polynomian

Polynomian is a term that appears in some mathematical glossaries to describe objects or ideas that are governed by polynomial relations or growth. It is not a standard, universally adopted term in mainstream mathematics, and its precise meaning can vary between sources. In general, a polynomian can refer to a function, sequence, or model that can be described by a polynomial expression in one or more variables.

Definition and scope commonly associate polynomian with objects that can be expressed as polynomial functions. For a single variable, a polynomian function would have the form f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 with real coefficients. In multiple variables, a polynomian might be any finite sum of monomials in x_1, x_2, ..., x_k with nonnegative integer exponents. The core idea is that the entire structure of the object is determined by a polynomial equation or a polynomial formula.

Properties often attributed to polynomian objects include closure under addition and multiplication, mirroring the behavior of polynomials. Derivatives of polynomials are also polynomials, and composition of polynomials yields another polynomial. These features distinguish polynomian objects from non-polynomial functions such as exponential or trigonometric ones, in which exact polynomial descriptions do not exist.

Usage and variants vary by context. Some writers use polynomian as a broad descriptor for any polynomial-described phenomenon, while others reserve it for a formal class within a specific framework. See also: polynomial, polynomial function, polynomial time.