cl-banner

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.

 

© AFP entry

BibTeX 

@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},
}
Nach oben scrollen