论文标题
精确$ P $ - 岩浆中的计算
Exact $p$-adic computation in Magma
论文作者
论文摘要
我们描述了一种针对岩浆计算机代数系统的新算术系统，用于与$ p $ - adic数字合作，从某种意义上说，数字懒洋洋地表示无限$ p $ adadic的精度。这是第一个高度特色的这种实现。这具有提高用户友好性并加快某些计算以及强行产生可证明的结果的好处。我们为其设计提供理论和实用的理由，并描述一些用例。目的是，本文对想要在其他语言中实施类似功能的任何人都有好处。
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.
