Polynomiaalis

Polynomiaalis is an adjective used in mathematics, particularly in Dutch-language texts, to refer to things related to polynomials or polynomial functions. A polynomial is an expression built from a finite sum of terms, each of which is a coefficient multiplied by a nonnegative integer power of a variable. In one variable, a polynomial with coefficients a0, a1, ..., an has the form a0 + a1 x + a2 x^2 + ... + an x^n. Multivariate polynomials involve several variables, such as p(x, y) = x^2 y + 3xy + 5.

Polynomials are typically studied with coefficients drawn from a ring or field. The set of all polynomials with coefficients in a fixed ring R is called the polynomial ring R[x], and similarly R[x1, x2, ..., xk] for multivariate polynomials. The degree of a nonzero polynomial is the largest exponent appearing with a nonzero coefficient; the zero polynomial is assigned a degree by convention in some contexts as undefined or negative infinity.

Key properties include closure under addition and multiplication, making polynomials form a ring; evaluation at a particular value substitutes that value for the variable and yields an element of the coefficient ring. Factorization into irreducible polynomials is a central topic in algebra, and the Fundamental Theorem of Algebra describes roots of polynomials over the complex numbers.

Usage of the term polynomiaalis emphasizes the polynomialic nature of a object or property, such as polynomiaalis degree, polynomiaalis function, or polynomiaalis behavior, without implying a separate mathematical object beyond the polynomials themselves.