# Publicaties

## Solving Systems of Polynomial Equations KU Leuven

Systems of polynomial equations arise naturally from many problems in applied mathematics and engineering. Examples of such problems come from robotics, chemical engineering, computer vision, dynamical systems theory, signal processing and geometric modeling, among others. The numerical solution of systems of polynomial equations is considered a challenging problem in computational mathematics. Important classes of existing methods are algebraic ...

## Numerical root finding via Cox rings KU Leuven

## Truncated Normal Forms for Solving Polynomial Systems KU Leuven

© 2018 Association for Computing Machinery.All Rights Reserved. In this poster we present the results of [10]. We consider the problem of finding the common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to find the solutions and to compute the structure of the quotient ring R/I from the cokernel of a resultant map. This leads to what we call ...

## A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations KU Leuven

We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$ variables. We assume that the polynomials are generic in the sense that the number of solutions in $\mathbb{C}^n$ equals the B\'ezout number. The main contribution of this paper is an automated choice of basis for ...

## Solving Polynomial Systems via Truncated Normal Forms KU Leuven

We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal $I$ in a ring $R$ of polynomials over $\mathbb{C}$. We propose a general algebraic framework to find the solutions and to compute the structure of the quotient ring $R/I$ from the null space of a Macaulay-type matrix. The affine dense, affine sparse, homogeneous, and multihomogeneous cases are treated. In the presented ...