Hermite matrices from approximate roots: the multivariate case
Implement certified Hermite matrices from approximate roots for zero-dimensional polynomial systems.
- Suitable for
- Master's thesis
- Supervision
- Tülay Ayyıldız
- Prerequisites
- Commutative algebra basics; numerical linear algebra; programming
Hermite matrices of a zero-dimensional polynomial system can be computed from approximate roots and then certified (Journal of Symbolic Computation, 2023). This allows exact information, such as the number of real solutions, to be recovered from numerical data.
Goal
Turn the theory into a working implementation for multivariate systems, and study its behaviour experimentally on regular, singular and near-singular examples.