Abstract
Symmetric polynomials over F p in n indeterminates x 1,..., x n are expressible as rational functions of the first n power sums s j =x jl + ...+ x jn with exponents j not divisible by p. There exist fairly simple regular specializations of these power sums by elements from F p so that all denominators of such rational expressions remain nonzero. This leads to a new class of fast parallel algorithms for the determinant or the characteristic polynomial of n×n matrices over any field of characteristic p with arithmetic circuit depth θ(logn)2.
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© 1993 Springer-Verlag Berlin Heidelberg
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Schönhage, A. (1993). Fast parallel computation of characteristic polynomials by Leverrier's power sum method adapted to fields of finite characteristic. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_90
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DOI: https://doi.org/10.1007/3-540-56939-1_90
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