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LinearAlgebra[Modular]

  

MatrixPower

  

compute a power of a square mod m Matrix

 

Calling Sequence

Parameters

Description

Examples

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

withLinearAlgebraModular:

AMod13,Matrix2,0,0,2,integer[]

A2002

(1)

Compute A^0 (identity)

MatrixPower13,A,0

1001

(2)

Compute A^1

MatrixPower13,A,1

2002

(3)

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

MatrixPower13,A,20

9009

(4)

See Also

LinearAlgebra/Details

LinearAlgebra[Modular]

LinearAlgebra[Modular][Create]

LinearAlgebra[Modular][Mod]