# Polynomial/Related Articles

From Citizendium, the Citizens' Compendium

*See also changes related to Polynomial, or pages that link to Polynomial or to this page or whose text contains "Polynomial".*

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- Algebraic geometry [r]: Discipline of mathematics that studies the geometric properties of the objects defined by algebraic equations.
^{[e]} - Algebraic independence [r]: The property of elements of an extension field which satisfy only the trivial polynomial relation.
^{[e]} - Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients.
^{[e]} - Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity.
^{[e]} - Basis (linear algebra) [r]: A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others.
^{[e]} - Binomial theorem [r]: for any natural number
*n*.^{[e]} - Calculus [r]: The elementary study of real (or complex) functions involving derivatives and integration.
^{[e]} - Catalog of special functions [r]:
*Add brief definition or description* - Completing the square [r]: Rewriting a quadratic polynomial as a constant multiple of a linear polynomial plus a constant.
^{[e]} - Complex number [r]: Numbers of the form
*a+bi*, where*a*and*b*are real numbers and*i*denotes a number satisfying .^{[e]} - Content (algebra) [r]: The highest common factor of the coefficients of a polynomial.
^{[e]} - Cubic equation [r]: A polynomial equation with of degree 3 (i.e.,
*x*^{3}+*px*^{2}+*qx*+r=0).^{[e]} - Cyclotomic polynomial [r]: A polynomial whose roots are primitive roots of unity.
^{[e]} - Discriminant of a polynomial [r]: An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences between the roots.
^{[e]} - E (mathematics) [r]: Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logarithms.
^{[e]} - Elementary function [r]: Mathematical functions built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary arithmetic operations (+ – × ÷).
^{[e]} - Entire function [r]: is a function that is holomorphic in the whole complex plane.
^{[e]} - Exponential growth [r]: Increase of a quantity x with time t according to the equation x = Kat, where K and a are constants, a is greater than 1, and K is greater than 0.
^{[e]} - Fibonacci polynomials [r]: Polynomial sequence which can be considered as a generalisation of the Fibonacci numbers.
^{[e]} - Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
^{[e]} - Field extension [r]: A field containing a given field as a subfield.
^{[e]} - Fraction (mathematics) [r]: A concept used to convey a proportional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
^{[e]} - Fundamental Theorem of Algebra [r]: Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a root.
^{[e]} - Galois theory [r]: Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions.
^{[e]} - Gamma function [r]: A mathematical function that extends the domain of factorials to non-integers.
^{[e]} - Graph coloring [r]: Graph labelling, which assigns labels traditionally called 'colours' to elements of a graph subject to certain constraints.
^{[e]} - Group (mathematics) [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation.
^{[e]} - Hall polynomial [r]: The structure constants of Hall algebra.
^{[e]} - Holomorphic function [r]: Function from to is called
**holomorphic**in domain if for every open domain there exist derivative .^{[e]} - Integer [r]: The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
^{[e]} - Legendre-Gauss Quadrature formula [r]: the specific approximation of the integral with the sum of N terms, which becomes exact for the polynomial integrand of order < 2N.
^{[e]} - Littlewood polynomial [r]: A polynomial all of whose coefficients are plus or minus 1.
^{[e]} - Mathematics [r]: The study of quantities, structures, their relations, and changes thereof.
^{[e]} - Minimal polynomial [r]: The monic polynomial of least degree which a square matrix or endomorphism satisfies.
^{[e]} - Multiple (mathematics) [r]: The product of an integer with another integer.
^{[e]} - Multiplication [r]: The binary mathematical operation of scaling one number or quantity by another (multiplying).
^{[e]} - Null set [r]:
*Add brief definition or description* - Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
^{[e]} - Polynomial ring [r]: Ring formed from the set of polynomials in one or more variables with coefficients in another ring.
^{[e]} - Quadratic equation [r]: An equation of the form
*ax*^{2}+*bx*+*c*= 0 where*a*,*b*and*c*are constants.^{[e]} - Rational function [r]: Function that can be expressed as a quotient of polynomials, excluding division by zero.
^{[e]} - Reaction rate [r]: The amount of reactant or product that is formed or removed (in moles or mass units) per unit time per unit volume, in a particular reaction.
^{[e]} - Real number [r]: A limit of the Cauchy sequence of rational numbers.
^{[e]} - Resultant (algebra) [r]: An invariant which determines whether or not two polynomials have a factor in common.
^{[e]} - Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid.
^{[e]} - Root of unity [r]: An algebraic quantity some power of which is equal to one.
^{[e]} - Splitting field [r]: A field extension generated by the roots of a polynomial.
^{[e]} - Transcendental number [r]: A number which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients.
^{[e]} - Trigonometric function [r]: Function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, and cosecant.
^{[e]} - Vector space [r]: A set of vectors that can be added together or scalar multiplied to form new vectors
^{[e]}