FGLM Algorithm

FGLM is one of the main algorithms in computer algebra, named after its designers Faugère, Gianni, Lazard and Mora, who introduced it in 1993. Its input is a Groebner basis of a zero-dimensional ideal in a ring of polynomials over a field, computed with respect to one monomial order, together with a second monomial order; its output is a Groebner basis of the same ideal with respect to that second ordering. The algorithm runs in time on the order of n times D cubed, where n is the number of variables and D is the degree of the ideal, and is implemented in most computer algebra systems as a fundamental conversion tool.