Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain $\mathfrak{m}$-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm.
[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Computer Science - Symbolic Computation, FOS: Computer and information sciences, polynomial system solving, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], FOS: Mathematics, change of monomial order, Symbolic Computation (cs.SC), Hensel lifting, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Gröbner basis
[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Computer Science - Symbolic Computation, FOS: Computer and information sciences, polynomial system solving, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], FOS: Mathematics, change of monomial order, Symbolic Computation (cs.SC), Hensel lifting, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Gröbner basis
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