33 citations · 81 across the 24 of their papers we have counts for
10 papers · 1 filter
Punctual Hilbert Schemes and Certified Approximate Singularities
Angelos Mantzaflaris, Bernard Mourrain, Agnes Szanto
In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a poly…
Closed formula for univariate subresultants in multiple roots
Carlos D'Andrea, Teresa Krick, Agnes Szanto +1
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 r…
Subresultants in multiple roots: an extremal case
Alin Bostan, Carlos D'Andrea, Teresa Krick +2
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…
Symmetric Interpolation, Exchange Lemma and Sylvester Sums
Teresa Krick, Agnes Szanto, Marcelo Valdettaro
The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows…
Subresultants, Sylvester sums and the rational interpolation problem
Carlos D'Andrea, Teresa Krick, Agnes Szanto
We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without…
Sylvester's double sums: an inductive proof of the general case
Teresa Krick, Agnes Szanto
In 1853 J. Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial s…