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5.1.32 fglm
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Syntax: fglm (ring_name,ideal_name)-
Type: ideal
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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.-
Note: The ideal must be zero-dimensional and given as a reduced Groebner basis in the given ring.
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