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

 

Title: Implementing field extensions of the form Q[sqrt(b)]
Author: René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at)
Submission date: 2014-02-06
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.

Change history: [2014-07-11]: Moved NthRoot_Impl to Sqrt-Babylonian.
BibTeX:
@article{Real_Impl-AFP,
  author  = {René Thiemann},
  title   = {Implementing field extensions of the form Q[sqrt(b)]},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2014,
  note    = {\url{http://isa-afp.org/entries/Real_Impl.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: GNU Lesser General Public License (LGPL)
Depends on: Show, Sqrt_Babylonian
Used by: QR_Decomposition