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) » « Shrink index
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.
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.
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.
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
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.
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.
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).
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
Algebraic varieties are the central objects of study in algebraic geometry.
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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.
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
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.
In mathematics, the associative property is a property of some binary operations.
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.
Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.
In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial.
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.
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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.
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.
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.
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.
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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).
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.
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.
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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.
In mathematics, the adjective constant means non-varying.
In mathematics, a constant function is a function whose (output) value is the same for every input value.
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.
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
In algebra, a cubic function is a function of the form in which is nonzero.
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
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).
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.
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).
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.
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
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.
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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.
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.
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.
In mathematics, an equation is a statement of an equality containing one or more variables.
In arithmetic, Euclidean division is the process of division of two integers, which produces a quotient and a remainder smaller than the divisor.
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.
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.
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
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.
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.
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.
Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.
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.
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.
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.
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
Functional notation is the notation for expressing functions as f(x) which was first used by Leonhard Euler in 1734.
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
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.
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".
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.
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.
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.
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
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.
A hybrid word or hybridism is a word that etymologically derives from at least two languages.
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
In mathematics an identity is an equality relation A.
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.
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.
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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.
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.
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.
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.
In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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.
In mathematics, Lill's method is a visual method of finding the real roots of polynomials of any degree.
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).
This is a list of polynomial topics, by Wikipedia page.
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a matrix polynomial is a polynomial with square matrices as variables.
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.
Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk, Protestant reformer and mathematician.
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.
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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.
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
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.
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
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").
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.
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).
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
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.
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.
In algebra, a polynomial functor is a functor on the category \mathcalV of finite-dimensional vector spaces that depends polynomially on vector spaces.
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.
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.
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.
In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.
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.
In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of polynomial.
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.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.
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.
In elementary algebra, the quadratic formula is the solution of the quadratic equation.
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.
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.
In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.
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.
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.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
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.
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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.
Robert Recorde (c.1512–1558) was a Welsh physician and mathematician.
In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.
In mathematics and engineering, the s-plane is the complex plane on which Laplace transforms are graphed.
In algebra, a sextic polynomial is a polynomial of degree six.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society.
The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.
In mathematics, a spline is a function defined piecewise by polynomials.
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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.
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.
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
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.
A system of polynomial equations is a set of simultaneous equations f1.
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.
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.
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.
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.
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials.
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.
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.
In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable.
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.
In mathematics, Vieta's formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
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.
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).
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