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math.AG2021
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…
math.AG2021
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…