As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

ZeroTest is an option to various linear algebra functions that gives a function to use in testing whether symbolic expressions should be treated as zero.

AiryAiZero[k] represents the k\[Null]^th zero of the Airy function Ai(x).AiryAiZero[k, x_0] represents the k\[Null]^th zero less than x_0.

PolynomialMod[poly, m] gives the polynomial poly reduced modulo m. PolynomialMod[poly, {m_1, m_2, ...}] reduces modulo all of the m_i.

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

PolynomialQ[expr, var] yields True if expr is a polynomial in var, and yields False otherwise. PolynomialQ[expr, {var_1, ...}] tests whether expr is a polynomial in the var_i.

PolynomialReduce[poly, {poly_1, poly_2, ...}, {x_1, x_2, ...}] yields a list representing a reduction of poly in terms of the poly_i. The list has the form {{a_1, a_2, ...}, ...

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...

AiryBiZero[k] represents the k\[Null]^th zero of the Airy function Bi(x).AiryBiZero[k, x_0] represents the k\[Null]^th zero less than x_0.

PolynomialRemainder[p, q, x] gives the remainder from dividing p by q, treated as polynomials in x.