ZpL: a p-adic precision package
For mathematicians and computer algebra system users working with p-adic numbers, this package improves precision tracking accuracy over existing tools.
The paper presents ZpL, a new package for p-adic precision tracking in the SM system, achieving sharper precision bounds than previous implementations across linear algebra, commutative algebra, and differential equations examples.
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.