[isabelle] AFP: Implementing field extensions of the form Q[sqrt(b)]

An new AFP entry is available:

Implementing field extensions of the form Q[sqrt(b)]
by René Thiemann

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.




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