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 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.