A monomialMathworldPlanetmath is a product of non-negative powers of variables. It may also include an optional coefficient (which is sometimes ignored when discussing particular properties of monomials). A polynomialMathworldPlanetmath can be thought of as a sum over a set of monomials.

For example, the following are monomials.


If there are n variables from which a monomial may be formed, then a monomial may be represented without its coefficient as a vector of n naturals. Each position in this vector would correspond to a particular variable, and the value of the element at each position would correspond to the power of that variable in the monomial. For instance, the monomial x2yz3 formed from the set of variables {w,x,y,z} would be represented as (0213)T. A constant would be a zero vectorMathworldPlanetmath.

Given this representationPlanetmathPlanetmath, we may define a few more concepts. First, the degree of a monomial is the sum of the elements of its vector representation. Thus, the degree of x2yz3 is 0+2+1+3=6, and the degree of a constant is 0. If a polynomial is represented as a sum over a set of monomials, then the degree of a polynomial can be defined as the degree of the monomial of largest degree belonging to that polynomial.

Title monomial
Canonical name Monomial
Date of creation 2013-03-22 12:34:32
Last modified on 2013-03-22 12:34:32
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 5
Author bbukh (348)
Entry type Definition
Classification msc 12-00
Defines degree of a monomial