The multivariate Hermite method for counting real and complex solutions to polynomial systems
Algebraic Geometry
2026-01-21 v2
Abstract
This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final section includes an implementation in Macaulay2, a free and open-source computer algebra system.
Cite
@article{arxiv.2510.23897,
title = {The multivariate Hermite method for counting real and complex solutions to polynomial systems},
author = {Volodymyr Oleksiyuk},
journal= {arXiv preprint arXiv:2510.23897},
year = {2026}
}
Comments
Added a reference to the RealRoots package