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Everything about Polynomial
Type of mathematical expression
In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is. An example with three indeterminates is. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PolynomialA 5-minute orientation
- Skim a recent paper: Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristorInfluential work since 2022
- Pick up a classic book: A first course in abstract algebraThe most-reprinted book on the subject
- Read the landmark paper: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum ComputerCited 6,084 times
- Go sideways: Monic polynomialA closely related topic
- Go sideways: Irreducible polynomialA closely related topic
📖 Definitions
Noun An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as anxn+an−1xn−1+...+a0x0.
Noun A taxonomic designation (such as of a subspecies) consisting of more than two terms.
Adjective Able to be described or limited by a polynomial.
Adjective Of a polynomial name or entity.
🏆 Landmark papers (most cited)
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
Quantum field theory and the Jones polynomial
A new polynomial-time algorithm for linear programming
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
Polynomial Codes Over Certain Finite Fields
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
ASTRAL-III: polynomial time species tree reconstruction from partially resolved gene trees
🆕 Influential since 2022
Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor
Exploiting robust quadratic polynomial hyperchaotic map and pixel fusion strategy for efficient image encryption
Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption
Ensemble regression based on polynomial regression-based decision tree and its application in the in-situ data of tunnel boring machine
Two-Dimensional Parametric Polynomial Chaotic System
📚 Books worth reading
A first course in abstract algebraJohn B. Fraleigh · 1967
A First Course in Abstract Algebra [Seventh 7th Edition]John B. Fraleigh · 1969
Classical and Quantum Orthogonal Polynomials in One VariableMourad E. H. Ismail · 2005
Bernstein polynomialsG. G. Lorentz · 1953- 📕Polynomial Identities and Combinatorial MethodsAntonio Giambruno, Amitai Regev · 2003
General orthogonal polynomialsHerbert Stahl · 1992
Polynomials and the mod 2 Steenrod AlgebraGrant Walker, Reginald M. W. Wood · 2017- 📕Orthogonal PolynomialsEvguenii A. Rakhmanov · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Monic polynomial 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 coefficien…
- Irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.…
- Polynomial ring In mathematics, 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…
- Factorization In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object…
- Discriminant In mathematics, the discriminant of a polynomial is an expression in its coefficients that provides information about its roots without explicitly calculating…
- Coefficient In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or any other type of expression. It may be a…
- Rational function In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator…
- Formal power series In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual…