The minimal polynomial of an algebraic number ζ is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(ζ) = 0 and whose leading coefficient is 1. The minimal polynomial can be computed using MinimalPolynomial[zeta, var] in the Wolfram Language package AlgebraicNumberFieldsˋ .

algebraic number | conjugate elements | Eisenstein's irreducibility criterion | extension field minimal polynomial | matrix minimal polynomial | splitting field