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LinearAlgebra[Modular][MatrixPower] - compute a power of a square mod m Matrix
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Calling Sequence
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MatrixPower(m, A, n)
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Parameters
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m
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modulus
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A
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square mod m Matrix
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n
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-
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nonnegative integer power
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Description
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The MatrixPower function efficiently computes the nth power of the input mod m Matrix via binary powering.
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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](..).
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Examples
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![with(LinearAlgebra[Modular])](/support/helpjp/helpview.aspx?si=4522/file06080/math85.png)
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![A := Mod(13, Matrix([[2, 0], [0, 2]]), integer[])](/support/helpjp/helpview.aspx?si=4522/file06080/math89.png)
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![A := Matrix([[2, 0], [0, 2]])](/support/helpjp/helpview.aspx?si=4522/file06080/math92.png)
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Compute A^0 (identity)
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![Matrix([[1, 0], [0, 1]])](/support/helpjp/helpview.aspx?si=4522/file06080/math101.png)
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Compute A^1
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![Matrix([[2, 0], [0, 2]])](/support/helpjp/helpview.aspx?si=4522/file06080/math110.png)
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Compute A^20 (diagonal = 2^20 mod 13 = 9)
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![Matrix([[9, 0], [0, 9]])](/support/helpjp/helpview.aspx?si=4522/file06080/math119.png)
| (4) |
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Download Help Document
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