33 citations · 81 across the 24 of their papers we have counts for
26 papers
A note on the multivariate symmetric Hermite Interpolant
Teresa Krick, Agnes Szanto
In this note we explicit the notion of Hermite interpolant of a multivariate symmetric polynomial, generalizing the notion of Lagrange interpolant to the case when there are roots…
Univariate Rational Sums of Squares
Teresa Krick, Bernard Mourrain, Agnes Szanto
Given rational univariate polynomials f and g such that gcd(f, g) and f / gcd(f, g) are relatively prime, we show that g is non-negative on all the real roots of f if and only if g…
Certified Hermite Matrices from Approximate Roots
Tulay Ayyildiz Akoglu, Agnes Szanto
Let I=<f_1, ..., f_m> be a zero dimensional radical ideal Q[x_1,...,x_n]. Assume that we are given approximations {z_1,...,z_k} in C^n for the common roots V(I)={xi_1,...,xi_k}. In…
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…
Smooth Points on Semi-algebraic Sets
Katherine Harris, Jonathan D. Hauenstein, Agnes Szanto
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on sem…
Subresultants of and , Jacobi polynomials and complexity
A. Bostan, T. Krick, A. Szanto +1
In an earlier article together with Carlos D'Andrea [BDKSV2017], we described explicit expressions for the coefficients of the order- polynomial subresultant of and $(…