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