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Exact \(p\)-adic computation in Magma. (English) Zbl 07312490
Summary: We describe a new arithmetic system for the Magma computer algebra system for working with \(p\)-adic numbers exactly, in the sense that numbers are represented lazily to infinite \(p\)-adic precision. This is the first highly featured such implementation. This has the benefits of increasing user-friendliness and speeding up some computations, as well as forcibly producing provable results. We give theoretical and practical justification for its design and describe some use cases. The intention is that this article will be of benefit to anyone wanting to implement similar functionality in other languages.
MSC:
11-04 Software, source code, etc. for problems pertaining to number theory
11S82 Non-Archimedean dynamical systems
12-08 Computational methods for problems pertaining to field theory
12J25 Non-Archimedean valued fields
68W30 Symbolic computation and algebraic computation
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