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

In the construction of a Matrix, if triangular or triangular[upper] is included in the calling sequence as an indexing function (shape), an upper triangular Matrix is returned.

This indexing function may also be qualified as either triangular[unit] or triangular[lower] (hence, also as triangular[upper, unit] and triangular[lower, unit]).

Note:  The Matrix need not be square.

The specification is similar in the construction of an Array.

If an object is defined by using the triangular or triangular[upper] indexing function, the elements located in the lower triangle cannot be reassigned.

The situation is similar in a construction that uses triangular[lower] or triangular[lower, unit] as an indexing function.

$M≔\mathrm{Matrix}\left(3\,\left[\left[x\right]\,\left[y\,y\right]\,\left[z\,z\,z\right]\right]\,\mathrm{shape}=\mathrm{triangular}\left[\mathrm{lower}\right]\right)$

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

$M\left[1,3\right]≔5$

Error, attempt to assign to upper triangle of lower triangular rtable