Closed formula for univariate subresultants in multiple roots
Commutative Algebra
2018-12-12 v3 Algebraic Geometry
Abstract
We generalize Sylvester single sums to multisets (sets with repeated elements), and show that these sums compute subresultants of two univariate polyomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials, and is obtained by using multivariate symmetric interpolation via an Exchange Lemma.
Cite
@article{arxiv.1612.05160,
title = {Closed formula for univariate subresultants in multiple roots},
author = {Carlos D'Andrea and Teresa Krick and Agnes Szanto and Marcelo Valdettaro},
journal= {arXiv preprint arXiv:1612.05160},
year = {2018}
}