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 multi-index_power [2013/09/17 00:24]nikolaj multi-index_power [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/17 00:24 nikolaj 2013/09/17 00:24 nikolaj 2013/09/17 00:23 nikolaj 2013/09/17 00:23 nikolaj 2013/09/16 22:24 nikolaj 2013/09/16 22:08 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:52 nikolaj 2013/09/16 21:52 nikolaj 2013/09/16 21:39 nikolaj 2013/09/16 21:39 nikolaj 2013/09/16 21:38 nikolaj 2013/09/16 21:38 nikolaj 2013/09/16 21:37 nikolaj created Next revision Previous revision 2013/09/17 00:24 nikolaj 2013/09/17 00:24 nikolaj 2013/09/17 00:23 nikolaj 2013/09/17 00:23 nikolaj 2013/09/16 22:24 nikolaj 2013/09/16 22:08 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:53 nikolaj 2013/09/16 21:52 nikolaj 2013/09/16 21:52 nikolaj 2013/09/16 21:39 nikolaj 2013/09/16 21:39 nikolaj 2013/09/16 21:38 nikolaj 2013/09/16 21:38 nikolaj 2013/09/16 21:37 nikolaj created Line 1: Line 1: ===== Multi-index power ===== ===== Multi-index power ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $G$ ...  group | + | @#55CCEE: context ​    | @#55CCEE: $G$ ...  group | - | @#88DDEE: $g \in \text{Sequence}(G)$ | + | @#55CCEE: context ​    | @#55CCEE: $g \in \text{Sequence}(G)$ | - | @#88DDEE: $\alpha \in \text{Sequence}(\mathbb N)$ | + | @#55CCEE: context ​    | @#55CCEE: $\alpha \in \text{Sequence}(\mathbb N)$ | - | @#88DDEE: $\mathrm{length}(g)=\mathrm{length}(\alpha)$ | + | @#55CCEE: context ​    | @#55CCEE: $\mathrm{length}(g)=\mathrm{length}(\alpha)$ | - | @#FFBB00: $\langle g,​\alpha\rangle \mapsto g^\alpha := \prod_{i=1}^{\mathrm{length}(\alpha)} g_i^{\alpha_i}$ | + | @#FFBB00: definiendum ​| @#FFBB00: $\langle g,​\alpha\rangle \mapsto g^\alpha := \prod_{i=1}^{\mathrm{length}(\alpha)} g_i^{\alpha_i}$ | We also write $|\gamma|=\sum_i^{\mathrm{length}(\gamma)} \gamma_i$. We also write $|\gamma|=\sum_i^{\mathrm{length}(\gamma)} \gamma_i$. Line 17: Line 17: is taken to be a multiindex, then $|\gamma|=6$ and we write is taken to be a multiindex, then $|\gamma|=6$ and we write - $f^{(\gamma)}(x) \equiv \frac{\partial^{|\gamma|}}{\partial x\gamma} f \equiv \frac{\partial^3}{\partial x_1^3} \frac{\partial}{\partial x_2} \frac{\partial^2}{\partial x_5^2} f$ + $f^{(\gamma)}(x) \equiv \frac{\partial^{|\gamma|}}{\partial x^\gamma} f \equiv \frac{\partial^3}{\partial x_1^3} \frac{\partial}{\partial x_2} \frac{\partial^2}{\partial x_5^2} f$ === Reference === === Reference === Wikipedia: [[http://​en.wikipedia.org/​wiki/​Multi-index_notation|Multi-index notation]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Multi-index_notation|Multi-index notation]] ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== [[Group]], [[Integer]],​ [[Sequence length]] [[Group]], [[Integer]],​ [[Sequence length]]