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

René Thiemann

The Archive of Formal Proofs, 2014.


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


author = {René Thiemann},
title = {Implementing field extensions of the form $\rats[\sqrt{b}]$},
journal = "Archive of Formal Proofs",
month = feb,
year = 2014,
note = {\url{}, Formal proof development},
ISSN = {2150-914x},
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