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### Abstract

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.

### License

### History

- July 11, 2014
- Moved NthRoot_Impl to Sqrt-Babylonian.