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Calcium: computing in exact real and complex fields

Fredrik Johansson 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\ldots,a_n)$ where the extensions numbers $a_k$ may be algebraic or transcendental. The system combines efficient field operations with automatic discovery and certification of algebraic relations, resulting in a practical computational model of $\mathbb{R}$ and $\mathbb{C}$ in which equality is rigorously decidable for a large class of numbers.
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Submitted on : Tuesday, November 3, 2020 - 3:16:10 PM
Last modification on : Friday, December 3, 2021 - 12:20:06 PM
Long-term archiving on: : Thursday, February 4, 2021 - 6:04:20 PM


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  • HAL Id : hal-02986375, version 1
  • ARXIV : 2011.01728


Fredrik Johansson. Calcium: computing in exact real and complex fields. 2020. ⟨hal-02986375v1⟩



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