A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, e.g., , , or . A monomial can also be thought of as a nonzero summand of a polynomial (Becker and Weispfenning 1993, p. 191; Cox et al. 1996). A monomial with the coefficient excluded is usually called a term.

Unfortunately, in some older works, the definitions of monomial and term are sometimes reversed. Care is therefore needed in attempting to distinguish these conflicting usages.

The Wolfram Language command MonomialList[poly, , , ...] gives the list of monomials with respect to the variables in the specified polynomial.

The monomials and are orthogonal on the unit circle in the complex plane (Dumitriu et al. 2004) since

(1)

The monomial functions are defined as

(2)

where is the set of permutations giving distinct terms in the sum and is considered to be infinite (Dumitriu et al. 2004). For example.

(3)

Care is needed when consulting the literature, since the distinction between terms and monomials is not always observed. For example, Dummit and Foote (2004, p. 234) define a monomial as a polynomial with only one nonzero term, without defining what is meant by "term."