LinearAlgebra[Modular] - Maple Programming Help

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LinearAlgebra[Modular]

 Identity
 create mod m identity Matrix

 Calling Sequence Identity(m, n, dtype, order)

Parameters

 m - modulus n - number of rows and columns in output identity Matrix dtype - datatype of output object order - (optional) ordering of output object

Description

 • The Identity function creates a mod m identity Matrix of the specified type and dimensions.
 • The allowable datatypes are hardware integer (dtype=integer[4]/integer[8] or integer[]), hardware float (dtype=float[8]), or Maple integer (dtype=integer). If specified, order can be C_order or Fortran_order. If not specified, C_order is used.
 • This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Identity(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][Identity](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}[\mathrm{Modular}]\right):$
 > $\mathrm{A1}≔\mathrm{Identity}\left(31,20,\mathrm{integer}[]\right)$
 ${\mathrm{A1}}{≔}\left[\begin{array}{c}{\mathrm{20 x 20}}{\mathrm{Matrix}}\\ {\mathrm{Data Type:}}{\mathrm{integer}}{[}{8}{]}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{C_order}}\end{array}\right]$ (1)
 > $\mathrm{A2}≔\mathrm{Identity}\left(31,20,\mathrm{float}[8],\mathrm{Fortran_order}\right)$
 ${\mathrm{A2}}{≔}\left[\begin{array}{c}{\mathrm{20 x 20}}{\mathrm{Matrix}}\\ {\mathrm{Data Type:}}{\mathrm{float}}{[}{8}{]}\\ {\mathrm{Storage:}}{\mathrm{rectangular}}\\ {\mathrm{Order:}}{\mathrm{Fortran_order}}\end{array}\right]$ (2)
 > $\mathrm{A3}≔\mathrm{Identity}\left(31,3,\mathrm{integer}\right)$
 ${\mathrm{A3}}{≔}\left[\begin{array}{rrr}{1}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {1}\end{array}\right]$ (3)
 > $\mathrm{A4}≔\mathrm{Identity}\left(31,5,\mathrm{float}[8]\right)$
 ${\mathrm{A4}}{≔}\left[\begin{array}{ccccc}{1.}& {0.}& {0.}& {0.}& {0.}\\ {0.}& {1.}& {0.}& {0.}& {0.}\\ {0.}& {0.}& {1.}& {0.}& {0.}\\ {0.}& {0.}& {0.}& {1.}& {0.}\\ {0.}& {0.}& {0.}& {0.}& {1.}\end{array}\right]$ (4)