Subresultants in multiple roots: an extremal case

Alin Bostan (1) , Carlos d'Andrea (2) , Teresa Krick (3) , Agnès Szanto (4) , Marcelo Valdettaro (5)

1 SPECFUN - Symbolic Special Functions : Fast and Certified
2 UB - Universitat de Barcelona
3 Departamento de Matemática [Buenos Aires]
4 Department of Computer Science
5 Departamento de Computación [Buenos Aires]

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x − α)^m and (x − β)^n with respect to the set of Bernstein polynomials {(x − α)^j (x − β) ^{d−j} , 0 ≤ j ≤ d}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.

Mots clés: Subresultants; Hankel matrices; Ostrowski's determinant; Pfaff–Saalschütz identity

Domaines: Mathématiques [math]

Alin Bostan, Carlos d'Andrea, Teresa Krick, Agnès Szanto, Marcelo Valdettaro. Subresultants in multiple roots: an extremal case. Linear Algebra and its Applications, 2017, 529, pp.185-198. ⟨10.1016/j.laa.2017.04.019⟩. ⟨hal-01588546⟩