX("xyzt");
NCo.SetOrdering("LLEX");
F1 := [[1,"xx"], [-1,"yx"]];
F2 := [[1,"xy"], [-1,"ty"]];
F3 := [[1,"xt"], [-1,"tx"]];
F4 := [[1,"yt"], [-1,"ty"]];
G := [F1,F2,F3,F4];
GB:=NCo.GB(G);
[NCo.LW(E) | E In GB]; -- the leading word ideal of <G> w.r.t. the length-lexicographic word ordering
["yt", "xt", "xy", "xx", "tyy", "yyx"]
-------------------------------
See also
