polinommal

Polinommal is not a standard term in English-language mathematics. In most contexts, the object it attempts to name is simply a polynomial. When encountered, polinommal is usually either a misspelling or a regional/historical variant of the word polynomial. Nonetheless, in discussions where the term is used, it is treated as referring to the same algebraic object: a polynomial or an element of a polynomial ring.

Formally, a univariate polinommal with coefficients in a ring R is an expression of the form a0 + a1 x + a2 x2 + … + an xn, where each ai lies in R and an ≠ 0. The degree of the polinommal is the largest i with ai ≠ 0. The set of all such polinommals over R, equipped with natural addition and multiplication of coefficients, forms the polynomial ring R[x].

Polinommals can be generalized to multiple variables, yielding multivariate polynomials in x1, x2, …, xm. Standard concepts carry over: constant polynomials, monomials, leading coefficient, and, for rings that are integral domains or fields, properties such as factorization into irreducibles and, over fields, unique factorization. Evaluation of a polinommal at an element r of R yields a value in R, and roots are the elements of R that map the polinommal to zero.

Typical uses of polynomials (and, by extension, polinommal) include encoding sequences through generating functions, solving equations, interpolation, and appearing as coordinates on algebraic varieties in geometry.

See also: polynomial, polynomial ring, multivariate polynomial, irreducible polynomial, factorization.