arXiv subjects

Eulalia Montoro

Publications and source records attributed to Eulalia Montoro.

2 recordsLinked to original sources

arXiv2021

Bounds for degrees of syzygies of polynomials defining a grade two ideal

We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of m polynomials in n variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results.

math.AC↗

arXiv2019

Minimal solutions of the rational interpolation problem

We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended Euclidean Algorithm. As a consequence, we obtain explicit descriptions for solutions of "minimal" degrees in terms of the degrees of elements appearing in the EEA. This allows us to describe the minimal degree in a $μ$-basis of a polynomial planar parametrization in terms of a "critical" degree arising in the EEA.

math.AC↗