We apply data refinement to implement the real numbers, where we support all numbers in the field extension Q[sqrt(b)], i.e., all numbers of the form p + q * sqrt(b) for rational numbers p and q and some fixed natural number b. To this end, we also developed algorithms to precisely compute roots of a rational number, and to perform a factorization of natural numbers which eliminates duplicate prime factors.
Our results have been used to certify termination proofs which involve polynomial interpretations over the reals.
- July 11, 2014
- Moved NthRoot_Impl to Sqrt-Babylonian.