# Calcium: computing in exact real and complex fields

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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Preprints, Working Papers, ...
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Cited literature [37 references]

https://hal.inria.fr/hal-02986375
Contributor : Fredrik Johansson <>
Submitted on : Tuesday, November 3, 2020 - 3:16:10 PM
Last modification on : Wednesday, November 4, 2020 - 3:34:04 AM

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### Identifiers

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

### Citation

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

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