ApCoCoA-1:NC.LWIdeal: Difference between revisions
From ApCoCoAWiki
No edit summary |
m replaced <quotes> tag by real quotes |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Version|1}} | |||
<command> | <command> | ||
<title>NC.LWIdeal</title> | <title>NC.LWIdeal</title> | ||
| Line 9: | Line 10: | ||
<example> | <example> | ||
Use QQ[x,y,z,t]; | Use QQ[x,y,z,t]; | ||
NC.SetOrdering( | NC.SetOrdering("LLEX"); | ||
F1 := [[x^2], [-y,x]]; | F1 := [[x^2], [-y,x]]; | ||
F2 := [[x,y], [-t,y]]; | F2 := [[x,y], [-t,y]]; | ||
| Line 23: | Line 24: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>NC.GB</see> | <see>ApCoCoA-1:NC.GB|NC.GB</see> | ||
<see>NC.LW</see> | <see>ApCoCoA-1:NC.LW|NC.LW</see> | ||
<see>NC.SetOrdering</see> | <see>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</see> | ||
<see>Introduction to CoCoAServer</see> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 37: | Line 38: | ||
<key>NC.LWIdeal</key> | <key>NC.LWIdeal</key> | ||
<key>LWIdeal</key> | <key>LWIdeal</key> | ||
<wiki-category>Package_ncpoly</wiki-category> | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 13:35, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NC.LWIdeal
Leading word ideal of a finitely generated two-sided ideal in a non-commutative polynomial ring.
Syntax
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]]
-------------------------------
See also
