Singular Manual: sagbi

  | #### D.4.32.3 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

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