104 articles
Maple (software)
Maple, also known as the Maple computer algebra system, is a general-purpose mathematics software developed by Maplesoft, conceived at the University of Waterloo in November 1980.
Matching polynomial
The matching polynomial of a graph is a polynomial whose coefficients count the graph's matchings by size, introduced by Farrell in 1979 and studied by Heilmann and Lieb.
Matroid
A matroid, also called a combinatorial pregeometry, is a combinatorial structure abstracting linear independence in vector spaces and cycle-freedom in graphs, introduced by Hassler Whitney in 1935.
Modular exponentiation
Modular exponentiation, also called Modpow, computes the remainder when a base raised to an exponent is divided by a modulus, and is the core operation of RSA and Diffie-Hellman.
Modular lattice
A modular lattice is a lattice satisfying the modular law, a weakening of distributivity formulated by Richard Dedekind around 1900; examples include subspaces of a vector space and normal subgroups of a group.
Monomial order
A monomial order is a total order on the monomials of a polynomial ring, compatible with multiplication, that fixes the leading terms used in Gröbner basis computation.
Montgomery modular multiplication
Montgomery modular multiplication, or Montgomery reduction, is an algorithm introduced by Peter L. Montgomery in 1985 that computes products modulo an integer without division, enabling fast modular arithmetic in public-key cryptography.
Moore graph
A Moore graph is a regular graph of given degree and diameter containing the maximum possible number of vertices, attaining the Moore bound; examples include the Petersen graph.
Newton's identities
Newton's identities, also called the Newton–Girard identities, are relations expressing the power sums of variables in terms of elementary symmetric polynomials, first published by Newton in 1707.
Numerical algebraic geometry
Numerical algebraic geometry (NAG) is a tool set for approximating solutions to polynomial equation systems using numerical algorithms, initiated by Andrew Sommese and Charles Wampler.
Order theory
Order theory is the branch of mathematics that studies partially ordered sets, or posets, together with structures built on them such as lattices and ordered algebraic systems.
Orthogonal polynomials
Orthogonal polynomials are sequences of polynomials whose distinct members are orthogonal under a weighted inner product; introduced by Legendre in 1783, they underlie Gaussian quadrature, quantum mechanics, and approximation theory.
Parity bit
A parity bit, also called a check bit, is an extra binary digit appended to data so the count of 1s is even or odd, detecting single-bit errors.
Parking function
A parking function is a sequence of positive integers where cars with those preferences can all park in a line of spots, named by Konheim and Weiss in 1966.
Partial fraction decomposition
Partial fraction decomposition, or partial fraction expansion, rewrites a rational function as a polynomial plus simpler fractions, the standard first step for integrating rational functions.
Plethysm
Plethysm is an operation on symmetric functions, written f[g], in which one symmetric function is substituted into another, introduced by D. E. Littlewood in 1936.
Polynomial long division
Polynomial long division, also known as the polynomial division algorithm, divides one polynomial by another to produce a quotient and a remainder, like arithmetic long division.
Rational reconstruction
Rational reconstruction is a computer algebra problem: recovering the rational number n/d from its residue a modulo m under size bounds, first solved by Paul S. Wang in 1981.
Reduce (computer algebra system)
REDUCE is a portable, general-purpose computer algebra system begun by Anthony C. Hearn at Stanford in 1963 for physics calculations, and free, open-source software under a modified BSD license since 2008.
Reed–Muller code
Reed–Muller codes are a family of linear error-correcting codes whose codewords are evaluations of multivariate polynomials over finite fields, introduced in 1954 by David E. Muller.
Reed–Solomon error correction
Reed–Solomon error correction is a family of error-correcting codes, introduced by Irving Reed and Gustave Solomon in 1960, used in QR codes, CDs, and spacecraft.
Regular chain (algebra)
In computer algebra, a regular chain is a triangular set of polynomials whose leading coefficients are regular modulo the saturated ideal of earlier polynomials, introduced by Kalkbrener in 1991.
Residuated lattice
A residuated lattice is an algebraic structure combining a lattice with a monoid whose multiplication admits residuals, introduced by Ward and Dilworth in the late 1930s.
Resultant
The resultant, also called the polynomial resultant or eliminant, is an expression in the coefficients of two polynomials that vanishes exactly when they share a root.
Risch algorithm
The Risch algorithm is a decision procedure, formulated by Robert H. Risch in 1969 and 1970, that determines whether an elementary function has an elementary antiderivative and finds it in closed form.
Robinson–Schensted correspondence
The Robinson–Schensted correspondence, also called the Robinson–Schensted algorithm, is a bijection in combinatorics that assigns to each permutation a pair of standard Young tableaux of the same shape.
SageMath
SageMath, formerly Sage, is a free, open-source mathematics software system started in 2005 by William Stein as an alternative to Magma, Maple, Mathematica, and MATLAB.
Sheffer sequence
A Sheffer sequence, also called a Sheffer polynomial or poweroid, is a polynomial sequence in umbral calculus that includes the Hermite, Laguerre, and Charlier polynomials.
Simplicial complex
A simplicial complex, also called a geometric simplicial complex, is a combinatorial structure of vertices and simplices used to encode topological spaces as finite data.
Singleton bound
The Singleton bound is an upper limit on the minimum distance of an error-correcting code: a code of length n, dimension k, and distance d satisfies d ≤ n − k + 1.