Quadratic Extensions in ACL2
Logic in Computer Science
2020-09-30 v1
Abstract
Given a field K, a quadratic extension field L is an extension of K that can be generated from K by adding a root of a quadratic polynomial with coefficients in K. This paper shows how ACL2(r) can be used to reason about chains of quadratic extension fields Q = K_0, K_1, K_2, ..., where each K_i+1 is a quadratic extension field of K_i. Moreover, we show that some specific numbers, such as the cube root of 2 and the cosine of pi/9, cannot belong to any of the K_i, simply because of the structure of quadratic extension fields. In particular, this is used to show that the cube root of 2 and cosine of pi/9 are not rational.
Cite
@article{arxiv.2009.13766,
title = {Quadratic Extensions in ACL2},
author = {Ruben Gamboa and John Cowles and Woodrow Gamboa},
journal= {arXiv preprint arXiv:2009.13766},
year = {2020}
}
Comments
In Proceedings ACL2 2020, arXiv:2009.12521