Singular Manual: sagbiReduce

  | #### D.4.34.2 sagbiReduce Procedure from library `sagbi.lib` (see sagbi_lib). Usage: sagbiReduce(I, A[, tr, mt]); I, A ideals, tr, mt optional integers Return: ideal of remainders of I after SAGBI reduction by A Assume: basering is not a qring Purpose:
          The optional argument tr=tailred determines whether tail reduction will be performed.
           - If (tailred=0), no tail reduction is done.
           - If (tailred<>0), tail reduction is done.
           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=x2,2*x2y+y,x3y2;
    poly p1=x^5+x2y+y;
    poly p2=x^16+x^12*y^5+6*x^8*y^4+x^6+y^4+3;
    ideal P=p1,p2;
    //---------------------------------------------
    //SAGBI reduction of polynomial p1 by algebra A.
    //Default call, that is, no tail-reduction is done.
    sagbiReduce(p1,A);
    ==> x5+x2y+y
    //---------------------------------------------
    //SAGBI reduction of set of polynomials P by algebra A,
    //now tail-reduction is done.
    sagbiReduce(P,A,1);
    ==> _[1]=x5+1/2y
    ==> _[2]=x6y5-8y4

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