Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

Mathematica includes functionality to factor polynomials symbolically.

PossibleZeroQ[expr] gives True if basic symbolic and numerical methods suggest that expr has value zero, and gives False otherwise.

PolynomialQuotient[p, q, x] gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.

BesselYZero[n, k] represents the k\[Null]^th zero of the Bessel function of the second kind Y_n (x).BesselYZero[n, k, x_0] represents the k\[Null]^th zero greater than x_0.

BesselJZero[n, k] represents the k\[Null]^th zero of the Bessel function J_n (x).BesselJZero[n, k, x_0] represents the k\[Null]^th zero greater than x_0.

MinimalPolynomial[s, x] gives the minimal polynomial in x for which the algebraic number s is a root.

SymmetricPolynomial[k, {x_1, ..., x_n}] gives the k\[Null]^th elementary symmetric polynomial in the variables x_1, ..., x_n.

InterpolatingPolynomial[{f_1, f_2, ...}, x] constructs an interpolating polynomial in x which reproduces the function values f_i at successive integer values 1, 2, ... of x. ...

The leading term of a polynomial can be chosen in many different ways. For multivariate polynomials, sorting by the total degree of the monomials is often useful. Different ...