Home Online Manual
Top
Back: monomialabortstd
Forward: phindex_lib
FastBack:
FastForward:
Up: customstd_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.14.2.2 satstd

Procedure from library customstd.lib (see customstd_lib).

Usage:
satstd(I[,J]); I ideal, J optional ideal

Assume:
J generated by variables

Purpose:
computes a standard basis of I and, if possible,
divides each polynomial during the computation by the variables in J. By default, J is assumed to be the ideal generated by all variables.

Note:
Even if I contains a monomial generated by the variables in J, there is no guarantee that it is found during the computation. If it is found, however, 1 is immediately returned.

Example:
 
LIB "customstd.lib";
ring r = 0,(x,y,z,u,v),dp;
ideal I = x2+x,y2+y,z2+z;
// returns normal standard basis, no changes during (trivial) computation
satstd(I,ideal(u,v));
==> _[1]=z2+z
==> _[2]=y2+y
==> _[3]=x2+x
// returns x+1 instead of x2+x
satstd(I,ideal(x));
==> _[1]=x+1
==> _[2]=z2+z
==> _[3]=y2+y
// returns standard basis with elements of degree up to 8 (instead of 16)
deg(satstd(I^8));
==> 8