based on an earlier version of the Wolfram Language.
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 has the world's broadest and deepest integrated web of polynomial algorithms. Carefully tuned strategies automatically select optimal algorithms, allowing large-scale polynomial algebra to become a routine part of many types of computations.
Solve — find generic solutions for variables
Eliminate — eliminate variables between equations
Resolve — eliminate general quantifiers
Reduce — reduce systems of equations and inequalities to canonical form
Modulus — specify a modulus
PolynomialMod — reduce coefficients in a polynomial
GaussianIntegers — do operations over Gaussian integers
Extension — specify a general algebraic extension field
Root — general representation of a polynomial root
MinimalPolynomial — minimal polynomial for a general algebraic number