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5 papers · 2 filters
Connecting Gröbner Bases Programs with Coq to do Proofs in Algebra, Geometry and Arithmetics
Loïc Pottier
We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set o…
The DMM bound: multivariate (aggregate) separation bounds
Ioannis Z. Emiris, Bernard Mourrain, Elias Tsigaridas
In this paper we derive aggregate separation bounds, named after Davenport-Mahler-Mignotte (\dmm), on the isolated roots of polynomial systems, specifically on the minimum distance…
Gradual sub-lattice reduction and a new complexity for factoring polynomials
Mark Van Hoeij, Andrew Novocin
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type s…
NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions
Marc Mezzarobba
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations…
Generic design of Chinese remaindering schemes
Jean-Guillaume Dumas, Thierry Gautier, Jean-Louis Roch
We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integ…