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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, and let Ordering be a word ordering on . 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  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