Engineering↗
Distinct Degree Factorisation
Separating irreducible factors by degree using GCDs against Frobenius powers, and the early-abort strategies that make it fast.
Tag
Finite Field
Every page in the KEVOS library tagged Finite Field. 8 pages.
Engineering↗
Finite Field Arithmetic in Practice
Selecting representations and algorithms for real finite field workloads, with the operation mixes that arise in factoring, decomposition and point counting.
Engineering↗
Finite Field Element Representation
Representing elements of a finite field as polynomials modulo an irreducible, choosing the modulus, and the trade-offs against logarithmic and normal bases.
Engineering↗
Gaussian Elimination over Finite Fields
Elimination over a finite field, structured methods for very large sparse systems, and why the linear algebra stage limits sieving methods.
Engineering↗
Root Finding over Finite Fields
Finding roots of a polynomial in a finite field by GCD with the Frobenius polynomial followed by probabilistic splitting.
Engineering↗
Splitting Separable Algebras over Finite Fields
Decomposing a finite-dimensional commutative algebra over a finite field into its simple components, generalising polynomial factorisation.
Engineering↗
The Berlekamp Factorisation Algorithm
Berlekamp's linear algebra approach to factoring over a finite field, the Berlekamp subalgebra, and when it outperforms the GCD pipeline.
Engineering↗
Factorisation of Polynomials Modulo a Prime
Squarefree decomposition, distinct-degree factorisation by gcd with x^(q^d) − x, equal-degree splitting by Cantor-Zassenhaus, and Berlekamp's linear-algebra approach.
Related
Other tags in the library.
mathematics 387
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algebra handbook 85
graduate mathematics 85
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templates and examples 78
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universal algebra 62
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principles of project management 58
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Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
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template 34
Operational Excellence 32
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project leadership 31
project teams 31
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behaviour change 26
habits 26
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