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LinearAlgebra[Modular][Swap] - swap data between two mod m Matrices or Vectors of the same datatype
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Calling Sequence
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Swap(m, ctype, A, B)
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Parameters
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m
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modulus
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A
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mod m Matrix or Vector, including subspec
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B
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mod m Matrix or Vector, including subspec
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ctype
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(optional) swap type
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Description
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The Swap function exchanges data between two mod m Matrices or Vectors.
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Note that the dimensions of the object specified by A must match those specified for B.
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In all cases, the datatype of the output object must match the datatype of the input object.
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The ctype parameter is used to specify the type of swap to be performed. Valid options are upper for the upper triangular part of a Matrix, lower for the lower triangular part of a Matrix, and  and  for the corresponding copy operation without the diagonal.
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Note: These swap types are only valid for square Matrices.
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The Swap function allows the use of sub-Matrix and sub-Vector specifications for both input and output. For example, the function can be used to exchange a row of a Matrix with a row of another Matrix (or the same Matrix), or exchange data between a column in a Matrix and a row Vector.
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Note: If A and B overlap, the behavior of Swap is undefined.
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This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Swap(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][Swap](..).
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Examples
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![with(LinearAlgebra[Modular])](/support/helpjp/helpview.aspx?si=4505/file06088/math145.png)
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![A := Create(13, 4, 4, random, integer[])](/support/helpjp/helpview.aspx?si=4505/file06088/math149.png)
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![B := Create(13, 4, 4, random, integer[])](/support/helpjp/helpview.aspx?si=4505/file06088/math153.png)
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![Matrix([[6, 7, 7, 3], [10, 3, 6, 6], [10, 12, 7, 6], [1, 2, 0, 11]]), Matrix([[12, 10, 12, 0], [5, 9, 12, 3], [5, 2, 5, 10], [6, 7, 5, 10]])](/support/helpjp/helpview.aspx?si=4505/file06088/math160.png)
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Swap entire Matrices.
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![Matrix([[12, 10, 12, 0], [5, 9, 12, 3], [5, 2, 5, 10], [6, 7, 5, 10]]), Matrix([[6, 7, 7, 3], [10, 3, 6, 6], [10, 12, 7, 6], [1, 2, 0, 11]])](/support/helpjp/helpview.aspx?si=4505/file06088/math173.png)
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Exchange rows 1 and 4 in A.
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![Matrix([[12, 10, 12, 0], [5, 9, 12, 3], [5, 2, 5, 10], [6, 7, 5, 10]])](/support/helpjp/helpview.aspx?si=4505/file06088/math182.png)
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![Matrix([[6, 7, 5, 10], [5, 9, 12, 3], [5, 2, 5, 10], [12, 10, 12, 0]])](/support/helpjp/helpview.aspx?si=4505/file06088/math193.png)
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Swap row vector and third column of A.
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![V := Create(13, 0, 4, random, integer[])](/support/helpjp/helpview.aspx?si=4505/file06088/math199.png)
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](/support/helpjp/helpview.aspx?si=4505/file06088/math202.png)
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![Matrix([[6, 7, 5, 10], [5, 9, 12, 3], [5, 2, 5, 10], [12, 10, 12, 0]])](/support/helpjp/helpview.aspx?si=4505/file06088/math209.png)
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![Matrix([[6, 7, 2, 10], [5, 9, 5, 3], [5, 2, 5, 10], [12, 10, 10, 0]])](/support/helpjp/helpview.aspx?si=4505/file06088/math220.png)
| (7) |
Swap transposed upper triangular part of A with self (in-place transpose).
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![Matrix([[6, 7, 2, 10], [5, 9, 5, 3], [5, 2, 5, 10], [12, 10, 10, 0]])](/support/helpjp/helpview.aspx?si=4505/file06088/math229.png)
| (8) |
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![Matrix([[6, 5, 5, 12], [7, 9, 2, 10], [2, 5, 5, 10], [10, 3, 10, 0]])](/support/helpjp/helpview.aspx?si=4505/file06088/math240.png)
| (9) |
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