The irreduc function tests whether a multivariate polynomial over an algebraic number field is irreducible.  It returns true if a is irreducible, false otherwise.  Note that a constant polynomial by convention is reducible.

The call irreduc(a) tests for irreducibility over the field implied by the coefficients present; if all the coefficients are rational, then the irreducibility test is over the rationals.

The call irreduc(a, K) tests for irreducibility over the algebraic number field defined by K. K must be a single RootOf, a list or set of RootOfs, a single radical, or a list or set of radicals.