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Classification of Finite Fields with Applications

Date

Authors

Chan, Hing Lun

Norrish, Michael

Publisher

Kluwer Academic Publishers

Abstract

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 Open image in new window, with coefficients over a finite fields.

Keywords

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

URI

http://hdl.handle.net/1885/297070

Collections

ANU Research Publications

Source

Journal of Automated Reasoning

Type

Journal article

DOI

10.1007/s10817-018-9485-1

Restricted until

2099-12-31

Downloads

File

Description

s10817-018-9485-1.pdf (619.89 KB)

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