Singular

D.14.2.2 satstd

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.

Note:

The result is a standard basis of a partially saturated ideal wrt. the the variables in J.
If the I is homogeneous and the ordering dp, the result is completely saturated wrt. to the last variable (wrt. to the first for Dp).

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