Finite field linear algebra subroutines

Jean-Guillaume Dumas 1 Thierry Gautier 2 Clement Pernet 2
2 APACHE - Parallel algorithms and load sharing
ID-IMAG - Informatique et Distribution, Inria Grenoble - Rhône-Alpes, UJF - Université Joseph Fourier - Grenoble 1
Abstract : In this paper we study different implementations of finite field arithmetic, essential foundation of computer algebra. We focus on Galois fields of word size cardinality at most, with any characteristic. Classical representations as machine integers, floating point numbers, polynomials and Zech logarithms are compared. Furthermore, very efficient implementations of finite field dot products, matrix-vector products and matrix-matrix products (namely the symbolic equivalent of level 1, 2 and 3 BLAS) are presented. Our implementations have many symbolic linear algebra applications: symbolic triangularization, system solving, exact determinant computation, matrix normal form are such examples.
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Jean-Guillaume Dumas, Thierry Gautier, Clement Pernet. Finite field linear algebra subroutines. International Symposium on Symbolic and Algebraic Computation (ISSAC'02), Jul 2002, Lille, France. pp.63-74, ⟨10.1145/780506.780515⟩. ⟨hal-02018841⟩



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