Engineering↗
Essential Discriminant Divisors
Primes that divide the index for every choice of defining polynomial, why they exist, and what they force computationally.
Tag
Prime Decomposition
Every page in the KEVOS library tagged Prime Decomposition. 8 pages.
Engineering↗
Newton Polygon Methods for Prime Decomposition
Using Newton polygons to decompose primes locally, handling the cases where factoring modulo p is insufficient.
Engineering↗
Prime Decomposition in Quadratic Fields
How rational primes split, remain inert or ramify in a quadratic field, decided entirely by the Kronecker symbol.
Engineering↗
Prime Decomposition when p Does Not Divide the Index
Decomposing a prime that does not divide the index, by factoring the defining polynomial modulo that prime.
Engineering↗
Prime Decomposition: Theory and Ramification
How rational primes factor in the maximal order, ramification indices and residue degrees, and the degree relation that constrains them.
Engineering↗
The Buchmann-Lenstra Prime Decomposition Method
Decomposing any prime, including those dividing the index, by splitting the algebra of the order modulo that prime.
Engineering↗
The Four Core Computational Tasks of Number Fields
The four fundamental computational problems for a number field, their dependencies, and what counts as a complete answer to each.
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.
Related
Other tags in the library.
mathematics 387
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project management 158
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algebra handbook 85
graduate mathematics 85
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Operational Excellence 32
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project leadership 31
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