Modern computer algebra
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Exact sparse matrix-vector multiplication on GPU's and multicore architectures
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Simultaneous modular reduction and Kronecker substitution for small finite fields
Journal of Symbolic Computation
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We present an algorithm to perform a simultaneous modular reduction of several residues. This enables to compress polynomials into integers and perform several modular operations with machine integer arithmetic. The idea is to convert the X-adic representation of modular polynomials, with X an indeterminate, to a q-adic representation where q is an integer larger than the field characteristic. With some control on the different involved sizes it is then possible to perform some of the q-adic arithmetic directly with machine integers or floating points. Depending also on the number of performed numerical operations one can then convert back to the q-adic or X-adic representation and eventually mod out high residues. In this note we present a new version of both conversions: more tabulations and a way to reduce the number of divisions involved in the process are presented. The polynomial multiplication is then applied to arithmetic and linear algebra in small finite field extensions.