Calcium: computing in exact real and complex fields

11/03/2020

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by   Fredrik Johansson, et al.

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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 ℚ(a_1,…,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 ℝ and ℂ in which equality is rigorously decidable for a large class of numbers.