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5.1.39 fglm

Syntax:
fglm ( ring_name, ideal_name )
Type:
ideal
Purpose:
computes for the given ideal in the given ring a reduced Groebner basis in the current ring, by applying the so-called FGLM (Faugere, Gianni, Lazard, Mora) algorithm.
The main application is to compute a lexicographical Groebner basis from a reduced Groebner basis with respect to a degree ordering. This can be much faster than computing a lexicographical Groebner basis directly.
Assume:
The ideal must be zero-dimensional and given as a reduced Groebner basis in the given ring. The monomial ordering must be global.
Note:
The only permissible differences between the given ring and the current ring are the monomial ordering and a permutation of the variables, resp. parameters.
Example:
 
  ring r=0,(x,y,z),dp;
  ideal i=y3+x2, x2y+x2, x3-x2, z4-x2-y;
  option(redSB);   // force the computation of a reduced SB
  i=std(i);
  vdim(i);
==> 28
  ring s=0,(z,x,y),lp;
  ideal j=fglm(r,i);
  j;
==> j[1]=y4+y3
==> j[2]=xy3-y3
==> j[3]=x2+y3
==> j[4]=z4+y3-y
See fglmquot; option; qring; ring; std; stdfglm; vdim.