Most recent change of MultiIndex

Edit made on June 09, 2013 by ColinWright at 15:20:18

Deleted text in red / Inserted text in green
WM
HEADERS_END
A multi-index is simply a tuple of natural numbers, for which the following operations are defined. For two n-dimensional multi-indices EQN:\alpha=(\alpha_1,\alpha_2,\ldots,\alpha_n)\in\mathbb{N}_0^n EQN:\beta=(\beta_1,\beta_2,\ldots,\beta_n)\in\mathbb{N}_0^n , we define

* Partial ordering
** EQN:\beta\geq\alpha\Leftrightarrow\beta_i\geq\alpha_i\;\forall\;i\in\mathbb{N}^n\;,

* Component-wise summation
** EQN:\alpha\pm\beta=\left(\alpha_1\pm\beta_1,\alpha_2\pm\beta_2,\ldots,\alpha_n\pm\beta_n\right)\;,

* Absolute value
** EQN:\left|\alpha\right|=\sum_{i=1}^n\alpha_i\;,

* Factorial
** EQN:\alpha!=\prod_{i=1}^n\alpha_1!\;, EQN:\alpha!=\prod_{i=1}^n\alpha_i!\;,

* Power (for EQN:\b{x}\in\mathbb{R}^n\.)
** EQN:\b{x}^\alpha=\prod_{i=1}^nx_i\alpha_i\;.