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

René Thiemann

The Archive 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.

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