BUILT-IN MATHEMATICA SYMBOL

IrreduciblePolynomialQ

IrreduciblePolynomialQ[poly]
tests whether poly is an irreducible polynomial over the rationals.

IrreduciblePolynomialQ[poly, Modulus->p]
tests whether poly is irreducible modulo a prime p.

IrreduciblePolynomialQ[poly, Extension->{a₁, a₂, ...}]
tests whether poly is irreducible over the field extension generated by the algebraic numbers .

IrreduciblePolynomialQ[poly, Extension->All]
tests whether poly is absolutely irreducible over the complex numbers.

Details and Options Details and Options

The polynomial poly can involve any number of variables.
IrreduciblePolynomialQ[poly, GaussianIntegers->True] tests whether poly is irreducible over the Gaussian rationals.
If any coefficients in poly are complex numbers, irreducibility testing is done over the Gaussian rationals.
With the default setting Extension->None, IrreduciblePolynomialQ[poly] will treat algebraic number coefficients in poly like independent variables.
IrreduciblePolynomialQ[poly, Extension->Automatic] extends the domain of coefficients to include any algebraic numbers that appear in poly.
IrreduciblePolynomialQ automatically threads over lists.