1,187 research outputs found
Resultants and subresultants of p-adic polynomials
We address the problem of the stability of the computations of resultants and
subresultants of polynomials defined over complete discrete valuation rings
(e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms
are highly unstable on average and we explain, in many cases, how one can
stabilize them without sacrifying the complexity. On the way, we completely
determine the distribution of the valuation of the principal subresultants of
two random monic p-adic polynomials having the same degree
Hypergeometric L-functions in average polynomial time
We describe an algorithm for computing, for all primes , the
mod- reduction of the trace of Frobenius at of a fixed hypergeometric
motive in time quasilinear in . This combines the Beukers--Cohen--Mellit
trace formula with average polynomial time techniques of Harvey et al.Comment: 15 pages, 1 figure; v4 several exposition improvements as suggested
the referee
Tracking p-adic precision
We present a new method to propagate -adic precision in computations,
which also applies to other ultrametric fields. We illustrate it with many
examples and give a toy application to the stable computation of the SOMOS 4
sequence
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