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.
  author  = {René Thiemann},
  title   = {Implementing field extensions of the form Q[sqrt(b)]},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2014,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: GNU Lesser General Public License (LGPL)
Depends on: Deriving, Show, Sqrt_Babylonian
Used by: QR_Decomposition
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.