PolynomialQuotientRemainder[p, q, x] gives a list of the quotient and remainder of p and q, treated as polynomials in x.

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

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

PolynomialExtendedGCD[poly_1, poly_2, x] gives the extended GCD of poly_1 and poly_2 treated as univariate polynomials in x.PolynomialExtendedGCD[poly_1, poly_2, x, Modulus ...

AlgebraicNumberPolynomial[a, x] gives the polynomial in x corresponding to the AlgebraicNumber object a.

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

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 ...

ZetaZero[k] represents the k\[Null]^th zero of the Riemann zeta function on the critical line.ZetaZero[k, t] represents the k\[Null]^th zero with imaginary part greater than ...

Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...