5.1.123 stdhilb

Procedure from library standard.lib (see standard_lib).

Syntax:

stdhilb ( ideal_expression )
stdhilb ( ideal_expression, intvec_expression )

Type:

ideal

Purpose:

computes the standard basis of the homogeneous ideal in the basering, via a Hilbert driven standard basis computation.
An optional second argument will be used as 1st Hilbert function.

Assume:

The optional second argument is the first Hilbert series as computed by hilb.

Example:

   ring  r=0,(x,y,z),dp;
ideal i=y3+x2,x2y+x2,x3-x2,z4-x2-y;
ideal i1=stdhilb(i); i1;
→ i1[1]=y3+x2
→ i1[2]=x2y+x2
→ i1[3]=x3-x2
→ i1[4]=z4-x2-y
// the latter computation is equivalent to:
intvec v=hilb(i,1);
→ // ** i is no standardbasis
ideal i2=stdhilb(i,v); i2;
→ i2[1]=y3+x2
→ i2[2]=x2y+x2
→ i2[3]=x3-x2
→ i2[4]=z4-x2-y

See also: groebner; std; stdfglm.