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LinearAlgebra[Modular][ZigZag] - in place conversion of mod m Matrix to ZigZag form
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Calling Sequence
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ZigZag(m, A)
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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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Description
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The ZigZag function applies a sequence of similarity transformations to the  mod m Matrix A to obtain the ZigZag form of A.
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A ZigZag form is an almost block diagonal structure having fewer than  nonzero entries.
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A ZigZag form can be used to obtain the Smith normal form and the Frobenius form of a Matrix. The Frobenius form of a Matrix is the same as the Frobenius form of its ZigZag form.
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This command is part of the LinearAlgebra[Modular] package, so it can be used in the form ZigZag(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][ZigZag](..).
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Examples
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![with(LinearAlgebra[Modular])](/support/helpjp/helpview.aspx?si=4514/file06090/math93.png)
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| (1) |
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![A := Mod(p, Matrix(5, 5, proc (i, j) options operator, arrow; if i <= j then rand() else 0 end if end proc), integer[])](/support/helpjp/helpview.aspx?si=4514/file06090/math104.png)
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![A := Matrix([[77, 96, 10, 86, 58], [0, 36, 80, 22, 44], [0, 0, 39, 60, 39], [0, 0, 0, 43, 12], [0, 0, 0, 0, 55]])](/support/helpjp/helpview.aspx?si=4514/file06090/math107.png)
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![Matrix([[77, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 44, 8, 36, 76]])](/support/helpjp/helpview.aspx?si=4514/file06090/math122.png)
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![Matrix([[0, 0, 0, 0, 7], [1, 0, 0, 0, 10], [0, 1, 0, 0, 49], [0, 0, 1, 0, 4], [0, 0, 0, 1, 56]]), Matrix([[0, 0, 0, 0, 7], [1, 0, 0, 0, 10], [0, 1, 0, 0, 49], [0, 0, 1, 0, 4], [0, 0, 0, 1, 56]])](/support/helpjp/helpview.aspx?si=4514/file06090/math129.png)
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