The Vandermonde Indexing Function - Maple Programming Help

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The Vandermonde Indexing Function

Description

 • The Vandermonde indexing function can be used to construct rtable objects of type Array or Matrix.
 • In the specification of a Matrix, if Vandermonde[V] is included in the calling sequence as an indexing function, where V is a Vector or a list of algebraic values or a name, a Vandermonde Matrix is returned.
 Note:    A Vandermonde Matrix is a Matrix with entries M[i,j] = V[i]^(j-1).
 • The specification is the same in the construction of an Array.

Examples

 > $A≔\mathrm{Array}\left({\mathrm{Vandermonde}}_{\left[1,2,3,4,5\right]},1..4,1..3\right)$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {1}& {1}\\ {1}& {2}& {4}\\ {1}& {3}& {9}\\ {1}& {4}& {16}\end{array}\right]$ (1)
 > $M≔\mathrm{Matrix}\left(3,\mathrm{shape}={\mathrm{Vandermonde}}_{⟨a,b,c⟩}\right)$
 ${M}{≔}\left[\begin{array}{ccc}{1}& {a}& {{a}}^{{2}}\\ {1}& {b}& {{b}}^{{2}}\\ {1}& {c}& {{c}}^{{2}}\end{array}\right]$ (2)
 > $M≔\mathrm{Matrix}\left(3,\mathrm{shape}={\mathrm{Vandermonde}}_{v}\right)$
 ${M}{≔}\left[\begin{array}{ccc}{1}& {{v}}_{{1}}& {{v}}_{{1}}^{{2}}\\ {1}& {{v}}_{{2}}& {{v}}_{{2}}^{{2}}\\ {1}& {{v}}_{{3}}& {{v}}_{{3}}^{{2}}\end{array}\right]$ (3)