33 citations · 81 across the 24 of their papers we have counts for
7 papers · 1 filter
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…
Irredundant Triangular Decomposition
Gleb Pogudin, Agnes Szanto
Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds fo…
On deflation and multiplicity structure
Jonathan D. Hauenstein, Bernard Mourrain, Agnes Szanto
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction…
Certifying isolated singular points and their multiplicity structure
Jonathan D. Hauenstein, Bernard Mourrain, Agnes Szanto
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion…
Approximate radical for clusters: a global approach using Gaussian elimination or SVD
Itnuit Janovitz-Freireich, Lajos Ronyai, Agnes Szanto
We present a method based on Dickson's lemma to compute the "approximate radical" of a zero dimensional ideal I in C[x1, . . ., xm] which has zero clusters: the approximate radical…