Polynomials

2017-07-27T17:49:01+03:00[Europe/Moscow] en true Cubic function, Abel–Ruffini theorem, Binomial theorem, Fundamental theorem of algebra, Polynomial remainder theorem, Symmetric polynomial, Linear function (calculus), Legendre polynomials, Symmetric algebra, Polynomial matrix, Pfaffian, Factorization of polynomials, Kauffman polynomial, Polynomial greatest common divisor, Polylogarithmic function, Touchard polynomials, Theory of equations, Romanovski polynomials, Matrix polynomial, Primitive part and content, Octic equation flashcards Polynomials
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  • 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.
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