Tag
Computational Number Theory
58 resources tagged “Computational Number Theory” across the knowledge library.
58 items · page 3 of 3
Guide6 Aug 2026The Euclidean Algorithm and GCD ComputationEuclid's algorithm and its worst case, the binary GCD, Lehmer's method for multiprecision operands, and how to choose between them by operand size.6 min readRead MoreGuide6 Aug 2026The Extended Euclidean Algorithm and Modular InversesThe extended Euclidean algorithm, its loop invariants, half-extended variants, modular inversion, and rational reconstruction from a partial remainder sequence.5 min readRead MoreGuide6 Aug 2026The Hermite Normal FormDefinition and uniqueness of the Hermite normal form, algorithms for computing it, entry explosion and its remedies, and its role as the representation of choice for modules and ideals.5 min readRead MoreGuide6 Aug 2026The Jacobi Sum Primality TestThe Adleman-Pomerance-Rumely test and its Cohen-Lenstra refinement: cyclotomic extensions, characters and Jacobi sums, the basic test, and the final trial division stage.4 min readRead MoreGuide6 Aug 2026The LLL Lattice Reduction AlgorithmThe LLL algorithm: reduction conditions, the swap-and-reduce loop, the potential function that proves polynomial termination, quality guarantees, and the deep-insertion and floating-point variants.5 min readRead MoreGuide6 Aug 2026The Number Field SieveThe number field sieve: polynomial selection, sieving over two sides, the algebraic factor base and character columns, the square root step in a number field, and the special number field sieve.5 min readRead MoreGuide6 Aug 2026The Quadratic Sieve and MPQSThe quadratic sieve, sieving by roots of a polynomial, the multiple polynomial variation, large prime variations, and the linear algebra stage.4 min readRead MoreGuide6 Aug 2026The Smith Normal Form and Its ApplicationsThe Smith normal form, elementary divisors, the structure theorem for finitely generated abelian groups, and the application to class group structure determination.4 min readRead MoreGuide6 Aug 2026The Subresultant Algorithm, Resultants and DiscriminantsThe subresultant polynomial remainder sequence, the resultant as a determinant and as a product over roots, the discriminant, and their use in elimination and in number field arithmetic.5 min readRead MoreGuide6 Aug 2026Trace, Norm and the Characteristic PolynomialDefinitions of trace and norm as sums and products over embeddings, their computation via the regular representation, multiplicativity, and their use in detecting units and computing ideal norms.4 min readRead More