12
$\begingroup$

What is the difference between the "degree" of a polynomial and its "total degree"?

$\endgroup$

1 Answer 1

14
$\begingroup$

The total degree of a polynomial in more than one variable is the maximal of the sums of all the powers of the variables in one single monomial. For example

$$\deg(x_1^2x_2x_3^4-3x_2+4x_1x_4^5-x_1x_2^3x^2)=7$$

You can also define the local or particular degree for some particular variable, say:

$$\deg_1(x_1^2x_2x_3^4-3x_2+4x_1x_4^5-x_1x_2^3x^2)=2\;,\;\;\deg_4(x_1^2x_2x_3^4-3x_2+4x_1x_4^5-x_1x_2^3x^2)=5\ldots$$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .