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| Title of object: |
homogeneous polynomial |
| Canonical Name: |
HomogenousPolynomial |
| Type: |
Definition |
| Created on: |
2003-01-04 17:15:55.925746-05 |
| Modified on: |
2003-01-13 22:57:15.862897-05 |
| Classification: |
msc:12-XX |
Revision comment (for changes between this and next version):
Preamble:
Content:
A polynomial $P(x_1, \cdots, x_n)$ of degree $k$ is called homogeneous if
$P(cx_1, \cdots, cx_n) = c^{k}P(x_1, \cdots, x_n)$ for all constants $c$.
An equivalent definition is that all terms of the polynomial have the same degree (i.e. $k$).
As an important example of homogeneous polynomials one can mention the symmetric polynomials. |
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