Closed formula for univariate subresultants in multiple roots

D'ANDREA, CARLOS; VALDETTARO, MARCELO; KRICK, TERESA; SZANTO, AGNES

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Año: 2019 vol. 565 p. 123 - 155

0024-3795

We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials 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.