Page "Monic polynomial" Paragraph 30

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 < sub > 1 </ sub >,..., x < sub > n </ sub >) 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 < sub > 1 </ sub >,..., x < sub > n </ sub >, 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.