Difference between revisions of "ApCoCoA-1:NCo.LWIdeal"
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Revision as of 17:34, 9 May 2013
NC.LTIdeal
Leading word ideal of a finitely generated two-sided ideal in a free monoid ring.
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. 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> ["yt", "xt", "xy", "xx", "tyy", "yyx"] -------------------------------
See also