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We describe here the package {\tt subdivision\\_solver} for the mathematicalsoftware {\tt SageMath}. It provides a solver on real numbers for squaresystems of large dense polynomials. By large polynomials we mean multivariatepolynomials with large degrees, which coefficients have large bit-size. Whilestaying robust, symbolic approaches to solve systems of polynomials see theirperformances dramatically affected by high degree and bit-size of inputpolynomials.Available numeric approaches suffer from the cost of the evaluationof large polynomials and their derivatives.Our solver is based on intervalanalysis and bisections of an initial compact domain of $\R^n$ where solutionsare sought. Evaluations on intervals with Horner scheme is performed by thepackage {\tt fast\\_polynomial} for {\tt SageMath}.The non-existence of asolution within a box is certified by an evaluation scheme that uses a Taylorexpansion at order 2, and existence and uniqueness of a solution within a boxis certified with krawczyk operator.The precision of the working arithmetic isadapted on the fly during the subdivision process and we present a newheuristic criterion to decide if the arithmetic precision has to be increased.

A Subdivision Solver for Systems of Large Dense Polynomials