The symmetric indexing function can be used to construct tables and rtable objects of type Array or Matrix.

In the construction of 2-dimensional objects, the symmetric indexing function specifies that the (i, j)th element equals the (j, i)th element.

In general, this indexing function specifies that all entries of an object whose indices are equal under permutations are the same.

The indices are rearranged according to a system-determined canonical ordering.

$M≔\mathrm{Matrix}\left(1..3\,1..3\,\mathrm{shape}=\mathrm{symmetric}\right)$

$M≔\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

$M\left[1,2\right]≔5$

$M_{1,2}≔5$

$M$

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

$A≔\mathrm{Array}\left(\mathrm{symmetric}\,1..5\,1..5\right)\:$

$A$

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

$A\left[3,4\right]≔x\:$

$A\left[4,3\right]$

$x$

$A\left[4,3\right]≔y\:$

$A\left[3,4\right]$

$y$

$A$

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

$T≔\mathrm{table}\left(\mathrm{symmetric}\right)\:$

$T\left[\mathrm{function},\mathrm{continuous},\mathrm{odd}\right]≔f\:$

$T\left[\mathrm{odd},\mathrm{continuous},\mathrm{function}\right]$

$f$