Classification of Finite Fields with Applications

被引：0
|
作者：
Hing-Lun Chan
Michael Norrish
机构：
[1] Australian National University,
[2] Canberra Research Laboratory,undefined
[3] Data61,undefined
来源：
Journal of Automated Reasoning | 2019年 / 63卷
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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学科分类号：
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 [inline-graphic not available: see fulltext], with coefficients over a finite fields.
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页码：667 / 693
页数：26
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