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LinearAlgebra[Modular][Copy] - copy mod m Matrix or Vector to a new or already existing mod m Matrix or Vector
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Calling Sequence
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Copy(m, ctype, A, B, order)
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Parameters
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m
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modulus
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A
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input object (copy from), including subspec
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B
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(optional) output object (copy to), including subspec
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order
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(optional) ordering of output object
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ctype
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(optional) copy type; lower, upper, uppernodiag, or lowernodiag
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Description
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The Copy function copies data from one mod m Matrix or Vector to another, or to a new Matrix or Vector.
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If B or order are not specified, a new output object with the same ordering as the input object A is returned. If B is not specified, the returned object has the specified ordering either C_order or Fortran_order.
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If order is not specified, the copy is performed into the output object B and NULL is returned. Note that the dimensions of the object specified for 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 copy 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 copy types are only valid for square Matrices.
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The Copy function allows the use of sub-Matrix and sub-Vector specifications for both input and output. For example, the function can be used to copy a row of a Matrix to a row of another Matrix, or convert a Matrix into a Vector.
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Note: If A and B overlap, the behavior of Copy is undefined.
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This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Copy(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][Copy](..).
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Examples
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![with(LinearAlgebra[Modular])](/support/helpjp/helpview.aspx?si=4501/file06065/math173.png)
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![A := Mod(13, Matrix(4, 4, proc (i, j) options operator, arrow; rand() end proc), integer[])](/support/helpjp/helpview.aspx?si=4501/file06065/math177.png)
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![A := Matrix([[10, 0, 8, 12], [2, 6, 0, 11], [9, 2, 11, 7], [4, 11, 12, 11]])](/support/helpjp/helpview.aspx?si=4501/file06065/math180.png)
| (1) |
Copy entire Matrix.
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![Matrix([[10, 0, 8, 12], [2, 6, 0, 11], [9, 2, 11, 7], [4, 11, 12, 11]])](/support/helpjp/helpview.aspx?si=4501/file06065/math189.png)
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Copy row 3 to row Vector.
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](/support/helpjp/helpview.aspx?si=4501/file06065/math198.png)
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![Vector[row]](/support/helpjp/helpview.aspx?si=4501/file06065/math205.png)
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Copy column 2 to column Vector.
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](/support/helpjp/helpview.aspx?si=4501/file06065/math214.png)
| (5) |
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![Vector[column]](/support/helpjp/helpview.aspx?si=4501/file06065/math221.png)
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Copy column 2 to a 4x1 Matrix.
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![L := Matrix([[0], [6], [2], [11]])](/support/helpjp/helpview.aspx?si=4501/file06065/math230.png)
| (7) |
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| (8) |
Copy row 3,2 of A to row 2,3 of B.
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![B := Create(13, 4, 4, integer[])](/support/helpjp/helpview.aspx?si=4501/file06065/math243.png)
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![B := Matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])](/support/helpjp/helpview.aspx?si=4501/file06065/math246.png)
| (9) |
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![Matrix([[10, 0, 8, 12], [2, 6, 0, 11], [9, 2, 11, 7], [4, 11, 12, 11]]), Matrix([[0, 0, 0, 0], [9, 2, 11, 7], [2, 6, 0, 11], [0, 0, 0, 0]])](/support/helpjp/helpview.aspx?si=4501/file06065/math261.png)
| (10) |
This is an error, as B is too small.
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![B := Create(13, 4, 3, integer[])](/support/helpjp/helpview.aspx?si=4501/file06065/math267.png)
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![B := Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]])](/support/helpjp/helpview.aspx?si=4501/file06065/math270.png)
| (11) |
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This example results in an error, as datatypes cannot be mixed.
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![B := Create(13, 4, 4, float[8])](/support/helpjp/helpview.aspx?si=4501/file06065/math286.png)
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![B := Matrix([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]])](/support/helpjp/helpview.aspx?si=4501/file06065/math289.png)
| (12) |
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An example of upper and lower copy.
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![Matrix([[10, 0, 8, 12], [0, 6, 0, 11], [0, 0, 11, 7], [0, 0, 0, 11]])](/support/helpjp/helpview.aspx?si=4501/file06065/math308.png)
| (13) |
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![B := Create(13, 4, 4, integer[])](/support/helpjp/helpview.aspx?si=4501/file06065/math312.png)
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![Matrix([[0, 0, 0, 0], [2, 0, 0, 0], [9, 2, 0, 0], [4, 11, 12, 0]])](/support/helpjp/helpview.aspx?si=4501/file06065/math323.png)
| (14) |
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