Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Polynomial

Index Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. [1]

162 relations: Abel–Ruffini theorem, Absolute value, Abstract algebra, Addition, Algebra, Algebra over a field, Algebraic element, Algebraic equation, Algebraic expression, Algebraic fraction, Algebraic geometry, Algebraic variety, Algorithm, Antiderivative, Argument of a function, Associative algebra, Associative property, Asymptote, Évariste Galois, Binomial (polynomial), Calculus, Cambridge University Press, Characteristic polynomial, Chemistry, Chromatic polynomial, Coefficient, Commutative algebra, Commutative property, Commutative ring, Compact space, Complex number, Computational complexity theory, Computer, Computer algebra system, Constant (mathematics), Constant function, Constant term, Continuous function, Cubic function, Degree of a polynomial, Derivative, Differentiable function, Diophantine equation, Discrete Fourier transform, Distributive property, Domain of a function, Economics, Eigenvalues and eigenvectors, Eisenstein's criterion, Entire function, ..., Equation, Euclidean division, Euclidean domain, Exponential polynomial, Exponentiation, Expression (mathematics), Factorization of polynomials, Fermat's Last Theorem, Fermat's little theorem, Field (mathematics), Finite field, Formal power series, Fourier series, Function (mathematics), Function composition, Functional notation, Fundamental theorem of algebra, Galois theory, Gaussian elimination, Golden ratio, Graph (discrete mathematics), Graph of a function, Group theory, Hilbert's tenth problem, Homogeneous function, Homogeneous polynomial, Horner's method, Hybrid word, Ideal (ring theory), Identity (mathematics), Identity matrix, Indeterminate (variable), Integer, Integral domain, Interpolation, Interval (mathematics), Irrational number, Irreducible polynomial, Laplace transform, Laurent polynomial, Lill's method, Linear combination, List of polynomial topics, Mathematical analysis, Mathematics, Matrix polynomial, Matrix ring, Michael Stifel, Minimal polynomial (field theory), Modular arithmetic, Monic polynomial, Monomial, Multiplication, Multiplicity (mathematics), Natural number, Niels Henrik Abel, Numerical analysis, Parabola, Periodic function, Physics, Polynomial, Polynomial functor, Polynomial greatest common divisor, Polynomial long division, Polynomial mapping, Polynomial remainder theorem, Polynomial ring, Polynomial transformation, Power series, Prime number, Product (mathematics), Quadratic equation, Quadratic formula, Quartic function, Quintic function, Quotient, Rational function, Rational number, Real number, René Descartes, Restriction (mathematics), Ring (mathematics), Ring of polynomial functions, Robert Recorde, Root-finding algorithm, S-plane, Sextic equation, Slope, Smoothness, Social science, Society for Industrial and Applied Mathematics, Spline (mathematics), Square matrix, Stone–Weierstrass theorem, Substitution (algebra), Subtraction, Summation, System of linear equations, System of polynomial equations, Taylor's theorem, Term (logic), The Nine Chapters on the Mathematical Art, The Whetstone of Witte, Time complexity, Trigonometric interpolation, Unique factorization domain, Unit (ring theory), Univariate, Variable (mathematics), Vieta's formulas, Word problem (mathematics education), Zero of a function. Expand index (112 more) »

Abel–Ruffini theorem

In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.

New!!: Polynomial and Abel–Ruffini theorem · See more »

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

New!!: Polynomial and Absolute value · See more »

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

New!!: Polynomial and Abstract algebra · See more »

Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

New!!: Polynomial and Addition · See more »

Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

New!!: Polynomial and Algebra · See more »

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

New!!: Polynomial and Algebra over a field · See more »

Algebraic element

In mathematics, if is a field extension of, then an element of is called an algebraic element over, or just algebraic over, if there exists some non-zero polynomial with coefficients in such that.

New!!: Polynomial and Algebraic element · See more »

Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

New!!: Polynomial and Algebraic equation · See more »

Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

New!!: Polynomial and Algebraic expression · See more »

Algebraic fraction

In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.

New!!: Polynomial and Algebraic fraction · See more »

Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

New!!: Polynomial and Algebraic geometry · See more »

Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

New!!: Polynomial and Algebraic variety · See more »

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

New!!: Polynomial and Algorithm · See more »

Antiderivative

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.

New!!: Polynomial and Antiderivative · See more »

Argument of a function

In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.

New!!: Polynomial and Argument of a function · See more »

Associative algebra

In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.

New!!: Polynomial and Associative algebra · See more »

Associative property

In mathematics, the associative property is a property of some binary operations.

New!!: Polynomial and Associative property · See more »

Asymptote

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

New!!: Polynomial and Asymptote · See more »

Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

New!!: Polynomial and Évariste Galois · See more »

Binomial (polynomial)

In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial.

New!!: Polynomial and Binomial (polynomial) · See more »

Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

New!!: Polynomial and Calculus · See more »

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

New!!: Polynomial and Cambridge University Press · See more »

Characteristic polynomial

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.

New!!: Polynomial and Characteristic polynomial · See more »

Chemistry

Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

New!!: Polynomial and Chemistry · See more »

Chromatic polynomial

The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.

New!!: Polynomial and Chromatic polynomial · See more »

Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

New!!: Polynomial and Coefficient · See more »

Commutative algebra

Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.

New!!: Polynomial and Commutative algebra · See more »

Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

New!!: Polynomial and Commutative property · See more »

Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

New!!: Polynomial and Commutative ring · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

New!!: Polynomial and Compact space · See more »

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

New!!: Polynomial and Complex number · See more »

Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

New!!: Polynomial and Computational complexity theory · See more »

Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

New!!: Polynomial and Computer · See more »

Computer algebra system

A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.

New!!: Polynomial and Computer algebra system · See more »

Constant (mathematics)

In mathematics, the adjective constant means non-varying.

New!!: Polynomial and Constant (mathematics) · See more »

Constant function

In mathematics, a constant function is a function whose (output) value is the same for every input value.

New!!: Polynomial and Constant function · See more »

Constant term

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.

New!!: Polynomial and Constant term · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

New!!: Polynomial and Continuous function · See more »

Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

New!!: Polynomial and Cubic function · See more »

Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

New!!: Polynomial and Degree of a polynomial · See more »

Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

New!!: Polynomial and Derivative · See more »

Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

New!!: Polynomial and Differentiable function · See more »

Diophantine equation

In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).

New!!: Polynomial and Diophantine equation · See more »

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

New!!: Polynomial and Discrete Fourier transform · See more »

Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

New!!: Polynomial and Distributive property · See more »

Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

New!!: Polynomial and Domain of a function · See more »

Economics

Economics is the social science that studies the production, distribution, and consumption of goods and services.

New!!: Polynomial and Economics · See more »

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

New!!: Polynomial and Eigenvalues and eigenvectors · See more »

Eisenstein's criterion

In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers—that is, for it to be unfactorable into the product of non-constant polynomials with rational coefficients.

New!!: Polynomial and Eisenstein's criterion · See more »

Entire function

In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.

New!!: Polynomial and Entire function · See more »

Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

New!!: Polynomial and Equation · See more »

Euclidean division

In arithmetic, Euclidean division is the process of division of two integers, which produces a quotient and a remainder smaller than the divisor.

New!!: Polynomial and Euclidean division · See more »

Euclidean domain

In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of the integers.

New!!: Polynomial and Euclidean domain · See more »

Exponential 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 function.

New!!: Polynomial and Exponential polynomial · See more »

Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

New!!: Polynomial and Exponentiation · See more »

Expression (mathematics)

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

New!!: Polynomial and Expression (mathematics) · See more »

Factorization of polynomials

In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

New!!: Polynomial and Factorization of polynomials · See more »

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

New!!: Polynomial and Fermat's Last Theorem · See more »

Fermat's little theorem

Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.

New!!: Polynomial and Fermat's little theorem · See more »

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

New!!: Polynomial and Field (mathematics) · See more »

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

New!!: Polynomial and Finite field · See more »

Formal power series

In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.

New!!: Polynomial and Formal power series · See more »

Fourier series

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.

New!!: Polynomial and Fourier series · See more »

Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

New!!: Polynomial and Function (mathematics) · See more »

Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

New!!: Polynomial and Function composition · See more »

Functional notation

Functional notation is the notation for expressing functions as f(x) which was first used by Leonhard Euler in 1734.

New!!: Polynomial and Functional notation · See more »

Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

New!!: Polynomial and Fundamental theorem of algebra · See more »

Galois theory

In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.

New!!: Polynomial and Galois theory · See more »

Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

New!!: Polynomial and Gaussian elimination · See more »

Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

New!!: Polynomial and Golden ratio · See more »

Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

New!!: Polynomial and Graph (discrete mathematics) · See more »

Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

New!!: Polynomial and Graph of a function · See more »

Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

New!!: Polynomial and Group theory · See more »

Hilbert's tenth problem

Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.

New!!: Polynomial and Hilbert's tenth problem · See more »

Homogeneous function

In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.

New!!: Polynomial and Homogeneous function · See more »

Homogeneous polynomial

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.

New!!: Polynomial and Homogeneous polynomial · See more »

Horner's method

In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S..) is either of two things.

New!!: Polynomial and Horner's method · See more »

Hybrid word

A hybrid word or hybridism is a word that etymologically derives from at least two languages.

New!!: Polynomial and Hybrid word · See more »

Ideal (ring theory)

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.

New!!: Polynomial and Ideal (ring theory) · See more »

Identity (mathematics)

In mathematics an identity is an equality relation A.

New!!: Polynomial and Identity (mathematics) · See more »

Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

New!!: Polynomial and Identity matrix · See more »

Indeterminate (variable)

In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series.

New!!: Polynomial and Indeterminate (variable) · See more »

Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

New!!: Polynomial and Integer · See more »

Integral domain

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

New!!: Polynomial and Integral domain · See more »

Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

New!!: Polynomial and Interpolation · See more »

Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

New!!: Polynomial and Interval (mathematics) · See more »

Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

New!!: Polynomial and Irrational number · See more »

Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.

New!!: Polynomial and Irreducible polynomial · See more »

Laplace transform

In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.

New!!: Polynomial and Laplace transform · See more »

Laurent polynomial

In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field \mathbb is a linear combination of positive and negative powers of the variable with coefficients in \mathbb.

New!!: Polynomial and Laurent polynomial · See more »

Lill's method

In mathematics, Lill's method is a visual method of finding the real roots of polynomials of any degree.

New!!: Polynomial and Lill's method · See more »

Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

New!!: Polynomial and Linear combination · See more »

List of polynomial topics

This is a list of polynomial topics, by Wikipedia page.

New!!: Polynomial and List of polynomial topics · See more »

Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

New!!: Polynomial and Mathematical analysis · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Polynomial and Mathematics · See more »

Matrix polynomial

In mathematics, a matrix polynomial is a polynomial with square matrices as variables.

New!!: Polynomial and Matrix polynomial · See more »

Matrix ring

In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.

New!!: Polynomial and Matrix ring · See more »

Michael Stifel

Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk, Protestant reformer and mathematician.

New!!: Polynomial and Michael Stifel · See more »

Minimal polynomial (field theory)

In field theory, a branch of mathematics, the minimal polynomial of a value α is, roughly speaking, the polynomial of lowest degree having coefficients of a specified type, such that α is a root of the polynomial.

New!!: Polynomial and Minimal polynomial (field theory) · See more »

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

New!!: Polynomial and Modular arithmetic · See more »

Monic polynomial

In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

New!!: Polynomial and Monic polynomial · See more »

Monomial

In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.

New!!: Polynomial and Monomial · See more »

Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

New!!: Polynomial and Multiplication · See more »

Multiplicity (mathematics)

In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.

New!!: Polynomial and Multiplicity (mathematics) · See more »

Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

New!!: Polynomial and Natural number · See more »

Niels Henrik Abel

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.

New!!: Polynomial and Niels Henrik Abel · See more »

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

New!!: Polynomial and Numerical analysis · See more »

Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

New!!: Polynomial and Parabola · See more »

Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

New!!: Polynomial and Periodic function · See more »

Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

New!!: Polynomial and Physics · See more »

Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

New!!: Polynomial and Polynomial · See more »

Polynomial functor

In algebra, a polynomial functor is a functor on the category \mathcalV of finite-dimensional vector spaces that depends polynomially on vector spaces.

New!!: Polynomial and Polynomial functor · See more »

Polynomial greatest common divisor

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.

New!!: Polynomial and Polynomial greatest common divisor · See more »

Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

New!!: Polynomial and Polynomial long division · See more »

Polynomial mapping

In algebra, a polynomial mapping P: V \to W between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in W; i.e., it can be written as where L_j: V \to k are linear functionals.

New!!: Polynomial and Polynomial mapping · See more »

Polynomial remainder theorem

In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.

New!!: Polynomial and Polynomial remainder theorem · See more »

Polynomial ring

In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.

New!!: Polynomial and Polynomial ring · See more »

Polynomial transformation

In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of polynomial.

New!!: Polynomial and Polynomial transformation · See more »

Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

New!!: Polynomial and Power series · See more »

Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

New!!: Polynomial and Prime number · See more »

Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

New!!: Polynomial and Product (mathematics) · See more »

Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

New!!: Polynomial and Quadratic equation · See more »

Quadratic formula

In elementary algebra, the quadratic formula is the solution of the quadratic equation.

New!!: Polynomial and Quadratic formula · See more »

Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

New!!: Polynomial and Quartic function · See more »

Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

New!!: Polynomial and Quintic function · See more »

Quotient

In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.

New!!: Polynomial and Quotient · See more »

Rational function

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

New!!: Polynomial and Rational function · See more »

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

New!!: Polynomial and Rational number · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

New!!: Polynomial and Real number · See more »

René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

New!!: Polynomial and René Descartes · See more »

Restriction (mathematics)

In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.

New!!: Polynomial and Restriction (mathematics) · See more »

Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

New!!: Polynomial and Ring (mathematics) · See more »

Ring of polynomial functions

In mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring.

New!!: Polynomial and Ring of polynomial functions · See more »

Robert Recorde

Robert Recorde (c.1512–1558) was a Welsh physician and mathematician.

New!!: Polynomial and Robert Recorde · See more »

Root-finding algorithm

In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.

New!!: Polynomial and Root-finding algorithm · See more »

S-plane

In mathematics and engineering, the s-plane is the complex plane on which Laplace transforms are graphed.

New!!: Polynomial and S-plane · See more »

Sextic equation

In algebra, a sextic polynomial is a polynomial of degree six.

New!!: Polynomial and Sextic equation · See more »

Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

New!!: Polynomial and Slope · See more »

Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

New!!: Polynomial and Smoothness · See more »

Social science

Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society.

New!!: Polynomial and Social science · See more »

Society for Industrial and Applied Mathematics

The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.

New!!: Polynomial and Society for Industrial and Applied Mathematics · See more »

Spline (mathematics)

In mathematics, a spline is a function defined piecewise by polynomials.

New!!: Polynomial and Spline (mathematics) · See more »

Square matrix

In mathematics, a square matrix is a matrix with the same number of rows and columns.

New!!: Polynomial and Square matrix · See more »

Stone–Weierstrass theorem

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.

New!!: Polynomial and Stone–Weierstrass theorem · See more »

Substitution (algebra)

In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols (often called variables or indeterminates); the operation consists of systematically replacing occurrences of some symbol by a given value.

New!!: Polynomial and Substitution (algebra) · See more »

Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

New!!: Polynomial and Subtraction · See more »

Summation

In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.

New!!: Polynomial and Summation · See more »

System of linear equations

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.

New!!: Polynomial and System of linear equations · See more »

System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1.

New!!: Polynomial and System of polynomial equations · See more »

Taylor's theorem

In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.

New!!: Polynomial and Taylor's theorem · See more »

Term (logic)

In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

New!!: Polynomial and Term (logic) · See more »

The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.

New!!: Polynomial and The Nine Chapters on the Mathematical Art · See more »

The Whetstone of Witte

The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes of Surde Nombers.

New!!: Polynomial and The Whetstone of Witte · See more »

Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

New!!: Polynomial and Time complexity · See more »

Trigonometric interpolation

In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials.

New!!: Polynomial and Trigonometric interpolation · See more »

Unique factorization domain

In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.

New!!: Polynomial and Unique factorization domain · See more »

Unit (ring theory)

In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.

New!!: Polynomial and Unit (ring theory) · See more »

Univariate

In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable.

New!!: Polynomial and Univariate · See more »

Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

New!!: Polynomial and Variable (mathematics) · See more »

Vieta's formulas

In mathematics, Vieta's formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.

New!!: Polynomial and Vieta's formulas · See more »

Word problem (mathematics education)

In science education, a word problem is a mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation.

New!!: Polynomial and Word problem (mathematics education) · See more »

Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

New!!: Polynomial and Zero of a function · See more »

Redirects here:

Algorithms for solving polynomial equations, Bivariate polynomial, Complex Polynomial, Integer polynomial, Linear polynomial, Multivariate polynomial, Order and degree of polynomial, Polynomial Function, Polynomial Functions, Polynomial curve, Polynomial expression, Polynomial function, Polynomial map, Polynomial multiplication, Polynomial notation, Polynomials, Quadnomial, Quadranomial, Real polynomial, Simple root, Simple root (polynomial), Solving polynomial equations, Standard Form of a Polynomial, Standard form of a polynomial, Univariate polynomial, Zero polynomial.

References

[1] https://en.wikipedia.org/wiki/Polynomial

OutgoingIncoming
Hey! We are on Facebook now! »