The MultiplyAlongDimension command multiplies together the elements in dimension dim of a N-dimensional Array to produce an Array with (N-1) dimensions.

When dim is not specified, the first non-singleton dimension is used for multiplying.  If the dimension specified is a higher dimension than the number of dimensions in the input, the input itself is returned.

If MultiplyAlongDimension is applied to a Vector, a constant is returned.

This function is part of the ArrayTools package, so it can be used in the short form MultiplyAlongDimension(..) only after executing the command with(ArrayTools. However, it can always be accessed through the long form of the command by using ArrayTools[MultiplyAlongDimension](..).

$\mathrm{with}\left(\mathrm{ArrayTools}\right)\:$

$M≔\mathrm{Matrix}\left(\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\right]\right)$

$M≔\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]$

$\mathrm{MultiplyAlongDimension}\left(M\,1\right)$

$\left[\begin{array}{ccc}ad& be& cf\end{array}\right]$

$\mathrm{MultiplyAlongDimension}\left(M\,2\right)$

$\left[\begin{array}{c}abc\\ def\end{array}\right]$

$v≔\mathrm{Vector}\left(\left[1\,2\,3\,4\right]\right)$

$v≔\left[\begin{array}{c}1\\ 2\\ 3\\ 4\end{array}\right]$

$\mathrm{MultiplyAlongDimension}\left(v\right)$

$24$