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ZpL: a p-adic precision package

Research paper by Xavier Caruso, David Roe, Tristan Vaccon

Indexed on: 23 Feb '18Published on: 23 Feb '18Published in: arXiv - Mathematics - Number Theory



Abstract

We present a new package ZpL for the mathematical software system SM. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in [4]. The underlying algorithms are mostly based on automatic dierentiation techniques. We introduce them, study their complexity and discuss our design choices. We illustrate the bene-ts of our package (in comparison with previous implementations) with a large sample of examples coming from linear algebra, com-mutative algebra and dierential equations.