### Implementing field extensions of the form Q[sqrt(b)]

René ThiemannArchive of Formal Proofs 2014.

### 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.

### BibTeX

@article{RT-AFP14a, author = {René Thiemann}, title = {Implementing field extensions of the form $\mathbb{Q}[\sqrt{b}]$}, journal = "Archive of Formal Proofs", month = feb, year = 2014, note = {\url{https://www.isa-afp.org/entries/Real_Impl.html}, Formal proof development}, ISSN = {2150-914x}, }