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D.4.25.3 sagbi

Procedure from library sagbi.lib (see sagbi_lib).

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.

Example:
 
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