The triangular Indexing Function - Maple Programming Help

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The triangular Indexing Function

Description

 • 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.

Examples

 > $M≔\mathrm{Matrix}\left(3,\left[\left[x\right],\left[y,y\right],\left[z,z,z\right]\right],\mathrm{shape}=\mathrm{triangular}\left[\mathrm{lower}\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{x}& {0}& {0}\\ {y}& {y}& {0}\\ {z}& {z}& {z}\end{array}\right]$ (1)
 > $M\left[1,3\right]≔5$