Singular

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