Singular

D.4.25.3 sagbi

Usage:

sagbi(A[, tr, mt]); A ideal, tr, mt optional integers

Return:

ideal, a SAGBI basis for A

Assume:

basering is not a qring

Purpose:

Computes a SAGBI basis for the subalgebra given by the generators in A.

The optional argument tr=tailred determines whether tail reduction will be performed. - If (tailred=0), no tail reduction is performed, - If (tailred<>0), tail reduction is performed. The other optional argument meth determines which method is used for Groebner basis computations. - If mt=0 (default), the procedure std is used. - If mt=1, the procedure slimgb is used.

LIB "sagbi.lib";
ring r= 0,(x,y,z),dp;
ideal A=x2,y2,xy+y;
//Default call, no tail-reduction is done.
sagbi(A);
==> _[1]=x2
==> _[2]=y2
==> _[3]=xy+y
==> _[4]=xy2+1/2y2
//---------------------------------------------
//Call with tail-reduction and method specified.
sagbi(A,1,0);
==> _[1]=x2
==> _[2]=y2
==> _[3]=xy+y
==> _[4]=xy2