MatrixPower - Maple Help

LinearAlgebra[Modular]

 MatrixPower
 compute a power of a square mod m Matrix

 Calling Sequence MatrixPower(m, A, n)

Parameters

 m - modulus A - square mod m Matrix n - nonnegative integer power

Description

 • The MatrixPower function efficiently computes the nth power of the input mod m Matrix via binary powering.
 • This command is part of the LinearAlgebra[Modular] package, so it can be used in the form MatrixPower(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][MatrixPower](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right):$
 > $A≔\mathrm{Mod}\left(13,\mathrm{Matrix}\left(\left[\left[2,0\right],\left[0,2\right]\right]\right),\mathrm{integer}\left[\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{2}& {0}\\ {0}& {2}\end{array}\right]$ (1)

Compute A^0 (identity)

 > $\mathrm{MatrixPower}\left(13,A,0\right)$
 $\left[\begin{array}{cc}{1}& {0}\\ {0}& {1}\end{array}\right]$ (2)

Compute A^1

 > $\mathrm{MatrixPower}\left(13,A,1\right)$
 $\left[\begin{array}{cc}{2}& {0}\\ {0}& {2}\end{array}\right]$ (3)

Compute A^20 (diagonal = 2^20 mod 13 = 9)

 > $\mathrm{MatrixPower}\left(13,A,20\right)$
 $\left[\begin{array}{cc}{9}& {0}\\ {0}& {9}\end{array}\right]$ (4)