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- (************** Content-type: application/mathematica **************
- CreatedBy='Mathematica 5.0'
- Mathematica-Compatible Notebook
- This notebook can be used with any Mathematica-compatible
- application, such as Mathematica, MathReader or Publicon. The data
- for the notebook starts with the line containing stars above.
- To get the notebook into a Mathematica-compatible application, do
- one of the following:
- * Save the data starting with the line of stars above into a file
- with a name ending in .nb, then open the file inside the
- application;
- * Copy the data starting with the line of stars above to the
- clipboard, then use the Paste menu command inside the application.
- Data for notebooks contains only printable 7-bit ASCII and can be
- sent directly in email or through ftp in text mode. Newlines can be
- CR, LF or CRLF (Unix, Macintosh or MS-DOS style).
- NOTE: If you modify the data for this notebook not in a Mathematica-
- compatible application, you must delete the line below containing
- the word CacheID, otherwise Mathematica-compatible applications may
- try to use invalid cache data.
- For more information on notebooks and Mathematica-compatible
- applications, contact Wolfram Research:
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- Notebook reader applications are available free of charge from
- Wolfram Research.
- *******************************************************************)
- (*CacheID: 232*)
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- Cell[CellGroupData[{
- Cell["Rotations", "Subsubsection"],
- Cell[BoxData[
- \(rotate[exp_, n_] :=
- ReleaseHold[
- Hold[exp] /. {w[k_] \[Rule] w[Mod[k + n, 4]],
- m[k_] \[Rule] m[Mod[k + n, 4]],
- u[k_] \[Rule] u[Mod[k + n, 4]]}]\)], "Input"],
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- Cell[BoxData[
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- Simplify[{exp, rotate[exp, 1], rotate[exp, 2],
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- Cell[BoxData[
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- Cell[CellGroupData[{
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- {\(w[2]\), \(w[3]\), \(w[0]\), \(w[1]\)},
- {\(w[3]\), \(w[0]\), \(w[1]\), \(w[2]\)}
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- Function[ BoxForm`e$,
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- }, Open ]],
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- {\(m[3]\), \(m[0]\), \(m[1]\), \(m[2]\)}
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- Cell[BoxData[
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- Cell[BoxData[
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- Cell[BoxData[
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- Cell[BoxData[
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- Cell[BoxData[
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- exp_] := \({rotations[exp], \(D[#, i] &\) /@
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- rotations[exp], \(D[#, i, j] &\) /@ rotations[exp]} /.
- i -> 0\) /. j -> 0\)], "Input"],
- Cell[BoxData[
- \(SetAttributes[deltas, HoldAll]\)], "Input"],
- Cell[BoxData[
- \(testedges := \(\((Simplify[
- ExpandAll[{# /. j -> 0, # /. i -> 1, # /. j \[Rule] 1, # /.
- i \[Rule] 0}]])\) &\)[Simplify[#]] &\)], "Input"],
- Cell["VVVV", "Text"],
- Cell[CellGroupData[{
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- InterpretationBox[
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- {\(src[i\ m[2] + m[3] - i\ m[3]]\)},
- {\(src[m[0] - j\ m[0] + j\ m[3]]\)}
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- MatrixForm[ {
- src[
- Plus[
- m[ 0],
- Times[ -1, i,
- m[ 0]],
- Times[ i,
- m[ 1]]]],
- src[
- Plus[
- m[ 1],
- Times[ -1, j,
- m[ 1]],
- Times[ j,
- m[ 2]]]],
- src[
- Plus[
- Times[ i,
- m[ 2]],
- m[ 3],
- Times[ -1, i,
- m[ 3]]]],
- src[
- Plus[
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- Times[ -1, j,
- m[ 0]],
- Times[ j,
- m[ 3]]]]}]]], "Output"]
- }, Open ]],
- Cell[CellGroupData[{
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