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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
See fglm; option; quotient; ring; std; vdim.