Engineering↗
Algebraic Numbers and Number Fields
Algebraic numbers and integers, minimal polynomials, number fields as finite extensions of Q, real and complex embeddings, the signature, and the primitive element theorem.
Tag
Number Fields I
Every page in the KEVOS library tagged Number Fields I. 6 pages.
Engineering↗
Class Groups, Units and the Regulator
The ideal class group, Dirichlet's unit theorem, the regulator, Minkowski's bound, and the analytic class number formula used to verify computed values.
Engineering↗
Decomposition of Prime Numbers in Number Fields
Ramification indices and residue degrees, the fundamental identity, Dedekind's theorem relating prime decomposition to polynomial factorisation modulo p, and computing valuations.
Engineering↗
Discriminants and Integral Bases
The field discriminant, integral bases, the index of an equation order, and why computing the maximal order reduces to factoring the polynomial discriminant.
Engineering↗
Orders and Ideals in Number Fields
Orders, the maximal order, fractional and integral ideals, unique factorisation of ideals in a Dedekind domain, ideal arithmetic by Hermite normal form, and the two-element repr…
Engineering↗
Representing Algebraic Numbers
The standard, matrix, conjugate-vector and minimal-polynomial representations of an algebraic number, their relative costs, and how to convert between them.
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Other tags in the library.
mathematics 387
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algebra handbook 85
graduate mathematics 85
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Context and scope 42
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template 34
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project leadership 31
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