In algebra, a cubic function is a function of the form where a is nonzero.
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.
Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
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.
Polynomial remainder theorem
In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.
Symmetric polynomial
In mathematics, a 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.
Linear function (calculus)
In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
Legendre polynomials
In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.
Symmetric algebra
In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.
Polynomial matrix
In mathematics, a polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials.
Pfaffian
In mathematics, the determinant of a skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depend on the size of the matrix.
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.
Kauffman polynomial
In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman.
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.
Polylogarithmic function
A polylogarithmic function in n is a polynomial in the logarithm of n, In computer science, polylogarithmic functions occur as the order of memory used by some algorithms (e.g., "it has polylogarithmic order").
Touchard polynomials
The Touchard polynomials, studied by Jacques Touchard (), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by where is a Stirling number of the second kind, i.
Theory of equations
In algebra, the theory of equations is the analysis of the nature and algebraic solutions of algebraic equations (also called polynomial equations), which are equations defined by a polynomial.
Romanovski polynomials
In mathematics, Romanovski polynomials is an informal term for one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics.
Matrix polynomial
In mathematics, a matrix polynomial is a polynomial with matrices as variables.
Primitive part and content
In algebra, the content of a polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients.
Octic equation
In algebra, an octic equation is an equation of the form where a ≠ 0.
Click to flip
Cubic function
In algebra, a cubic function is a function of the form where a is nonzero.
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.
Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
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.
Polynomial remainder theorem
In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.
Symmetric polynomial
In mathematics, a 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.
Linear function (calculus)
In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
Legendre polynomials
In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.
Symmetric algebra
In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.
Polynomial matrix
In mathematics, a polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials.
Pfaffian
In mathematics, the determinant of a skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depend on the size of the matrix.
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.
Kauffman polynomial
In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman.
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.
Polylogarithmic function
A polylogarithmic function in n is a polynomial in the logarithm of n, In computer science, polylogarithmic functions occur as the order of memory used by some algorithms (e.g., "it has polylogarithmic order").
Touchard polynomials
The Touchard polynomials, studied by Jacques Touchard (), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by where is a Stirling number of the second kind, i.
Theory of equations
In algebra, the theory of equations is the analysis of the nature and algebraic solutions of algebraic equations (also called polynomial equations), which are equations defined by a polynomial.
Romanovski polynomials
In mathematics, Romanovski polynomials is an informal term for one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics.
Matrix polynomial
In mathematics, a matrix polynomial is a polynomial with matrices as variables.
Primitive part and content
In algebra, the content of a polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients.
Octic equation
In algebra, an octic equation is an equation of the form where a ≠ 0.