Classification of Finite Fields with Applications

Journal of Automated Reasoning（2018）

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摘要

We present a formalisation of the theory of finite fields, from basic axioms to their classification, both existence and uniqueness, in HOL4 using the notion of subfields. The tools developed are applied to the characterisation of subfields of finite fields, and to the cyclotomic factorisation of polynomials of the form , with coefficients over a finite fields.

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关键词

Monoid, Group, Ring, Field, Finite field, Subfield, Quotient field, Extension field, Isomorphism, Minimal polynomials, Cyclotomic polynomials, Primitives, Existence, Uniqueness, Theorem proving, Formalisation, HOL4

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