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- ...lgorithms have been designed only for polynomials with coefficients in a [[finite field]], in the [[field of rationals]] or in a [[finitely generated field e ...nomial factorization]]. It is also used for various applications of finite fields, such as [[coding theory]] ([[cyclic redundancy]] codes and [[BCH code]]s), ...30 KB (4,658 words) - 09:50, 24 July 2024
- In this article, a local field is non-archimedean and has finite [[residue field]]. ...ase when <math>A, B</math> are complete; i.e., <math>L, K</math> are local fields.--> ...4 KB (592 words) - 19:05, 15 December 2021
Page text matches
- ...y [[smooth morphism|smooth]] [[projective variety]] ''X'' defined over a [[finite field]], the higher [[algebraic K-theory|algebraic K-groups]] vanish up to ==Finite fields== ...2 KB (287 words) - 05:50, 22 June 2022
- ...the '''algebraic ''K''-group of a field''' is important to compute. For a finite field, the complete calculation was given by [[Daniel Quillen]]. The map sending a finite-dimensional ''F''-vector space to its dimension induces an isomorphism ...3 KB (411 words) - 21:47, 12 August 2023
- ...inds of fields were originally introduced in [[p-adic analysis]] since the fields <math>\mathbb{Q}_p</math> are locally compact topological spaces constructe === Finite dimensional vector spaces === ...5 KB (757 words) - 12:43, 14 February 2024
- In this article, a local field is non-archimedean and has finite [[residue field]]. ...ase when <math>A, B</math> are complete; i.e., <math>L, K</math> are local fields.--> ...4 KB (592 words) - 19:05, 15 December 2021
- ...xtension|simple]] if and only if there are only finitely many intermediate fields between <math>K</math> and <math>L</math>. ...number of intermediate fields between <math>L</math> and <math>K</math> is finite, we distinguish two cases: ...2 KB (405 words) - 16:07, 1 January 2024
- ...\times</math> are precisely the open subgroups of <math>K^\times</math> of finite index. ...595 bytes (96 words) - 09:14, 7 July 2024
- ...an absolutely abelian field with ''K'' and which is [[unramified]] at all finite primes of ''K''. The '''genus number''' of ''K'' is the degree [''Γ(K)'':' ...bed as the maximal absolutely abelian extension of ''K'' unramified at all finite primes: this definition was used by Leopoldt and Hasse. ...2 KB (305 words) - 02:30, 3 June 2021
- ...i Evdokimov]], is an algorithm for [[factorization of polynomials]] over [[finite field]]s. It was the fastest algorithm known for this problem, from its pub | contribution = Factoring polynomials over finite fields with linear Galois groups: an additive combinatorics approach ...4 KB (621 words) - 00:43, 29 July 2024
- {{short description|For any integer N there are only finitely many number fields with discriminant at most N}} ...or any integer ''N'' there are only finitely many [[number fields]], i.e., finite [[field extension]]s ''K'' of the rational numbers '''Q''', such that the [ ...1 KB (185 words) - 13:33, 6 June 2024
- In [[mathematics]], a '''tower of fields''' is a sequence of [[field extension]]s A tower of fields may be finite or [[infinite sequence|infinite]]. ...2 KB (259 words) - 02:24, 4 July 2024
- ...und]] on [[limit cycles]] in generic finite-parameter families of [[vector fields]] on a sphere?}} ...eneric (mathematics)|generic]]{{disambiguation needed|date=February 2025}} finite-parameter family of [[smooth function|smooth]] [[vector field]]s on a spher ...4 KB (562 words) - 23:28, 5 February 2025
- ...e abelian extension of a number field is contained in one of its ray class fields. ...groups in 1897. Takagi proved the existence of the corresponding ray class fields in about 1920. Chevalley reformulated the definition of ray class groups in ...5 KB (814 words) - 13:34, 10 February 2025
- {{short description|Analogue of Stickelberger's theorem for real abelian fields}} ...harv|Washington|1997}}, to prove that some [[Tate–Shafarevich group]]s are finite, and in the proof of [[Mihăilescu's theorem]] {{harv|Schoof|2008}}. ...2 KB (333 words) - 11:10, 28 February 2025
- * A finite field has Tsen rank 1: this is the [[Chevalley–Warning theorem]]. * There exist fields of Tsen rank ''i'' for every integer ''i'' ≥ 0. ...4 KB (638 words) - 11:57, 25 April 2023
- ...rt description|Used to compare mixed characteristic situations with purely finite characteristic ones}} ...invented in order to) compare mixed characteristic situations with purely finite characteristic ones. Technical tools for making this precise are the tiltin ...5 KB (752 words) - 01:16, 30 March 2023
- {{short description|Lifts an action of a finite-dimensional Lie algebra on a manifold to a Lie group action}} ...th>M</math> can be integrated to a [[Lie group action|smooth action]] of a finite-dimensional [[Lie group]] <math>G</math>, i.e. there is a smooth action <ma ...3 KB (478 words) - 17:30, 18 August 2024
- ...iguration space (physics)|configuration space]] of free particle which has finite degrees of freedom, and <math>d^3 x</math> is the [[Lebesgue measure]] on < ...While in the classical theory we can restrict ourselves to suitably smooth fields, in quantum field theory we are forced to allow distributional field config ...3 KB (434 words) - 20:00, 24 July 2022
- ...the electric '''E'''<sub>''t''</sub> and magnetic '''H'''<sub>''t''</sub> fields on the surface of well-conducting bodies.<ref name="LL">{{cite book |last1= ...ace is large with respect to the [[skin effect|skin depth]], the resulting fields on the interior can be well approximated by plane waves, thus giving rise t ...3 KB (466 words) - 08:07, 19 May 2024
- It can be used to model operations over [[finite field]]s, The elements of GF(2<sup>''n''</sup>), i.e. a [[finite field]] whose order is a [[power of two]], ...5 KB (799 words) - 07:13, 2 October 2024
- ...athematics, a [[Field (mathematics)|field]] ''K'' with an [[Absolute value#Fields|absolute value]] is called '''spherically complete''' if the [[Intersection Spherically complete fields are important in [[archimedean property|nonarchimedean]] [[functional analy ...2 KB (334 words) - 19:37, 6 September 2024