polynomickou

Polynomickou is the feminine accusative singular form of the Czech adjective polynomický, used to describe items related to polynomials. In Czech, adjectives agree with the noun in gender, number, and case, so polynomickou can modify feminine nouns in the accusative singular, as in polynomickou funkci or polynomickou rovnici.

Polynomials are fundamental objects in algebra. A polynomial in one variable x over a field or commutative ring is an expression of the form a_0 + a_1 x + ... + a_n x^n, where a_i are coefficients and a_n ≠ 0. The degree is n, and the leading coefficient is a_n. Polynomials in several variables extend this idea to expressions in x, y, and so on.

Polynomials can be added, subtracted, multiplied, and, in many cases, divided to yield a quotient and remainder. The fundamental theorem of algebra states that over the complex numbers, every non-constant polynomial has as many roots (counted with multiplicity) as its degree. Polynomial equations (polynomickou rovnicí) are equations whose unknowns appear only as polynomial expressions. Polynomial functions (polynomickou funkcí) map inputs to outputs via a polynomial expression; over real or complex numbers, they are continuous and differentiable.

Applications include solving equations, factorization, interpolation (polynomial interpolation such as Lagrange or Newton forms), and approximation of functions via Taylor and related polynomial series. The term polynomickou appears in Czech mathematical writing to modify related nouns, while the underlying concepts are universal in algebra and numerical analysis.