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},
}