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Algebraic-group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure
Algebraic-group factorisation algorithm
Algebraic-group_factorisation_algorithm
Algorithm for integer factorization
Lenstra. It is an algebraic-group factorisation algorithm. Practically speaking, ECM is considered a special-purpose factoring algorithm, as it is most suitable
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Special-purpose algorithm for factoring integers
specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm. The factors it finds are ones for which the number preceding
Pollard's_p_−_1_algorithm
Integer factorization algorithm
theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by
Williams's_p_+_1_algorithm
Decomposition of a number into a product
Floyd and one by Brent. Algebraic-group factorization algorithms, among which are Pollard's p − 1 algorithm, Williams' p + 1 algorithm, and Lenstra elliptic
Integer_factorization
(Mathematical) decomposition into a product
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object
Factorization
Branch of mathematics that studies algebraic structures
Multiplicative group Primitive element (field theory) Field extension Algebraic extension Splitting field Algebraically closed field Algebraic element Algebraic closure
List of abstract algebra topics
List_of_abstract_algebra_topics
Matrix decomposition
squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as A = Q R , {\displaystyle
QR_decomposition
Accomplishments in factoring large integers
numbers that have no small factors). The first enormous distributed factorisation was RSA-129, a 129-digit challenge number described in the Scientific
Integer_factorization_records
Numerical eigenvalue calculation
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m {\displaystyle m} "most
Lanczos_algorithm
Branch of pure mathematics
complex numbers and techniques from analysis and calculus. Algebraic number theory employs algebraic structures such as fields and rings to analyze the properties
Number_theory
comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage. Matrix types
Comparison of linear algebra libraries
Comparison_of_linear_algebra_libraries
Algorithms for matrix decomposition
also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually)
Non-negative matrix factorization
Non-negative_matrix_factorization
String that is strictly smaller in lexicographic order than all of its rotations
1016/0022-247X(63)90070-2, MR 0158002. Schützenberger, M. P. (1965), "On a factorisation of free monoids", Proceedings of the American Mathematical Society,
Lyndon_word
Aspect of algebraic number theory
between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Algebraic structure
commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings
Polynomial_ring
Infinite dimensional Lie group
diagrammes de Feynman, renormalisation et factorisation de Wiener-Hopf (d'après A. Connes et D. Kreimer). [Hopf algebra of Feynman diagrams, renormalization
Butcher_group
Matrix decomposition in mathematics
are several variations where the general linear group is replaced by some other reductive algebraic group, due to Alexander Grothendieck (1957). Birkhoff
Birkhoff_factorization
Matrix factorisation in mathematics
In linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary
Schur_decomposition
Representation of a matrix as a product
analysis, different decompositions are used to implement efficient matrix algorithms. For example, when solving a system of linear equations A x = b {\displaystyle
Matrix_decomposition
17th-century conjecture proved by Andrew Wiles in 1994
Liouville, who later read a paper that demonstrated this failure of unique factorisation, written by Ernst Kummer. Kummer set himself the task of determining
Fermat's_Last_Theorem
French applied mathematician
structure et algorithmique parallèle pour la factorisation LU des matrices creuses, concerned parallel algorithms for LU decomposition of sparse matrices,
Laura_Grigori
mechanical, automated prime sieve in his paper "Factorisation of numbers". Lawrence's "Factorisation of numbers" is republished in French, sparking efforts
Timeline of computational mathematics
Timeline_of_computational_mathematics
American mathematician (1947–2020)
which include a method for speeding up the second stage of algebraic-group factorization algorithms using FFT techniques for fast polynomial evaluation at
Peter Montgomery (mathematician)
Peter_Montgomery_(mathematician)
Indian-American mathematician and computer scientist
analysis and computational mathematics. His emphasis is on developing novel algorithms that respect the underlying problem structure and are scalable to large
Inderjit_Dhillon
Jordan algebras, skew fields, and non-commutative unique factorisation domains. In 1957 Cohn published his first book, Lie Groups, on groups that are
Paul_Cohn
mathematician Mahāvīra writes down a factorisation for the difference of cubes. 9th century: Algorisms (arithmetical algorithms on numbers written in place-value
Timeline of scientific discoveries
Timeline_of_scientific_discoveries
pattern Akaike information criterion Algebra of random variables Algebraic statistics Algorithmic inference Algorithms for calculating variance All models
List_of_statistics_articles
Mathematical table
a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an
Multiplication_table
Polynomial function of degree 5
are formulas that yield the required solutions. However, there is no algebraic expression (that is, in terms of radicals) for the solutions of general
Quintic_function
Geometry problem on tiling by hypercubes
1090/S0273-0979-1980-14827-2, MR 0585178. Hajós, G. (1949), "Sur la factorisation des groupes abéliens", Československá Akademie Věd. Časopis Pro Pěstování
Keller's_conjecture
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
Boy/Male
Hindu, Indian
Group of God
Boy/Male
Tamil
Commander of group
Girl/Female
Bengali, Indian
Group of Lights
Girl/Female
Hindu
Goddess Lakshmi, Assembly, Group
Girl/Female
Tamil
Goddess Lakshmi, Assembly, Group
Girl/Female
Hindu
Goddess Lakshmi, Assembly, Group
Boy/Male
Indian
Group of people
Boy/Male
Muslim
Group of people
Girl/Female
Arabic
Soul; Group Leader
Boy/Male
Indian, Sanskrit
Conquering a Group
Surname or Lastname
English
English : metonymic occupational name for a dealer in coarse meal, Old English grūt, Old Norse grautr ‘porridge’.
Girl/Female
Tamil
Group lets of stars
Surname or Lastname
Scottish
Scottish : habitational name from a place in the parish of Gamrie, near Banff. The place is situated on a headland affording some sheltered anchorage, and is said to get its name from Middle English true hope; however, when first recorded in 1296 it already appears as Trup, so it is more likely to be of the same origin as Thorpe.English : variant of Throop.
Boy/Male
Hindu, Indian, Sanskrit
Group; Organisation; Gathering
Boy/Male
Indian, Kannada, Sanskrit
Group Leader
Girl/Female
Arabic
Soul; Group Leader
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Commander of Group
Girl/Female
Tamil
Goddess Lakshmi, Assembly, Group
Boy/Male
Arabic
Group; Army
Girl/Female
Tamil
Goddess Lakshmi, Assembly, Group
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
Surname or Lastname
English
English : unexplained.Probably an altered spelling of German Valee, a fairly common surname of French origin denoting someone who lived in a valley. The name in Germany is also spelled Wallee.
Boy/Male
Tamil
Rustom | à®°à¯à®¸à¯à®¤à¯‹à®®
Warrior
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi
Name of a Indian Music Raagini
Girl/Female
Teutonic
Inspired intelligence. Famous bearer: Veleda was a 1st century AD Germanic prophetess.
Boy/Male
English
Meadow with a cross.
Male
English
 Medieval English form of Anglo-Saxon Eoforwin, ERWIN means "boar friend." Compare with another form of Erwin.
Surname or Lastname
English (chiefly Midlands and northern England, especially Yorkshire)
English (chiefly Midlands and northern England, especially Yorkshire) : patronymic from Hann or the byname Hand.Irish : shortened Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).Irish : variant of McKittrick.Respelling of Scandinavian Hansen or Hansson.Jewish (Ashkenazic) : metronymic from the female personal name Hanna.A family by the name of Hanson were established in America by John Hanson, one of four brothers sent there by Queen Christina of Sweden in 1642. They were grandsons of an Englishman who had married into the Swedish royal family; he was descended from a certain Roger de Rastrick, who had lived in Yorkshire in the 13th century.
Boy/Male
Tamil
Bibhavasu | பிபவாஸà¯
The Sun, Fire
Boy/Male
Hindu
Devoted to truth, Love to truth
Boy/Male
Indian, Sanskrit
Lord Krishna
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
ALGEBRAIC GROUP-FACTORISATION-ALGORITHM
n.
An algebraic curve, so called from its resemblance to a heart.
p. pr. & vb. n.
of Group
n.
A variously limited assemblage of animals or plants, having some resemblance, or common characteristics in form or structure. The term has different uses, and may be made to include certain species of a genus, or a whole genus, or certain genera, or even several orders.
n.
Any comprehensive group of animals or plants including several subordinate related groups.
n.
One versed in algebra.
imp. & p. p.
of Group
n.
Arrangement in a group or in groups; grouping.
n.
A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement; as, a group of men or of trees; a group of isles.
v. t.
To fill up or finish with grout, as the joints between stones.
a.
Alt. of Algebraical
n.
One of the terms in an algebraic expression.
n.
To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of.
n.
A number of eighth, sixteenth, etc., notes joined at the stems; -- sometimes rather indefinitely applied to any ornament made up of a few short notes.
a.
Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings.
n.
An inflammatory affection of the larynx or trachea, accompanied by a hoarse, ringing cough and stridulous, difficult breathing; esp., such an affection when associated with the development of a false membrane in the air passages (also called membranous croup). See False croup, under False, and Diphtheria.
adv.
By algebraic process.
n.
An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic; as, groups of strata.
v. t.
To perform by algebra; to reduce to algebraic form.