There is an alternative convention, which may be useful e.g. in Gröbner basis contexts: a polynomial is called monic, if its leading coefficient (as a multivariate polynomial) is 1. In other words, assume that "p = p"("x"1"...,xn") is a non-zero polynomial in "n" variables, and that there is a given monomial order on the set of all ("monic") monomials in these variables, i.e., a total order of the free commutative monoid generated by "x"1"...,xn", with the unit as lowest element, and respecting multiplication. In that case, this order defines a highest non-vanishing term in "p", and "p" may be called monic, if that term has coefficient one.