tests whether poly is an irreducible polynomial over the rationals.
- 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.
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