The triangular Indexing Function - Maple Help

Home : Support : Online Help : Programming : Data Types : Rtables, Arrays, Matrices, and Vectors : Indexing Functions : indexfcn/triangular

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

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