The Fill function fills the mod m Matrix or Vector A with the specified value fillv. If a fill value, fillv, is not specified, 0 is used.  The value NULL is returned.

If fillv is the keyword random, the mod m Matrix or Vector A is filled with random values in the range $0..m-1$.

The Fill function allows you to use sub-Matrix and sub-Vector specifications for the mod m Matrix or Vector. For example, the function can be used to clear specific rows of a Matrix, or part of a Vector.

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Fill(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][Fill](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right)\:$

$A≔\mathrm{Mod}\left(13\,\mathrm{Matrix}\left(4\,4\,\left(i\,j\right)\mapsto \mathrm{rand}\left(\right)\right)\,\mathrm{integer}\left[\right]\right)$

$A≔\left[\begin{array}{cccc}10& 0& 8& 12\\ 2& 6& 0& 11\\ 9& 2& 11& 7\\ 4& 11& 12& 11\end{array}\right]$

$\mathrm{Fill}\left(13\,A\right)\:$

$A$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

$\mathrm{Fill}\left(13\,2\,A\,3\right)\:$

$A$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 2& 2& 2& 2\\ 0& 0& 0& 0\end{array}\right]$

$\mathrm{Fill}\left(13\,A\,1..-1\,2\right)\:$

$A$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 2& 0& 2& 2\\ 0& 0& 0& 0\end{array}\right]$

$B≔\mathrm{Create}\left(13\,0\,5\,\mathrm{float}\left[8\right]\right)$

$B≔\left[\begin{array}{ccccc}0.& 0.& 0.& 0.& 0.\end{array}\right]$

$\mathrm{Fill}\left(13\,5.0\,B\,2..-2\right)\:$

$B$

$\left[\begin{array}{ccccc}0.& 5.& 5.& 5.& 0.\end{array}\right]$

$A$

$\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 2& 0& 2& 2\\ 0& 0& 0& 0\end{array}\right]$

$\mathrm{Fill}\left(13\,'\mathrm{random}'\,A\right)\:$

$A$

$\left[\begin{array}{cccc}6& 7& 7& 3\\ 10& 3& 6& 6\\ 10& 12& 7& 6\\ 1& 2& 0& 11\end{array}\right]$