Jean-Guillaume Dumas

Publications133
h-index17
Citations1,256
Highly Influential Citations50
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LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA
TLDR
We describe the design of this generic library, sketch its current range of capabilities, and give several examples of its use. Expand
  • 102
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On Newton–Raphson Iteration for Multiplicative Inverses Modulo Prime Powers
TLDR
We study algorithms for the fast computation of modular inverses. Expand
  • 13
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Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
TLDR
This paper focuses on methods for the computer calculation of the homology of finite simplicial complexes and its applications (see comments on the other invariants in Section 7). Expand
  • 79
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FFPACK: finite field linear algebra package
TLDR
The FFLAS project has established that exact matrix multiplication over finite fields can be performed at the speed of the highly optimized numerical BLAS routines. Expand
  • 65
  • 4
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Efficient computation of the characteristic polynomial
TLDR
We deal with the computation of the characteristic polynomial of dense matrices over word size finite fields and over the integers. Expand
  • 34
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Finite field linear algebra subroutines
TLDR
In this paper we study different implementations of finite field arithmetic, essential foundation of computer algebra. Expand
  • 86
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Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
TLDR
In this article, we study high performance implementations of basic linear algebra routines over word size prime fields: especially matrix multiplication; our goal being to provide an exact alternate to the numerical BLAS library. Expand
  • 66
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Essentially optimal interactive certificates in linear algebra
TLDR
Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. Expand
  • 14
  • 2
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Caractérisation des Quenines et leur représentation spirale
Les nombres de Raymond Queneau sont les entiers n pour lesquels la quenine (permutation spirale envoyant tout nombre pair sur sa moitie et tout nombre impair sur son oppose ajoute a n) est d'ordre… Expand
  • 11
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On Efficient Sparse Integer Matrix Smith Normal Form Computations
TLDR
We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. Expand
  • 89
  • 1
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