104 articles
Factorization of polynomials
Factorization of polynomials is the computation expressing a polynomial as a product of irreducible factors over a given coefficient ring, a central problem in computational algebra.
Felipe Cucker
Felipe Cucker, also known as Juan Felipe Cucker Farkas, is a Spanish mathematician at City University of Hong Kong who co-founded the Society for the Foundations of Computational Mathematics.
FORM (symbolic manipulation system)
FORM is an open-source symbolic manipulation system created by Jos Vermaseren of NIKHEF, started in 1984 and released as open source in 2010, used for large quantum field theory calculations.
Free Lie algebra
A free Lie algebra is a Lie algebra on a free generating set, the Lie-algebra analog of a free group, with any map of the generators extending to a homomorphism.
Free monoid
The free monoid on a set is the monoid of all finite words over it, with concatenation as the operation and the empty word as identity.
GAP (computer algebra system)
GAP (Groups, Algorithms and Programming) is a free, open-source, extensible system for computation in discrete abstract algebra, emphasizing computational group theory and used in research and teaching.
Gaussian approximation (density evolution)
The Gaussian approximation is a one-dimensional simplification of density evolution, assuming decoder messages follow Gaussian distributions; introduced for LDPC codes by Chung, Richardson, and Urbanke in 2001.
GeoGebra
GeoGebra is a free, open-source suite of interactive mathematics software combining geometry, algebra, and calculus, founded by Markus Hohenwarter in 2001 and used by over 100 million students.
Geometric complexity theory
Geometric complexity theory is a program in computational complexity theory, founded by Ketan Mulmuley and Milind Sohoni in 2001, that uses algebraic geometry and representation theory to prove lower bounds such as P ≠ NP.
Gilbert–Varshamov bound
The Gilbert–Varshamov bound is a lower bound in coding theory: proved by Gilbert in 1952 and Varshamov in 1957, it guarantees codes of a certain size exist.
Golay code
The Golay codes are two perfect error-correcting block codes, one binary and one ternary, introduced by Marcel Golay in 1949 and used for error control in the Voyager mission.
Gröbner basis
A Gröbner basis (Groebner bases) is a generating set for an ideal in a polynomial ring, introduced by Bruno Buchberger in 1965 and named after his advisor Wolfgang Gröbner.
Hadamard matrix
A Hadamard matrix is a square matrix whose entries are all +1 or −1 and whose rows are mutually orthogonal, achieving the largest determinant possible of n^(n/2).
Hamming bound
The Hamming bound, also called the sphere-packing bound, is an upper limit on the size of an error-correcting code with given length and minimum distance.
Hasse diagram
A Hasse diagram is a drawing of a finite partially ordered set, showing an edge between two elements exactly when one covers the other, with greater elements higher.
Hermite normal form
The Hermite normal form (HNF) is a unique canonical echelon-like form of an integer matrix, reached by multiplying by a matrix of determinant ±1 while preserving the generated lattice.
Hermite polynomials
Hermite polynomials, also called the probabilists' Hermite polynomials in one of two conventions, are classical orthogonal polynomials on the real line with a Gaussian weight, central to the quantum harmonic oscillator.
Hill cipher
The Hill cipher is a classical polygraphic cipher invented by Lester S. Hill in 1929 that encrypts blocks of letters using an invertible key matrix modulo 26.
Holonomic function
A holonomic function, also called a D-finite function, satisfies a linear differential equation with polynomial coefficients; the class follows Zeilberger's holonomic systems approach and contains most special functions.
HP Prime
The HP Prime is a graphing calculator with a computer algebra system, color multi-touch screen, and rechargeable battery, introduced by Hewlett-Packard in autumn 2013 and still produced in a revised G2 version.
Incidence matrix
An incidence matrix is a matrix recording which elements of one set are incident with elements of another, with rows for vertices and columns for edges.
Jeu de taquin
Jeu de taquin is an algorithm in algebraic combinatorics, introduced by Marcel-Paul Schützenberger in 1977, that transforms a skew Young tableau into a straight-shape tableau by sliding entries.
Laplacian matrix
The Laplacian matrix, also called the graph Laplacian or Kirchhoff matrix, is a graph matrix L = D − A whose eigenvalues reveal connectivity, spanning trees, and clustering.
Lattice (order)
A lattice is a partially ordered set in which every pair of elements has a greatest lower bound (meet) and a least upper bound (join).
Lattice-ordered group
A lattice-ordered group, also called an ℓ-group, is a group with a partial order under which every two elements have a meet and join, preserved by all translations.
Low-density parity-check code
A low-density parity-check (LDPC) code is an error-correcting code defined by a sparse parity-check matrix, proposed by Robert G. Gallager at MIT in 1960 and used in 5G, Wi-Fi, and satellite broadcasting.
Lyndon word
A Lyndon word is a finite word over an ordered alphabet that is lexicographically smaller than all of its nontrivial rotations, introduced by Roger Lyndon in 1954.
Macaulay2
Macaulay2 is a free, open-source software system for research in algebraic geometry and commutative algebra, created by Daniel Grayson and Michael Stillman and funded by the National Science Foundation since 1992.
MacMahon partition analysis
MacMahon partition analysis is a combinatorial method introduced by Percy MacMahon in 1915 that counts solutions of linear Diophantine inequalities via the Omega operator, revived by George Andrews in the late 1990s.
Mahonian statistic
A Mahonian statistic is a statistic on permutations whose distribution equals that of the inversion number; the major index is the other prototype, both named for Percy MacMahon.