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, ...

Root[f, k] represents the exact k\[Null]^th root of the polynomial equation f[x] == 0. Root[{f, x_0}] represents the exact root of the general equation f[x] == 0 near x = ...

$MaxRootDegree specifies the maximum degree of polynomial to allow in Root objects.

RootIntervals[{poly_1, poly_2, ...}] gives a list of isolating intervals for the real roots of any of the poly_i, together with a list of which polynomials actually have each ...

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

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

Mathematica includes functionality to factor polynomials symbolically.

CharacteristicPolynomial[m, x] gives the characteristic polynomial for the matrix m. CharacteristicPolynomial[{m, a}, x] gives the generalized characteristic polynomial with ...

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

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 ...