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09/21/2022
A cubic algorithm for computing the Hermite normal form of a nonsingular integer matrix
A Las Vegas randomized algorithm is given to compute the Hermite normal ...
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02/18/2022
Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix
Consider a matrix 𝐅∈𝕂[x]^m × n of univariate polynomials over a field 𝕂....
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02/15/2022
Bohemian Matrix Geometry
A Bohemian matrix family is a set of matrices all of whose entries are d...
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11/18/2021
A fast algorithm for computing the Smith normal form with multipliers for a nonsingular integer matrix
A Las Vegas randomized algorithm is given to compute the Smith multiplie...
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09/02/2020
Computing critical points for invariant algebraic systems
Let 𝐊 be a field and ϕ, 𝐟 = (f_1, …, f_s) in 𝐊[x_1, …, x_n] be multivari...
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09/02/2020
Homotopy techniques for solving sparse column support determinantal polynomial systems
Let 𝐊 be a field of characteristic zero with 𝐊 its algebraic closure. Gi...
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02/01/2020
Efficient q-Integer Linear Decomposition of Multivariate Polynomials
We present two new algorithms for the computation of the q-integer linea...
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09/15/2019
Efficient Rational Creative Telescoping
We present a new algorithm to compute minimal telescopers for rational f...
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04/25/2019
Constructing minimal telescopers for rational functions in three discrete variables
We present a new algorithm for constructing minimal telescopers for rati...
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12/11/2018
Computing Nearby Non-trivial Smith Forms
We consider the problem of computing the nearest matrix polynomial with ...
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12/11/2017
Computing Lower Rank Approximations of Matrix Polynomials
Given an input matrix polynomial whose coefficients are floating point n...
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07/14/2016
Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix
Given a nonsingular n × n matrix of univariate polynomials over a field ...
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02/05/2016
A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix
Given a square, nonsingular matrix of univariate polynomials F∈K[x]^n × ...
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01/12/2016
Existence Problem of Telescopers: Beyond the Bivariate Case
In this paper, we solve the existence problem of telescopers for rationa...
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09/18/2014