Closed formula for univariate subresultantes in multiple roots

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

Niza

Congreso; MEGA2017 (Effective Methods in Algebraic Geometry); 2017

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.