Calcium: computing in exact real and complex fields
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 extension 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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