Polynomisesti

Polynomisesti is an adverb used in Finnish mathematical and scientific writing to describe a property that can be described by a polynomial or that grows at a polynomial rate. It is derived from polynomi, the Finnish form of polynomial.

In mathematics, a relation is described as polynomisesti if it can be modeled by a polynomial function p(n) = a0 + a1 n + ... + ak n^k, where k is a nonnegative integer and the ai are constants. The degree k determines the dominant growth behavior for large n; linear growth corresponds to k = 1, quadratic to k = 2, and higher degrees to larger polynomial growth. Polynomially bounded quantities satisfy f(n) = O(n^d) for some fixed d.

In computer science and complexity theory, polynomial time refers to algorithms whose running time is bounded by a polynomial in the input size. Describing this bound as polynomisesti growing or as having polynomial complexity is common in Finnish texts; the phrase contrasts with exponential growth, where the time or resource usage grows like c^n.

Polynomisesti can also describe numerical sequences, approximation errors, or physical quantities that are well captured by a polynomial model over a specified domain.

Etymology and usage notes: polynomi originates from Greek roots meaning "many terms," and the suffix -isesti marks the adverbial form in Finnish. The term is primarily used in technical Finnish writing and is less common outside mathematical and scientific contexts.