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arXiv · 2510.23897

The multivariate Hermite method for counting real and complex solutions to polynomial systems

Volodymyr Oleksiyuk
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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.

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Volodymyr Oleksiyuk. 2025-10-27. The multivariate Hermite method for counting real and complex solutions to polynomial systems. https://arxiv.org/abs/2510.23897

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