Polynomisch

Polynomisch is a German adjective used to describe things related to polynomials or their properties. In mathematics, a polynomial is an algebraic expression formed from variables and coefficients through addition, subtraction, and multiplication, using non-negative integer exponents. A polynomial in one variable x has the standard form a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0; in several variables, for example f(x, y) = x^2 y + 3xy^2 + 7, polynomials are defined similarly with terms consisting of products of powers of the variables. The degree of a polynomial is the largest total degree of its nonzero terms.

Polynomials form a ring under addition and multiplication and can be factored over a chosen field into irreducible polynomials. They are central in many areas of algebra, geometry, and numerical analysis. Polynomials are used to approximate smooth functions via Taylor polynomials and to perform interpolation, such as the Lagrange or Newton forms. They also serve as models for problems in coding theory, cryptography, and algorithmic algebra.

In computer science, the term polynomisch is sometimes used in reference to polynomial-time algorithms, whose running time is bounded by a polynomial in the size of the input; this concept is often discussed under the umbrella of the complexity class P. The precise usage can vary among authors, with polynomiell being a closely related term.

Example: p(x) = 2x^3 − 5x^2 + x − 6 is a polynomial of degree 3.