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Type of mathematical expression
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the
Polynomial
Estimate of time taken for running an algorithm
Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that may be slower than polynomial time
Time_complexity
Pair of polynomial sequences
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}
Chebyshev_polynomials
Complexity class used to classify decision problems
computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is
NP_(complexity)
Unsolved problem in computer science
the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More unsolved problems in computer science
P_versus_NP_problem
Polynomial whose roots are the eigenvalues of a matrix
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues
Characteristic_polynomial
Mathematical approximation of a function
of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function
Taylor_series
Polynomials used for interpolation
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a
Lagrange_polynomial
Mathematical expression
Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes
Newton_polynomial
Statistics concept
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable
Polynomial_regression
System of complete and orthogonal polynomials
mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of
Legendre_polynomials
Algebraic structure
especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally
Polynomial_ring
A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of
Annihilating_polynomial
Error-detecting code for detecting data changes
systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated
Cyclic_redundancy_check
Index of articles associated with the same name
Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. The chromatic polynomial, a polynomial whose values
Graph_polynomial
Plane algebraic curve
mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients
Polynomial_lemniscate
Mathematical concept
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The
Degree_of_a_polynomial
Function of the coefficients of a polynomial that gives information on its roots
precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number
Discriminant
Mathematical function defined piecewise by polynomials
function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields
Spline_(mathematics)
Polynomial with 1 as leading coefficient
In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the
Monic_polynomial
Algorithm for division of polynomials
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version
Polynomial_long_division
Measure of algorithmic complexity
computer science, a polynomial-time algorithm is – generally speaking – an algorithm whose running time is upper-bounded by some polynomial function of the
Strongly-polynomial_time
Polynomial without nontrivial factorization
an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of
Irreducible_polynomial
Complexity class
Each input to the problem is associated with a collection of short (polynomial length) solutions, which might or might not validly solve the input. The
NP-completeness
Mathematical function
elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Irreducible polynomial whose roots are nth roots of unity
{\displaystyle n} -th cyclotomic polynomial, for any positive integer n {\displaystyle n} , is the unique irreducible polynomial with integer coefficients that
Cyclotomic_polynomial
Topics referred to by the same term
mathematics, the order of a polynomial may refer to: the degree of a polynomial, that is, the largest exponent (for a univariate polynomial) or the largest sum
Order_of_a_polynomial
Sequence of differential equation solutions
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: x y ″
Laguerre_polynomials
Form of interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through
Polynomial_interpolation
Type of polynomial used in Numerical Analysis
numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician
Bernstein_polynomial
Knot invariant
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander
Alexander_polynomial
Greatest common divisor of polynomials
GCD or gcd) of two polynomials is a polynomial, of the highest possible degree, which is a factor of both the two original polynomials. This concept is
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Endofunctor on the category V of finite-dimensional vector spaces
polynomial functor is an endofunctor on the category V {\displaystyle {\mathcal {V}}} of finite-dimensional vector spaces that depends polynomially on
Polynomial_functor
Algebraic encoding of graph connectivity
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays
Tutte_polynomial
Topics referred to by the same term
mathematics, Conway polynomial can refer to: the Alexander–Conway polynomial in knot theory the Conway polynomial (finite fields) the polynomial of degree 71
Conway_polynomial
Concept in mathematics
subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n
Trigonometric_polynomial
Method for solving one problem using another
In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine
Polynomial-time_reduction
Polynomials arising in knot theory
theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant
HOMFLY_polynomial
Topics referred to by the same term
Polynomial identity may refer to: Algebraic identities of polynomials (see Factorization) Polynomial identity ring Polynomial identity testing This disambiguation
Polynomial_identity
Subexponential bound in computational complexity
science, a function f ( n ) {\displaystyle f(n)} is said to exhibit quasi-polynomial growth when it has an upper bound of the form f ( n ) = 2 O ( ( log
Quasi-polynomial_growth
Polynomial sequence
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets
Hermite_polynomials
Method of representing a random variable
Polynomial chaos (PC), also called polynomial chaos expansion (PCE) and Wiener chaos expansion, is a method for representing a random variable in terms
Polynomial_chaos
Concept in several complex variables
variables, polynomial convexity is a notion of convexity for compact subsets of complex Euclidean space defined using complex polynomials. It is analogous
Polynomial_convexity
Mathematical construct in computer algebra
Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots ,x_{n}]} over a
Gröbner_basis
Polynomial whose nonzero terms all have the same degree
In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example
Homogeneous_polynomial
Complexity class
every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution
NP-hardness
Every polynomial has a real or complex root
non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the
Polynomial_root-finding
Polynomial sequence
In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight
Gegenbauer_polynomials
Polynomial equation, generally univariate
an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial, usually with rational numbers
Algebraic_equation
Type of symmetric polynomials in mathematics
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the
Schur_polynomial
Function in algebraic graph theory
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a
Chromatic_polynomial
Set of polynomials where any two are orthogonal to each other
orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The
Orthogonal_polynomials
Computer science concept
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that
Polynomial_hierarchy
Mathematical invariant of a knot or link
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant
Jones_polynomial
Tool in mathematical dimension theory
In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively
Positive_polynomial
Polynomial invariant under variable permutations
symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally
Symmetric_polynomial
Type of functions in algebra
algebra, a polynomial map or polynomial mapping P : V → W {\displaystyle P:V\to W} between vector spaces over an infinite field k is a polynomial in linear
Polynomial_mapping
Point where function's value is zero
root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number
Zero_of_a_function
Factorization under function composition
mathematics, a polynomial decomposition expresses a polynomial f as the functional composition g ∘ h {\displaystyle g\circ h} of polynomials g and h, where
Polynomial_decomposition
Class of problems in computer science
machine in polynomial time, with an error probability of less than 1/2 for all instances. The abbreviation PP refers to probabilistic polynomial time. The
PP_(complexity)
Mathematical connection between field theory and group theory
introduced the subject for studying roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms
Galois_theory
Concept in abstract algebra
mathematics, the minimal polynomial of an element α {\displaystyle \alpha } of an extension field of a field is, roughly speaking, the polynomial of lowest degree
Minimal polynomial (field theory)
Minimal_polynomial_(field_theory)
Type of approximation algorithm
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Computational method
mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the
Factorization_of_polynomials
Failure of convergence in interpolation
oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation
Runge's_phenomenon
Algorithm to smooth data points
fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally
Savitzky–Golay_filter
Polynomial with reversed root positions
from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by p∗ or pR, is the polynomial p ∗ ( x ) = a n + a n − 1 x + ⋯ + a 0
Reciprocal_polynomial
Class of problems solvable in polynomial time
solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of
P_(complexity)
Polynomial with negative exponents
In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field F {\displaystyle \mathbb {F} } is a linear combination
Laurent_polynomial
In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential
Exponential_polynomial
On the remainder of division by x – r
the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states
Polynomial_remainder_theorem
In mathematics, the Hamiltonian cycle polynomial of an n×n-matrix is a polynomial in its entries, defined as ham ( A ) = ∑ σ ∈ H n ∏ i = 1 n a i , σ
Hamiltonian_cycle_polynomial
In algebra, a multivariate polynomial f ( x ) = ∑ α a α x α , where α = ( i 1 , … , i r ) ∈ N r , and x α = x 1 i 1 ⋯ x r i r , {\displaystyle f(x)=\sum
Quasi-homogeneous_polynomial
Rational fractions as sums of simple terms
and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several
Partial fraction decomposition
Partial_fraction_decomposition
Polynomial sequence
In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series
Bernoulli_polynomials
About products of primitive polynomials
Gauss's lemma, named after Carl Friedrich Gauss, is a theorem about polynomials over the integers, or, more generally, over a unique factorization domain
Gauss's_lemma_(polynomials)
In algebra, an alternating polynomial is a polynomial f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} such that if one switches any two of the
Alternating_polynomial
Product of pairwise differences
In algebra, the Vandermonde polynomial of an ordered set of n variables X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} , named after Alexandre-Théophile
Vandermonde_polynomial
In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934)
Meixner_polynomials
Concept in complexity theory
theory, a numeric algorithm runs in pseudo-polynomial time if its running time is bounded from above by a polynomial function of the two variables: the numeric
Pseudo-polynomial_time
Polynomial that permutes a ring
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g
Permutation_polynomial
Theorem in geometric group theory
Gromov's theorem on groups of polynomial growth, first proved by Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups
Gromov's theorem on groups of polynomial growth
Gromov's_theorem_on_groups_of_polynomial_growth
Topics referred to by the same term
Minimum polynomial can refer to: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists articles associated
Minimum_polynomial
Topics referred to by the same term
primitive polynomial may refer to: Primitive polynomial (field theory), a minimal polynomial of an extension of finite fields Primitive polynomial (ring theory)
Primitive_polynomial
Counts the number of necklaces of n colored beads picked from α available colors
In combinatorial mathematics, the necklace polynomial, or Moreau's necklace-counting function, introduced by C. Moreau (1872), counts the number of distinct
Necklace_polynomial
Algorithms for polynomial evaluation
In mathematics and computer science, polynomial evaluation refers to computation of the value of a polynomial when its indeterminates are substituted for
Polynomial_evaluation
Methods of error detection and correction in communications
after division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either
Mathematics of cyclic redundancy checks
Mathematics_of_cyclic_redundancy_checks
Relations between power sums and elementary symmetric functions
of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable
Newton's_identities
Type of shift register in computing
arithmetic as a polynomial mod 2. This means that the coefficients of the polynomial must be 1s or 0s. This is called the feedback polynomial or reciprocal
Linear-feedback shift register
Linear-feedback_shift_register
Approximation of a function by a polynomial
by a polynomial of degree k {\textstyle k} , called the k {\textstyle k} -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the
Taylor's_theorem
In mathematics, a generic polynomial refers usually to a polynomial whose coefficients are indeterminates. For example, if a, b, and c are indeterminates
Generic_polynomial
structures) is said to have polynomial delay if the time between the output of any one structure and the next is bounded by a polynomial function of the input
Polynomial_delay
Cryptographic algorithm created by Adi Shamir
specifically that k {\displaystyle k} points on the polynomial uniquely determines a polynomial of degree less than or equal to k − 1 {\displaystyle
Shamir's_secret_sharing
Polynomial sequence
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are
Jacobi_polynomials
Sequence valued in polynomials
All-one polynomials Abel polynomials Bell polynomials Bernoulli polynomials Cyclotomic polynomials Dickson polynomials Fibonacci polynomials Lagrange
Polynomial_sequence
Concept in computer science
bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error
BPP_(complexity)
This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics. Degree: The maximum exponents
List_of_polynomial_topics
Topics referred to by the same term
Minimal polynomial can mean: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists mathematics articles
Minimal_polynomial
POLYNOMIAL
POLYNOMIAL
POLYNOMIAL
POLYNOMIAL
Boy/Male
Bengali, Hindu, Indian, Mythological, Traditional
Lord Krishna
Female
English
Feminine form of English Edwin, EDWINA means "rich friend."
Female
Bulgarian
, violet.
Girl/Female
French
Victory.
Girl/Female
Indian, Marathi
Education
Boy/Male
Tamil
Happy, Happiness
Boy/Male
Arabic, Muslim
Servant of the Capable
Boy/Male
Indian
The End of an Era
Male
Greek
(ΣπÏÏος) Variant spelling of Greek Spyros, SPIROS means "spirit."
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name, probably an altered form of Baxenden, a place near Accrington, which is named with an unattested Old English word bæcstÄn ‘bakestone’ (a flat stone on which bread was baked) + denu ‘valley’. Middle English dale was sometimes substituted for Old English denu in northern place names.
POLYNOMIAL
POLYNOMIAL
POLYNOMIAL
POLYNOMIAL
POLYNOMIAL
n. & a.
Same as Polynomial.
a.
Possessing the same number of factors of a given kind; as, a homogeneous polynomial.
n.
An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
a.
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
n.
A polynomial of four terms connected by the signs plus or minus.
n.
A polynomial name or term.