5.1.40 fglmquot

Syntax:

fglmquot ( ideal_expression, poly_expression )

Type:

ideal

Purpose:

computes a reduced Groebner basis of the ideal quotient I:p of a zero-dimensional ideal I and a polynomial p using FGLM-techniques.

Assume:

The ideal must be zero-dimensional and given as a reduced Groebner basis in the given ring. The polynomial must be reduced with respect to the ideal.

Example:

ring r=0,(x,y,z),lp; ideal i=y3+x2,x2y+x2,x3-x2,z4-x2-y; option(redSB); // force the computation of a reduced SB i=std(i); poly p=reduce(x+yz2+z10,i); ideal j=fglmquot(i,p); j; ==> j[1]=z12 ==> j[2]=yz4-z8 ==> j[3]=y2+y-z8-z4 ==> j[4]=x+y-z10-z6-z4