Homogene Komponenten und homogene Polynome
Es sei
S
{\displaystyle {}S}
kommutativer Ring
und
R
=
S
[
X
1
,
…
,
X
n
]
{\displaystyle {}R=S[X_{1},\ldots ,X_{n}]}
Polynomring
über
S
{\displaystyle {}S}
n
{\displaystyle {}n}
F
∈
R
{\displaystyle {}F\in R}
F
=
∑
ν
a
ν
X
ν
{\displaystyle {}F=\sum _{\nu }a_{\nu }X^{\nu }}
F
=
∑
i
=
0
d
F
i
{\displaystyle {}F=\sum _{i=0}^{d}F_{i}\,}
mit
F
i
=
∑
ν
,
|
ν
|
=
i
a
ν
X
ν
{\displaystyle {}F_{i}=\sum _{\nu ,\,|\nu |=i}a_{\nu }X^{\nu }\,}
die homogene Zerlegung
F
{\displaystyle {}F}
F
i
{\displaystyle {}F_{i}}
homogenen Komponenten
F
{\displaystyle {}F}
Grad
i
{\displaystyle {}i}
F
{\displaystyle {}F}
homogen
F
{\displaystyle {}F}
F
i
{\displaystyle {}F_{i}}
![{\displaystyle {}R=S[X_{1},\ldots ,X_{n}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2de5f34b5b741c59eb50a2d5b5fcf2361ba7d1a)
