FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora.
The input of the algorithm is a Gröbner basis of a zero-dimensional ideal in the ring of polynomials over a field with respect to a monomial order and a second monomial order.
As its output, it returns a Gröbner basis of the ideal with respect to the second ordering.
The complexity of FGLM is O(nD3), where n is the number of variables of the polynomials and D is the degree of the ideal.
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