Computer Science > Logic in Computer Science
[Submitted on 29 Sep 2020]
Title:Quadratic Extensions in ACL2
View PDFAbstract: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.
Submission history
From: EPTCS [view email] [via EPTCS proxy][v1] Tue, 29 Sep 2020 04:10:55 UTC (15 KB)
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