Amortized multi-point evaluation of multivariate polynomials

The evaluation of a polynomial at several points is called the problem multi-point evaluation. Sometimes, set fixed and polynomials need to be evaluated this points. Several efficient algorithms for kind “amortized” have been developed recently special cases bivariate or when generic. In paper, we extend these results in an arbitrary number variables We prove softly linear complexity bound fixed. Our method relies on novel quasi-reduction algorithm multivariate polynomials, that operates simultaneously with respect orderings monomials.