Tag
Finite Field
8 resources tagged “Finite Field” across the knowledge library.
8 items
Article7 Aug 2026Distinct Degree FactorisationSeparating irreducible factors by degree using GCDs against Frobenius powers, and the early-abort strategies that make it fast.2 min readRead MoreArticle7 Aug 2026Finite Field Arithmetic in PracticeSelecting representations and algorithms for real finite field workloads, with the operation mixes that arise in factoring, decomposition and point counting.2 min readRead MoreArticle7 Aug 2026Finite Field Element RepresentationRepresenting elements of a finite field as polynomials modulo an irreducible, choosing the modulus, and the trade-offs against logarithmic and normal bases.2 min readRead MoreArticle7 Aug 2026Gaussian Elimination over Finite FieldsElimination over a finite field, structured methods for very large sparse systems, and why the linear algebra stage limits sieving methods.2 min readRead MoreArticle7 Aug 2026Root Finding over Finite FieldsFinding roots of a polynomial in a finite field by GCD with the Frobenius polynomial followed by probabilistic splitting.2 min readRead MoreArticle7 Aug 2026Splitting Separable Algebras over Finite FieldsDecomposing a finite-dimensional commutative algebra over a finite field into its simple components, generalising polynomial factorisation.2 min readRead MoreArticle7 Aug 2026The Berlekamp Factorisation AlgorithmBerlekamp's linear algebra approach to factoring over a finite field, the Berlekamp subalgebra, and when it outperforms the GCD pipeline.2 min readRead MoreGuide6 Aug 2026Factorisation of Polynomials Modulo a PrimeSquarefree decomposition, distinct-degree factorisation by gcd with x^(q^d) − x, equal-degree splitting by Cantor-Zassenhaus, and Berlekamp's linear-algebra approach.5 min readRead More