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Revision difference : homogeneous polynomial |
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| A polynomial $P(x_1, \cdots, x_n)$ of degree $k$ is called homogeneous if |
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 $c$. |
$P(cx_1, \cdots, cx_n) = c^{k}P(x_1, \cdots, x_n)$ for all constants $c$. |
| An equivalent definition is that all terms of the polynomial have the same degree (i.e. $k$). |
An equivalent definition is that all terms of the polynomial have the same degree (i.e. $k$). |
| Observe that a polynomial $P$ is homogeneous iff $\deg P = \ord P$. |
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| As an important example of homogeneous polynomials one can mention the symmetric polynomials. |
As an important example of homogeneous polynomials one can mention the symmetric polynomials. |
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