(mathematical analysis) A truncated Taylor series; the sum of the first n terms of a Taylor series.

(mathematics) A truncated Maclaurin series; the sum of the first n terms of a Maclaurin series.

(algebra) For a positive integer n, a polynomial whose roots are the primitive nᵗʰ roots of unity, so that its degree is Euler's totient function of n. That is, letting 𝜁ₙ=e^(i 2𝜋/n) be the first primitive nᵗʰ root of unity, then 𝛷ₙ(x)=∏_( stackrel )1<m<ngcd (n,m)=1(x-𝜁ₙᵐ) is the nᵗʰ such polynomial.

plural of polynomial ring

(algebra) A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomials (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.

plural of primitive polynomial

(algebra, ring theory) A polynomial over an integral domain R such that no noninvertible element of R divides all its coefficients at once; (more specifically) a polynomial over a GCD domain R such that the greatest common divisor of its coefficients equals 1.

plural of polynomial basis

(algebra, ring theory) A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).

(algebra, field theory) A polynomial over a given field that has distinct roots in the algebraic closure of said field (the number of roots being equal to the degree of the polynomial).