Quaternions

Lawrence C. Paulson 🌐

September 5, 2018

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This theory is inspired by the HOL Light development of quaternions, but follows its own route. Quaternions are developed coinductively, as in the existing formalisation of the complex numbers. Quaternions are quickly shown to belong to the type classes of real normed division algebras and real inner product spaces. And therefore they inherit a great body of facts involving algebraic laws, limits, continuity, etc., which must be proved explicitly in the HOL Light version. The development concludes with the geometric interpretation of the product of imaginary quaternions.
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Topics

Theories of Quaternions