14 citations · 26 across the 8 of their papers we have counts for
10 papers
A Symbolic Homotopy Algorithm for Solving Composable Polynomial Systems
Thi Xuan Vu
We study the problem of computing the isolated regular solutions of a system \((f_1,\ldots,f_n)\) of \(n\) polynomial equations in \(n\) variables \((X_1, \dots, X_n)\) over a fiel…
Computing Polynomial Representation in Subrings of Multivariate Polynomial Rings
Thi Xuan Vu
Let be a multivariate polynomial ring over a field of characteristic 0. Consider algebraically independent elements $g_…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
Computing critical points for algebraic systems defined by hyperoctahedral invariant polynomials
Thi Xuan Vu
Let be a field of characteristic zero and the corresponding multivariate polynomial ring. Given a sequence of polynomials $\mathbf{f}…
On the complexity of invariant polynomials under the action of finite reflection groups
Thi Xuan Vu
Let be a multivariate polynomial ring over a field . Let be a sequence of algebraically independent elements in $\…
Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix
George Labahn, Vincent Neiger, Thi Xuan Vu +1
Consider a matrix of univariate polynomials over a field . We study the problem of computing the column rank profile of $\ma…
Computing critical points for invariant algebraic systems
Jean-Charles Faugère, George Labahn, Mohab Safey El Din +2
Let be a field and , in be multivariate polynomials (with ) invariant under the action of $\m…
Homotopy techniques for solving sparse column support determinantal polynomial systems
George Labahn, Mohab Safey El Din, Éric Schost +1
Let be a field of characteristic zero with its algebraic closure. Given a sequence of polynomials $\mathbf{g} = (g_1, \ldots, g_s) \in \mathbf{…
Solving determinantal systems using homotopy techniques
Jonathan D. Hauenstein, Mohab Safey El Din, Éric Schost +1
Let $\K$ be a field of characteristic zero and $\Kbar$ be an algebraic closure of $\K$. Consider a sequence of polynomials in $\K[X\_1,\dots,X\_n]$, a polynomi…
Computing Canonical Bases of Modules of Univariate Relations
Vincent Neiger, Thi Xuan Vu
We study the computation of canonical bases of sets of univariate relations such that ; here, the input ele…