FGLM

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title: FGLM permalink: wiki/FGLM/ layout: wiki

Goal: Modify existing package Points to also include FGLM and related algorithms.

-- FGLM: Working. Still naive computation of the multiplication matrices (which do not need to be computed fully).

-- Points: Now uses the trick to only work with max(m-1,n) variables during the algorithm. Trick not yet implemented for FGLM.

-- Groebner basis from multiplication matrices: Now possible to give multiplication matrices with respect to some basis e_1,…,e_m AND coefficients such that 1 = c_1 e_1 + … + c_m e_m as input and get a Groebner basis as output. Points can be computed this way by defining diagonal matrices as multiplication matrices and 1= e_1 + … + e_m, i.e. the vector space basis is the separators.

--Normal form via points: Working.

Todo: Clean up code. Document. Write tests. Especially, check FGLM for different type of orderings.

Package is then good to go.

In the next version: FGLM: Use recursive arguments to gain speed. Implement the CM-correspondence for Lex.