Pierre Lairez

Wissenschaftlicher Mitarbeiter

Institut für Mathematik

TU Berlin

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TU Berlin
Fak. II, Sekr. 3-2
Straße des 17. Juni 136
10623 Berlin
Deutschland
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0049 30 314 27602
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MA 301
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P-adic numbers often appears in computer algebra when one want to solve a problem over a finite field $\mathbb F_p$ using an algorithm that performs divisions by $p$: we consider the data over the finite field as the approximation of some exact $p$-adic numbers, proceed to the computation over the field of $p$-adic numbers and then we obtain the result back in $\mathbb F_p$ by reducing modulo $p$. Naturally, we cannot compute with $p$-adic numbers with infinite precision, for the same reason as for real numbers. So we have to deal with approximations, and this raises questions about the numerical stability of algorithms when they are run with $p$-adic numbers.