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  2. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    If F is a field and f and g are polynomials in F[x] with g ≠ 0, then there exist unique polynomials q and r in F[x] with = + and such that the degree of r is smaller than the degree of g (using the convention that the polynomial 0 has a negative degree). The polynomials q and r are uniquely determined by f and g.

  3. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line; Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola.

  4. Outline of algebra - Wikipedia

    en.wikipedia.org/wiki/Outline_of_algebra

    This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero. Equations – equality of two mathematical expressions; Linear equation – an algebraic equation with a degree of one; Quadratic equation – an algebraic equation with a degree of two

  5. Algebraic expression - Wikipedia

    en.wikipedia.org/wiki/Algebraic_expression

    An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.

  6. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). [5] These operations may be performed on numbers, in which case they are often called arithmetic operations.

  7. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    The elements of an algebraic number field are usually represented as polynomials in a generator of the field which satisfies some univariate polynomial equation. To work with a polynomial system whose coefficients belong to a number field, it suffices to consider this generator as a new variable and to add the equation of the generator to the ...

  8. Zhegalkin polynomial - Wikipedia

    en.wikipedia.org/wiki/Zhegalkin_polynomial

    Zhegalkin showed that all Boolean operations could be written as ordinary numeric polynomials, representing the false and true values as 0 and 1, the integers mod 2. Logical conjunction is written as xy , and logical exclusive-or as arithmetic addition mod 2, (written here as x ⊕ y to avoid confusion with the common use of + as a synonym for ...

  9. Elementary function - Wikipedia

    en.wikipedia.org/wiki/Elementary_function

    In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).

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