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D.7.2.4 reduction
Procedure from library ainvar.lib (see ainvar_lib).
- Usage:
- reduction(p,I[,q,n]); p poly, I ideal, [q monomial, n int (optional)]
- Return:
- a polynomial equal to p-H(f1,...,fr), in case the leading
term LT(p) of p is of the form H(LT(f1),...,LT(fr)) for some
polynomial H in r variables over the base field, I=f1,...,fr;
if q is given, a maximal power a is computed such that q^a divides
p-H(f1,...,fr), and then (p-H(f1,...,fr))/q^a is returned;
return p if no H is found
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:
- this is a kind of SAGBI reduction in the subalgebra K[f1,...,fr] of
the basering
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;
reduction(p,dom);
==> 2xyzw-yzw2-2xvw+vw2
reduction(p,dom,w);
==> 2xyz-yzw-2xv+vw
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