Ruben Gamboa (University of Wyoming) |
John Cowles (University of Wyoming) |
Woodrow Gamboa (woodrowg@stanford.edu) |

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. |

Published: 29th September 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.327.6 | bibtex | |

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