D.6.2.5 completeReduction

Procedure from library ainvar.lib (see ainvar_lib).

Usage:

completeReduction(p,I[,q,n]); p poly, I ideal, [q monomial, n int]

Return:

a polynomial, the SAGBI reduction of the polynomial p with I via the procedure ’reduction’ as long as possible
if n=1, a different algorithm is chosen which is sometimes faster (default: n=0; q and n can be given (or not) in any order)

Note:

help reduction; shows an explanation of SAGBI reduction

Example:

LIB "ainvar.lib";
ring q=0,(x,y,z,u,v,w),dp;
poly p=x2yz-x2v;
ideal dom =x-w,u2w+1,yz-v;
completeReduction(p,dom);
→ 2xyzw-yzw2-2xvw+vw2
completeReduction(p,dom,w);
→ 0