order and degree of polynomial

Let f be a polynomialMathworldPlanetmathPlanetmathPlanetmath in two variablesMathworldPlanetmath, viz. f(x,y)=i,jaijxiyj.11In order to simplify the notation, the definition is given in terms of a polynomial in two variables, however the definition naturally scales to any number of variables.

Then the total degree of f is given by:


Note the degree of the zero-polynomial is -, since sup (per definition) is -, thus degf{0}{-}.

Similarly the order of f is given by:


Note the order of the zero-polynomial is (because inf=). Thus ordf{0}{}.

Please note that the term order is not as common as degree. In fact, it is perhaps more frequently associated with power series (a form of generalized polynomials) than with ordinary polynomials. Also be aware that the term order occasionally is used as a synonym for degree.

Title order and degree of polynomial
Canonical name OrderAndDegreeOfPolynomial
Date of creation 2013-03-22 13:38:21
Last modified on 2013-03-22 13:38:21
Owner jgade (861)
Last modified by jgade (861)
Numerical id 8
Author jgade (861)
Entry type Definition
Classification msc 12-00
Related topic ZeroPolynomial2
Defines order
Defines degree