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Clement Pernet - One of the best experts on this subject based on the ideXlab platform.

  • finite field linear algebra subroutines
    International Symposium on Symbolic and Algebraic Computation, 2002
    Co-Authors: Jeanguillaume Dumas, Thierry Gautier, Clement Pernet
    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.

Jeanguillaume Dumas - One of the best experts on this subject based on the ideXlab platform.

  • finite field linear algebra subroutines
    International Symposium on Symbolic and Algebraic Computation, 2002
    Co-Authors: Jeanguillaume Dumas, Thierry Gautier, Clement Pernet
    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.

Thierry Gautier - One of the best experts on this subject based on the ideXlab platform.

  • finite field linear algebra subroutines
    International Symposium on Symbolic and Algebraic Computation, 2002
    Co-Authors: Jeanguillaume Dumas, Thierry Gautier, Clement Pernet
    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.