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
SquareFreeQ — test if a polynomial is free of multiple factors
FactorSquareFree — pull out only factors that occur as squares or higher powers
FactorTerms — pull out only overall numerical 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
Decompose — decompose into a composition of polynomials
HornerForm — rearrange a polynomial into Horner form
SymmetricReduction — reduce a polynomial into a symmetric and non-symmetric part
InterpolatingPolynomial — construct a polynomial that goes through a list of points
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