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02/16/2023
Computing the Characteristic Polynomial of Endomorphisms of a finite Drinfeld Module using Crystalline Cohomology
We present a new algorithm for computing the characteristic polynomial o...
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02/07/2023
Newton iteration for lexicographic Gröbner bases in two variables
We present an m-adic Newton iteration with quadratic convergence for lex...
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07/09/2022
Bit complexity for computing one point in each connected component of a smooth real algebraic set
We analyze the bit complexity of an algorithm for the computation of at ...
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03/08/2022
Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results
Answering connectivity queries in real algebraic sets is a fundamental p...
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10/15/2021
Faster Modular Composition
A new Las Vegas algorithm is presented for the composition of two polyno...
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02/06/2021
Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
Linear recurrent sequences are those whose elements are defined as linea...
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11/04/2020
Connectivity in Semi-Algebraic Sets I
A semi-algebraic set is a subset of the real space defined by polynomial...
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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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05/05/2020
Subquadratic-Time Algorithms for Normal Bases
For any finite Galois field extension 𝖪/𝖥, with Galois group G = Gal(𝖪/𝖥...
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12/04/2019
Computing syzygies in finite dimension using fast linear algebra
We consider the computation of syzygies of multivariate polynomials in a...
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07/30/2019
Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module
Motivated by finding analogues of elliptic curve point counting techniqu...
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05/12/2019
Change of basis for m-primary ideals in one and two variables
Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we disc...
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05/10/2019
Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants
Complexity bounds for many problems on matrices with univariate polynomi...
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03/08/2019
Quadratic Probabilistic Algorithms for Normal Bases
It is well known that for any finite Galois extension field K/F, with Ga...
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02/28/2018
Solving determinantal systems using homotopy techniques
Let be a field of characteristic zero and be an algebraic closure of ....
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12/12/2017
Block-Krylov techniques in the context of sparse-FGLM algorithms
Consider a zero-dimensional ideal I in K[X_1,...,X_n]. Inspired by Faugè...
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12/02/2017
Drinfeld Modules with Complex Multiplication, Hasse Invariants and Factoring Polynomials over Finite Fields
We present a novel randomized algorithm to factor polynomials over a fin...
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07/06/2017
Algorithms for zero-dimensional ideals using linear recurrent sequences
Inspired by Faugère and Mou's sparse FGLM algorithm, we show how using l...
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05/30/2017
Fast Computation of the Roots of Polynomials Over the Ring of Power Series
We give an algorithm for computing all roots of polynomials over a univa...
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05/03/2017
Computing isomorphisms and embeddings of finite fields
Let F_q be a finite field. Given two irreducible polynomials f,g over F_...
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03/10/2017
On matrices with displacement structure: generalized operators and faster algorithms
For matrices with displacement structure, basic operations like multipli...
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09/14/2016
A Fast Algorithm for Computing the Truncated Resultant
Let P and Q be two polynomials in K[x, y] with degree at most d, where K...
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05/24/2016
Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization
Multi-homogeneous polynomial systems arise in many applications. We prov...
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05/19/2016
Computation of the Similarity Class of the p-Curvature
The p-curvature of a system of linear differential equations in positive...
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02/01/2016
Fast Computation of Minimal Interpolation Bases in Popov Form for Arbitrary Shifts
We compute minimal bases of solutions for a general interpolation proble...
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12/11/2015