Function Repository Resource:

PolynomialDegree

Source Notebook

Compute the degree of a polynomial in any number of variables

Contributed by: Dennis M Schneider

ResourceFunction["PolynomialDegree"][poly,vars]

returns the degree of a polynomial in vars.

Details and Options

The second argument vars can be a list of any number of variables.

Examples

Basic Examples (4)

Compute the degree of a basic polynomial expression:

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Compute the degree of a polynomial in two variables:

In[2]:=

$ResourceFunction["PolynomialDegree"][a + b x + c x^2 + x y^4, {x, y}]$

Out[2]=

The following expression is constant with respect to the variables z, w, u:

In[3]:=

$ResourceFunction["PolynomialDegree"][ a + \[Pi] x + c y^2 + x^2 y^4, {z, w, u}]$

Out[3]=

The following expression is not a polynomial in x and y:

In[4]:=

$ResourceFunction["PolynomialDegree"][ a + b x + c y^\[Pi] + x^2 y^4, {x, y}]$

Properties and Relations (1)

A constant polynomial has degree 0 but the zero polynomial (even though it is a constant polynomial) does not have a degree (though some authors assign it to have degree -1 or ):

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Publisher

Dennis M Schneider

Version History

1.0.0 – 30 July 2019

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License