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cs.SC2016★ 1 cited
Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems
Jean-Charles Faugere, Pierre-Jean Spaenlehauer, Jules Svartz
B{é}zout 's theorem states that dense generic systems of n multivariate quadratic equations in n variables have 2 n solutions over algebraically closed fields. When only a small su…
cs.SC2016
Critical Point Computations on Smooth Varieties: Degree and Complexity bounds
Mohab Safey El Din, Pierre-Jean Spaenlehauer
Let V C n be an equidimensional algebraic set and g be an n-variate polynomial with rational coefficients. Computing the critical points of the map that evaluates g at th…