This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Polynomial Factoring & Decomposition
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 sophisticated algorithms, carefully tuned at Wolfram Research over the course of two decades.
Factor fully factor any polynomial
FactorSquareFree pull out only factors that occur as squares or higher powers
FactorTerms pull out only overall numerical factors
FactorList, FactorSquareFreeList, FactorTermsList give lists of factors

Modulus specify a modulus for a finite field
Extension specify a general algebraic extension field
GaussianIntegers factor over Gaussian integers

Expand expand out polynomials
MonomialList the list of monomials in a specified ordering

Decompose decompose into a composition of polynomials
HornerForm rearrange a polynomial into Horner form
SymmetricReduction reduce a polynomial into a symmetric and nonsymmetric part
InterpolatingPolynomial construct a polynomial that goes through a list of points

Rational Functions
TUTORIALS