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obladesSUnForIOS.cdf
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obladesSUnForIOS.cdf
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(* Content-type: application/vnd.wolfram.cdf.text *)
(*** Wolfram CDF File ***)
(* http://www.wolfram.com/cdf *)
(* CreatedBy='Mathematica 11.1' *)
(*************************************************************************)
(* *)
(* The Mathematica License under which this file was created prohibits *)
(* restricting third parties in receipt of this file from republishing *)
(* or redistributing it by any means, including but not limited to *)
(* rights management or terms of use, without the express consent of *)
(* Wolfram Research, Inc. For additional information concerning CDF *)
(* licensing and redistribution see: *)
(* *)
(* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *)
(* *)
(*************************************************************************)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 1064, 20]
NotebookDataLength[ 199758, 4545]
NotebookOptionsPosition[ 199176, 4505]
NotebookOutlinePosition[ 199624, 4525]
CellTagsIndexPosition[ 199581, 4522]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["\<\
Code for the user interface and interface (the user should enable dynamic \
updating)\
\>", "Subsubsection",ExpressionUUID->"00000000-0000-0000-0000-000000000000"],
Cell[BoxData[
DynamicModuleBox[{$CellContext`rows$$ = 3, $CellContext`cols$$ =
2, $CellContext`mat$$ = {{6, 3}, {3, 5}, {3, 8}}, $CellContext`coupling$$ =
1, $CellContext`mul$$ = Dynamic[
Apply[obladePackage`multiplicity, $CellContext`mat$$]], \
$CellContext`myRange$$, $CellContext`myPart$$, $CellContext`tp$$ =
0, $CellContext`tpval$$},
DynamicBox[ToBoxes[
Manipulate[
Which[$CellContext`tp$$ == 0,
Row[{
Invisible[$CellContext`doit],
(CheckAbort[
If[Length[#] > 800,
Abort[], #],
Print[$CellContext`limittext, 800]]& )[
TimeConstrained[
If[Setting[$CellContext`mul$$] == 0, $CellContext`notadmissibletext,
TableForm[{
PopupMenu[
Dynamic[$CellContext`coupling$$],
Range[1,
Setting[$CellContext`mul$$]]],
Show[
obladePackage`plotOblades[
$CellContext`myPart$$[$CellContext`mat$$, 1],
$CellContext`myPart$$[$CellContext`mat$$, 2],
$CellContext`myPart$$[$CellContext`mat$$,
3], $CellContext`coupling$$], ImageSize -> Full]}]], 1.5,
Print[1.5, 1.5, " seconds"]]]}], $CellContext`tp$$ ==
1, $CellContext`tpval$$ = obladePackage`tensorproduct[
$CellContext`myPart$$[$CellContext`mat$$, 1],
$CellContext`myPart$$[$CellContext`mat$$, 2]], $CellContext`tp$$ ==
2, $CellContext`tp$$ =
0; $CellContext`mat$$ = {{3, 2, 3, 2, 2}, {2, 3, 2, 2, 3}, {4, 5, 4, 2,
5}}; TableForm[{
PopupMenu[
Dynamic[$CellContext`coupling$$],
Range[1,
Setting[$CellContext`mul$$]]],
Show[
obladePackage`plotOblades[
$CellContext`myPart$$[$CellContext`mat$$, 1],
$CellContext`myPart$$[$CellContext`mat$$, 2],
$CellContext`myPart$$[$CellContext`mat$$,
3], $CellContext`coupling$$], ImageSize -> Large]}]],
Evaluate[
With[{$CellContext`makeRow$ = Function[{$CellContext`rowIndex$},
Map[
Function[{$CellContext`colIndex$},
InputField[
Dynamic[
Part[$CellContext`mat$$, $CellContext`rowIndex$, \
$CellContext`colIndex$]], Number, FieldSize -> 3]],
$CellContext`myRange$$[$CellContext`cols$$]], HoldAll]},
Row[{
TextGrid[{{"\[Omega]1", ""}, {}, {"\[Omega]2", ""}, {}, {
OverBar["\[Omega]3"], ""}}],
Grid[
Map[$CellContext`makeRow$,
$CellContext`myRange$$[$CellContext`rows$$]],
Dividers -> {{False, False, False}, {False, False, Red}}],
Invisible["xxxxxx"],
Button[
Style[
"Update components", FontSize -> 14, Bold,
Blue], $CellContext`mat$$; $CellContext`coupling$$ = 1;
Increment[$CellContext`cols$$];
Decrement[$CellContext`cols$$]; $CellContext`tp$$ = 0],
Column[{
Button[
Style["Previous pictograph", Bold],
If[$CellContext`coupling$$ > 1,
Decrement[$CellContext`coupling$$]; Null]],
Button[
Style["Next pictograph", Bold],
If[$CellContext`coupling$$ < Setting[$CellContext`mul$$],
Increment[$CellContext`coupling$$]; Null]]}],
Column[$CellContext`abouttabletext]}]]],
Column[{
Panel[
Style[$CellContext`cols$$ + 1, FontSize -> 14, Bold],
Style["SU(n), with n =", Bold, FontSize -> 14], Left,
BaselinePosition -> Bottom],
Panel[
Style[
Column[{
"Pictographs for admissible triples",
"of irreducible representations", "of SU(n)", "O-blade version"},
Center], "Title"]]},
Invisible["xxxxxx"]],
Panel[$CellContext`mul$$,
Style["Multiplicity is", FontSize -> 14, Bold], Left],
Panel[$CellContext`coupling$$,
Style["The count index of this pictograph is", Bold], Left],
Column[$CellContext`aboutobladetext],
Button[
Style["SU(n): decrease n", FontSize -> 14, Bold],
If[$CellContext`rows$$ >
1, $CellContext`mat$$ =
Map[Drop[#, -1]& , $CellContext`mat$$]; $CellContext`coupling$$ = 1;
Decrement[$CellContext`cols$$]; Null]],
Button[
Style[
"SU(n): increase n", FontSize -> 14, Bold], $CellContext`mat$$ =
Transpose[
Append[
Transpose[$CellContext`mat$$],
Table[0, {3}]]]; $CellContext`coupling$$ = 1;
Increment[$CellContext`cols$$]; Null],
Button[
Style[
"Tensor product decomposition of \[Omega]1 \[CircleTimes] \[Omega]2 ",
FontSize -> 14, Bold, Blue], $CellContext`coupling$$ =
1; $CellContext`tp$$ = 1; Increment[$CellContext`cols$$];
Decrement[$CellContext`cols$$]; Null],
Button[
Style[
"An SU(6) example with multiplicity 592", FontSize -> 10, Bold, Brown,
TextAlignment -> Left], $CellContext`coupling$$ =
1; $CellContext`cols$$ = 6 - 1; $CellContext`tp$$ = 2;
Increment[$CellContext`cols$$]; Decrement[$CellContext`cols$$]; Null],
Button[
Style[
"Reset random SU(3) example", FontSize -> 10, Bold, Brown,
TextAlignment -> Left], $CellContext`cols$$ = 2; $CellContext`mat$$ =
With[{$CellContext`mat12 = Table[
RandomInteger[7], {2}, {3 - 1}]},
Append[$CellContext`mat12,
First[
RandomChoice[
Apply[
obladePackage`tensorproduct, $CellContext`mat12]]]]]; \
$CellContext`coupling$$ = 1; Increment[$CellContext`cols$$];
Decrement[$CellContext`cols$$]; $CellContext`tp$$ =
0], {{$CellContext`doit, 0, ""}, {0}, ControlType -> None},
TrackedSymbols :> {$CellContext`doit}, ContentSize -> {610, 600}],
StandardForm],
ImageSizeCache->{1320., {390., 395.}}],
SynchronousUpdating -> False,
DynamicModuleValues:>{{DownValues[$CellContext`myRange$$] = {HoldPattern[
$CellContext`myRange$$[
Pattern[$CellContext`s,
Blank[]]]] :> Range[$CellContext`s]}}, {
DownValues[$CellContext`myPart$$] = {HoldPattern[
$CellContext`myPart$$[
Pattern[$CellContext`expr,
Blank[]],
Pattern[$CellContext`s,
BlankSequence[]]]] :> Part[$CellContext`expr, $CellContext`s]}}},
Initialization:>{obladePackage`multiplicity[{
Pattern[Private`lam,
BlankSequence[]]}, {
Pattern[Private`mu,
BlankSequence[]]}, {
Pattern[Private`nu,
BlankSequence[]]}] := Switch[
ValueQ[obladePackage`currentgroup], False,
obladePackage`oblade[Length[{Private`lam}] + 1];
obladePackage`multiplicity[{Private`lam}, {Private`mu}, {Private`nu}],
True,
If[Length[{Private`lam}] == obladePackage`currentgroup - 1,
Length[
Private`tensorproductCC[{Private`lam}, {Private`mu},
Reverse[{Private`nu}]]],
obladePackage`oblade[Length[{Private`lam}] + 1];
obladePackage`multiplicity[{Private`lam}, {Private`mu}, {
Private`nu}]]],
TagSet[obladePackage`multiplicity,
MessageName[obladePackage`multiplicity, "usage"],
"multiplicity[lambda,mu,nu] gives the multiplicity of the term nu in the \
decomposition into irreducible components of a tensor product lambda \
\[CircleTimes] mu of two irreps of the Lie group SU(n), given by the \
components of their highest weights along the basis of fundamental weights. \
This integer is also called Littlewood-Richardson coefficient. Equivalently \
it is the multiplicity of the trivial representation in the triple tensor \
product: lambda \[CircleTimes] mu \[CircleTimes] Conjugate[nu]."],
obladePackage`currentgroup = 3,
TagSet[obladePackage`currentgroup,
MessageName[obladePackage`currentgroup, "usage"],
"currentgroup returns the argument n of the group SU(n) currently in \
use."], obladePackage`oblade[
Pattern[Private`var,
Blank[]]] :=
With[{Private`NN = Private`var}, Private`lambdaequations = And[
Apply[And,
Table[Private`lambda[Private`p, 0, 0] == Sum[
Private`j[
Private`p, Private`NN - (Private`s + Private`p), Private`s], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}]],
Apply[And,
Table[Private`lambda[0, Private`p, 0] == Sum[
Private`j[
Private`s, Private`p, Private`NN - (Private`s + Private`p)], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}]],
Apply[And,
Table[Private`lambda[0, 0, Private`p] == Sum[
Private`j[
Private`s, Private`NN - (Private`s + Private`p), Private`p], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}]]];
Private`edgesEW[Private`NN] = Table[
FoldList[Plus][
Table[
Private`j[
Private`t, Private`NN - Private`s, Private`s - Private`t], {
Private`s, Private`t, Private`NN - 1}]], {
Private`t, 1, Private`NN - 1}]; Private`edgesNESW[Private`NN] = Table[
FoldList[Plus][
Table[
Private`j[
Private`s - Private`p, Private`p, Private`NN - Private`s], {
Private`s, Private`p, Private`NN - 1}]], {
Private`p, 1, Private`NN - 1}]; Private`edgesNWSE[Private`NN] = Table[
FoldList[Plus][
Table[
Private`j[
Private`NN - Private`s, Private`s - Private`p, Private`p], {
Private`s, Private`p, Private`NN - 1}]], {
Private`p, 1, Private`NN - 1}]; Private`edgesEWlabels[
Pattern[Private`lev,
Blank[]]] := Table[
Take[
Table[(1/2) (4 + Private`p + Private`p^2) + (Private`lev - 1), {
Private`p, Private`lev, Private`NN}], {
Private`z, Private`z + 1}], {
Private`z, 1, Private`NN - Private`lev}]; Private`edgesNESWlabels[
Pattern[Private`lev,
Blank[]]] := Table[
Take[
Table[(1/2) (3 Private`p + Private`p^2) + (1/2) (Private`lev - 1)
Private`lev + (Private`lev - 1) Private`p, {
Private`p, 1, Private`NN}], {Private`z, Private`z + 1}], {
Private`z, 1, Private`NN - Private`lev}]; Private`edgesNWSElabels[
Pattern[Private`lev,
Blank[]]] := Table[
Take[
Range[
1 + (1/2) (-Private`lev + Private`NN) (1 - Private`lev +
Private`NN), 1 - Private`lev +
Private`NN + (1/2) (-Private`lev + Private`NN) (1 - Private`lev +
Private`NN)], {Private`z, Private`z + 1}], {
Private`z, 1, Private`NN - Private`lev}]; Private`components = Join[
Table[
Table[
Private`j[
Private`p, Private`NN - (Private`s + Private`p), Private`s], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}],
Table[
Table[
Private`j[
Private`s, Private`p, Private`NN - (Private`s + Private`p)], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}],
Table[
Table[
Private`j[
Private`s, Private`NN - (Private`s + Private`p), Private`p], {
Private`s, 0, Private`NN - Private`p}], {
Private`p, 1, Private`NN - 1}]];
Private`fundamentalcomponents = Union[
Flatten[Private`components]]; Private`positivityconstraints = And[
Apply[And,
Map[# >= 0& ,
Flatten[
Private`edgesEW[Private`NN]]]],
Apply[And,
Map[# >= 0& ,
Flatten[
Private`edgesNESW[Private`NN]]]],
Apply[And,
Map[# >= 0& ,
Flatten[
Private`edgesNWSE[Private`NN]]]]]; Private`buildlambdainput[{
Pattern[Private`l1,
BlankSequence[]]}, {
Pattern[Private`l2,
BlankSequence[]]}] := Flatten[{
MapThread[Rule, {
Table[
Private`lambda[Private`p, 0, 0], {
Private`p, 1, Private`NN - 1}], {Private`l1}}],
MapThread[Rule, {
Table[
Private`lambda[0, Private`p, 0], {
Private`p, 1, Private`NN - 1}], {Private`l2}}]}];
Private`buildlambdainput[{
Pattern[Private`l1,
BlankSequence[]]}, {
Pattern[Private`l2,
BlankSequence[]]}, {
Pattern[Private`l3,
BlankSequence[]]}] := Flatten[{
MapThread[Rule, {
Table[
Private`lambda[Private`p, 0, 0], {
Private`p, 1, Private`NN - 1}], {Private`l1}}],
MapThread[Rule, {
Table[
Private`lambda[0, Private`p, 0], {
Private`p, 1, Private`NN - 1}], {Private`l2}}],
MapThread[Rule, {
Table[
Private`lambda[0, 0, Private`p], {
Private`p, 1, Private`NN - 1}], {Private`l3}}]}];
Private`fundamentalcomponentsLabels =
ToString[Private`fundamentalcomponents]; Private`componentsEdgesAndnuc[{
Pattern[Private`lam,
BlankSequence[]]}, {
Pattern[Private`mu,
BlankSequence[]]}] := (
Private`componentsEdgesAndnuc[{Private`lam}, {Private`mu}] =
Module[{Private`redsol, Private`locrules, Private`nuclist,
Private`fundcompval, Private`edgesEWValues,
Private`edgesNESWValues, Private`edgesNWSEValues},
Private`redsol = Reduce[
And[
ReplaceAll[Private`lambdaequations,
Private`buildlambdainput[{Private`lam}, {Private`mu}]],
Private`positivityconstraints], Private`fundamentalcomponents,
Integers]; Private`locrules = ToRules[Private`redsol];
Private`fundcompval =
ReplaceAll[Private`fundamentalcomponents, {Private`locrules}];
Private`nuclist = ReplaceAll[
Table[
Private`lambda[0, 0, Private`p], {
Private`p, 1, Private`NN - 1}], {Private`locrules}];
Private`edgesEWValues = Table[
ReplaceAll[
Private`edgesEW[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; Private`edgesNESWValues = Table[
ReplaceAll[
Private`edgesNESW[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; Private`edgesNWSEValues = Table[
ReplaceAll[
Private`edgesNWSE[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; {
Private`fundcompval, Private`edgesEWValues,
Private`edgesNESWValues, Private`edgesNWSEValues,
Private`nuclist}]); Private`componentsEdgesAndnuc[{
Pattern[Private`lam,
BlankSequence[]]}, {
Pattern[Private`mu,
BlankSequence[]]}, {
Pattern[Private`nuc,
BlankSequence[]]}] := (
Private`componentsEdgesAndnuc[{Private`lam}, {Private`mu}, {
Private`nuc}] =
Module[{Private`redsol, Private`locrules, Private`nuclist,
Private`fundcompval, Private`edgesEWValues,
Private`edgesNESWValues, Private`edgesNWSEValues},
Private`redsol = Reduce[
And[
ReplaceAll[Private`lambdaequations,
Private`buildlambdainput[{Private`lam}, {Private`mu}, {
Private`nuc}]], Private`positivityconstraints],
Private`fundamentalcomponents, Integers];
Private`redsol = And[Private`redsol,
Apply[And,
Table[
Private`lambda[0, 0, Private`p] ==
Part[{Private`nuc}, Private`p], {
Private`p, 1, Private`NN - 1}]]];
If[Private`redsol =!= False, Private`locrules =
ToRules[Private`redsol],
Return[{0, 0, 0, 0, 0}]];
Private`fundcompval =
ReplaceAll[Private`fundamentalcomponents, {Private`locrules}];
Private`nuclist = ReplaceAll[
Table[
Private`lambda[0, 0, Private`p], {
Private`p, 1, Private`NN - 1}], {Private`locrules}];
Private`edgesEWValues = Table[
ReplaceAll[
Private`edgesEW[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; Private`edgesNESWValues = Table[
ReplaceAll[
Private`edgesNESW[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; Private`edgesNWSEValues = Table[
ReplaceAll[
Private`edgesNWSE[Private`NN],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval]}]; {
Private`fundcompval, Private`edgesEWValues,
Private`edgesNESWValues, Private`edgesNWSEValues,
Private`nuclist}]);
Private`AdjMatbis = adjmatPackageIOS`adjmatfct[Private`NN];
Private`rs = adjmatPackageIOS`nntoseed[Private`NN]; If[
MissingQ[
adjmatPackageIOS`nntoseed[Private`NN]],
Print[
"The nntoseed A-list in the adjmatPackage should be extended for \
plotOblade to work with this rank"]]; Private`plotSUNoblade[
Pattern[Private`mytripleofweights,
Blank[]],
Pattern[Private`loccoupling,
Blank[]]] :=
Module[{Private`adj, Private`vert = Private`mytripleofweights,
Private`grid, Private`gr2, Private`grla, Private`grmu, Private`grnu,
Private`grEW, Private`grNESW, Private`grNWSE},
Private`adj = Private`AdjMatbis;
Private`fullinfo = Private`componentsEdgesAndnuc[
Part[Private`mytripleofweights, 1],
Part[Private`mytripleofweights, 2],
Reverse[
Part[Private`mytripleofweights, 3]]];
Private`grid =
GraphPlot[
Private`adj, Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grla =
GraphPlot[Private`adj, VertexRenderingFunction -> (Apply[Which,
Flatten[
Table[{#2 == Private`lambdalabel[Private`NN, Private`s], {
Text[
Style[
Part[Private`vert, 1, Private`s], 20, Blue], #, {
Right, Bottom}],
Disk[#, 0.03], {Black}}}, {Private`s, 1, Private`NN - 1}],
1]]& ), Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grmu =
GraphPlot[Private`adj, VertexRenderingFunction -> (Apply[Which,
Flatten[
Table[{#2 == Private`mulabel[Private`NN, Private`s], {
Text[
Style[
Part[Private`vert, 2, Private`s], 20, Blue], #, {
Left, Bottom}],
Disk[#, 0.03], {Black}}}, {Private`s, 1, Private`NN - 1}],
1]]& ), Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grnu =
GraphPlot[Private`adj, VertexRenderingFunction -> (Apply[Which,
Flatten[
Table[{#2 == Private`nulabel[Private`NN, Private`s], {
Text[
Style[
Part[Private`vert, 3, Private`NN - Private`s], 20,
Blue], #, {Right, Top}],
Disk[#, 0.03], {Black}}}, {Private`s, 1, Private`NN - 1}],
1]]& ), Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grEW =
GraphPlot[Private`adj, EdgeRenderingFunction -> (Apply[Which,
Flatten[
Table[
Flatten[
Table[{
And[
First[#2] == First[Private`u], Last[#2] ==
Last[Private`u]], {
Text[
Style[
Part[
Reverse[
Part[
Part[Private`fullinfo, 2, Private`loccoupling],
Private`f]],
First[
Flatten[
Position[
Private`edgesEWlabels[Private`f], Private`u]]]], 20], (
Part[#, 1] + Part[#, 2])/2]}}, {Private`u,
Private`edgesEWlabels[Private`f]}], 1], {
Private`f, 1, Private`NN - 1}], 1]]& ),
Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grNESW =
GraphPlot[Private`adj, EdgeRenderingFunction -> (Apply[Which,
Flatten[
Table[
Flatten[
Table[{
And[
Last[#2] == First[Private`u], First[#2] ==
Last[Private`u]], {
Text[
Style[
Part[
Part[
Part[Private`fullinfo, 3, Private`loccoupling],
Private`f],
First[
Flatten[
Position[
Private`edgesNESWlabels[Private`f], Private`u]]]], 20], (
Part[#, 1] + Part[#, 2])/2]}}, {Private`u,
Private`edgesNESWlabels[Private`f]}], 1], {
Private`f, 1, Private`NN - 1}], 1]]& ),
Method -> {Automatic, "RandomSeed" -> Private`rs}];
Private`grNWSE =
GraphPlot[Private`adj, EdgeRenderingFunction -> (Apply[Which,
Flatten[
Table[
Flatten[
Table[{
And[
First[#2] == First[Private`u], Last[#2] ==
Last[Private`u]], {
Text[
Style[
Part[
Reverse[
Part[
Part[Private`fullinfo, 4, Private`loccoupling],
Private`f]],
First[
Flatten[
Position[
Private`edgesNWSElabels[Private`f], Private`u]]]], 20], (
Part[#, 1] + Part[#, 2])/2]}}, {Private`u,
Private`edgesNWSElabels[Private`f]}], 1], {
Private`f, 1, Private`NN - 1}], 1]]& ),
Method -> {Automatic, "RandomSeed" -> Private`rs}];
Show[Private`grid, Private`grla, Private`grmu, Private`grnu,
Private`grEW, Private`grNESW, Private`grNWSE]];
Private`plotAllOblades[
Pattern[Private`myweights,
Blank[]]] := Table[
Private`plotSUNoblade[Private`myweights, Private`pos], {
Private`pos, 1,
Apply[obladePackage`multiplicity, Private`myweights]}];
obladePackage`currentgroup = Private`NN],
TagSet[obladePackage`oblade,
MessageName[obladePackage`oblade, "usage"],
"Evaluation of oblade[n] initializes all relevant data for SU(n). It \
returns n and set the variable currentgroup to n."], Private`lambdaequations =
And[Private`lambda[1, 0, 0] ==
Private`j[1, 0, 2] + Private`j[1, 1, 1] + Private`j[1, 2, 0],
Private`lambda[2, 0, 0] == Private`j[2, 0, 1] + Private`j[2, 1, 0],
Private`lambda[0, 1, 0] ==
Private`j[0, 1, 2] + Private`j[1, 1, 1] + Private`j[2, 1, 0],
Private`lambda[0, 2, 0] == Private`j[0, 2, 1] + Private`j[1, 2, 0],
Private`lambda[0, 0, 1] ==
Private`j[0, 2, 1] + Private`j[1, 1, 1] + Private`j[2, 0, 1],
Private`lambda[0, 0, 2] == Private`j[0, 1, 2] + Private`j[1, 0, 2]],
Private`edgesEW[3] = {{
Private`j[1, 2, 0], Private`j[1, 1, 1] + Private`j[1, 2, 0]}, {
Private`j[2, 1, 0]}}, Private`edgesNESW[3] = {{
Private`j[0, 1, 2], Private`j[0, 1, 2] + Private`j[1, 1, 1]}, {
Private`j[0, 2, 1]}}, Private`edgesNWSE[3] = {{
Private`j[2, 0, 1], Private`j[1, 1, 1] + Private`j[2, 0, 1]}, {
Private`j[1, 0, 2]}}, Private`edgesEWlabels[
Pattern[Private`lev$,
Blank[]]] := Table[
Take[
Table[(1/2) (4 + Private`p + Private`p^2) + (Private`lev$ - 1), {
Private`p, Private`lev$, 3}], {Private`z, Private`z + 1}], {
Private`z, 1, 3 - Private`lev$}],
Attributes[Private`lev$] = {Temporary}, Private`edgesNESWlabels[
Pattern[Private`lev$,
Blank[]]] := Table[
Take[
Table[(1/2) (3 Private`p + Private`p^2) + (1/2) (Private`lev$ - 1)
Private`lev$ + (Private`lev$ - 1) Private`p, {Private`p, 1, 3}], {
Private`z, Private`z + 1}], {Private`z, 1, 3 - Private`lev$}],
Private`edgesNWSElabels[
Pattern[Private`lev$,
Blank[]]] := Table[
Take[
Range[
1 + (1/2) (-Private`lev$ + 3) (1 - Private`lev$ + 3), 1 - Private`lev$ +
3 + (1/2) (-Private`lev$ + 3) (1 - Private`lev$ + 3)], {
Private`z, Private`z + 1}], {Private`z, 1, 3 - Private`lev$}],
Private`components = {{
Private`j[1, 2, 0],
Private`j[1, 1, 1],
Private`j[1, 0, 2]}, {
Private`j[2, 1, 0],
Private`j[2, 0, 1]}, {
Private`j[0, 1, 2],
Private`j[1, 1, 1],
Private`j[2, 1, 0]}, {
Private`j[0, 2, 1],
Private`j[1, 2, 0]}, {
Private`j[0, 2, 1],
Private`j[1, 1, 1],
Private`j[2, 0, 1]}, {
Private`j[0, 1, 2],
Private`j[1, 0, 2]}}, Private`fundamentalcomponents = {
Private`j[0, 1, 2],
Private`j[0, 2, 1],
Private`j[1, 0, 2],
Private`j[1, 1, 1],
Private`j[1, 2, 0],
Private`j[2, 0, 1],
Private`j[2, 1, 0]}, Private`positivityconstraints =
And[Private`j[1, 2, 0] >= 0, Private`j[1, 1, 1] + Private`j[1, 2, 0] >= 0,
Private`j[2, 1, 0] >= 0, Private`j[0, 1, 2] >= 0,
Private`j[0, 1, 2] + Private`j[1, 1, 1] >= 0, Private`j[0, 2, 1] >= 0,
Private`j[2, 0, 1] >= 0, Private`j[1, 1, 1] + Private`j[2, 0, 1] >= 0,
Private`j[1, 0, 2] >= 0], Private`buildlambdainput[{
Pattern[Private`l1$,
BlankSequence[]]}, {
Pattern[Private`l2$,
BlankSequence[]]}] := Flatten[{
MapThread[Rule, {
Table[
Private`lambda[Private`p, 0, 0], {Private`p, 1, 3 - 1}], {
Private`l1$}}],
MapThread[Rule, {
Table[
Private`lambda[0, Private`p, 0], {Private`p, 1, 3 - 1}], {
Private`l2$}}]}], Private`buildlambdainput[{
Pattern[Private`l1$,
BlankSequence[]]}, {
Pattern[Private`l2$,
BlankSequence[]]}, {
Pattern[Private`l3$,
BlankSequence[]]}] := Flatten[{
MapThread[Rule, {
Table[
Private`lambda[Private`p, 0, 0], {Private`p, 1, 3 - 1}], {
Private`l1$}}],
MapThread[Rule, {
Table[
Private`lambda[0, Private`p, 0], {Private`p, 1, 3 - 1}], {
Private`l2$}}],
MapThread[Rule, {
Table[
Private`lambda[0, 0, Private`p], {Private`p, 1, 3 - 1}], {
Private`l3$}}]}], Attributes[Private`l1$] = {Temporary},
Attributes[Private`l2$] = {Temporary},
Attributes[Private`l3$] = {Temporary},
Private`fundamentalcomponentsLabels =
"{Private`j[0, 1, 2], Private`j[0, 2, 1], Private`j[1, 0, 2], \
Private`j[1, 1, 1], Private`j[1, 2, 0], Private`j[2, 0, 1], Private`j[2, 1, \
0]}", Private`componentsEdgesAndnuc[{6, 3}, {3, 5}] = {CompressedData["
1:eJx1lVFuhDAMBQMJ23P0SnuEHqC9/we0IPmJYZRGWoXFju03ccLn18/7e22t
vc/fR7vHUvNWcz9/az1f8+85tvK7/g/4HWVby/4q2+Wzl60r1wqfxFlgTy3x
TexetQzYEpt1xn9gPmpdbNR6qM4XfPZaRw3UwjpTR3w5LxPt1Gftq+yj9PX2
1G4u1G4uqSd+W2nv7cnFzMhlrXmvdd7bpT3ZJ66Z8X1XvWRmnu4J8mSfmCf7
pNe7iwvjhANZu5fImjx7cTkqJnmaNZm5v8nMPK2ZPBlztLu/yTg5yJo8zXpW
F/UmxijtFxf2ebSSNXmadWJGD3m6z5jbvWSO1hlNtpM1823tvtcyOnzJmnnM
2rnJms/mSWbm6V5yL1MXmblfhnxZ63/nzpp47szMd9mm94xBZjxj5kIN0eu6
vP8+f1u77zzXYy6zOLPvkLVTn7V7/6LFdWbPZj1r7d4H6uN662MPWoNZz/q4
1bqcSeZj//qeDjPWae3+3lEf87kWn61r/AF1B24C
"], {{{5, 5}, {3}}, {{5, 4}, {2}}, {{5, 3}, {1}}, {{5, 2}, {0}}, {{4,
4}, {3}}, {{5, 5}, {2}}, {{4, 3}, {2}}, {{5, 4}, {1}}, {{4, 2}, {
1}}, {{5, 3}, {0}}, {{4, 1}, {0}}, {{5, 6}, {2}}, {{3, 3}, {3}}, {{4,
4}, {2}}, {{5, 5}, {1}}, {{3, 2}, {2}}, {{4, 3}, {1}}, {{5, 4}, {
0}}, {{3, 1}, {1}}, {{4, 2}, {0}}, {{3, 0}, {0}}, {{4, 5}, {2}}, {{5,
6}, {1}}, {{2, 2}, {3}}, {{3, 3}, {2}}, {{4, 4}, {1}}, {{5, 5}, {
0}}, {{2, 1}, {2}}, {{3, 2}, {1}}, {{4, 3}, {0}}, {{2, 0}, {1}}, {{3,
1}, {0}}, {{3, 4}, {2}}, {{4, 5}, {1}}, {{5, 6}, {0}}, {{1, 1}, {
3}}, {{2, 2}, {2}}, {{3, 3}, {1}}, {{4, 4}, {0}}, {{1, 0}, {2}}, {{2,
1}, {1}}, {{3, 2}, {0}}, {{2, 0}, {0}}, {{4, 6}, {1}}, {{2, 3}, {
2}}, {{3, 4}, {1}}, {{4, 5}, {0}}, {{0, 0}, {3}}, {{1, 1}, {2}}, {{2,
2}, {1}}, {{3, 3}, {0}}, {{1, 0}, {1}}, {{2, 1}, {0}}, {{3, 5}, {
1}}, {{4, 6}, {0}}, {{1, 2}, {2}}, {{2, 3}, {1}}, {{3, 4}, {0}}, {{0,
0}, {2}}, {{1, 1}, {1}}, {{2, 2}, {0}}, {{1, 0}, {0}}, {{2, 4}, {
1}}, {{3, 5}, {0}}, {{0, 1}, {2}}, {{1, 2}, {1}}, {{2, 3}, {0}}, {{0,
0}, {1}}, {{1, 1}, {0}}, {{3, 6}, {0}}, {{1, 3}, {1}}, {{2, 4}, {
0}}, {{0, 1}, {1}}, {{1, 2}, {0}}, {{0, 0}, {0}}, {{2, 5}, {0}}, {{0,
2}, {1}}, {{1, 3}, {0}}, {{0, 1}, {0}}, {{1, 4}, {0}}, {{0, 2}, {
0}}, {{0, 3}, {0}}}, {{{0, 0}, {0}}, {{2, 1}, {0}}, {{4, 2}, {0}}, {{
6, 3}, {0}}, {{0, 0}, {1}}, {{1, 1}, {0}}, {{2, 1}, {1}}, {{3, 2}, {
0}}, {{4, 2}, {1}}, {{5, 3}, {0}}, {{6, 3}, {1}}, {{0, 1}, {0}}, {{0,
0}, {2}}, {{1, 1}, {1}}, {{2, 2}, {0}}, {{2, 1}, {2}}, {{3, 2}, {
1}}, {{4, 3}, {0}}, {{4, 2}, {2}}, {{5, 3}, {1}}, {{6, 3}, {2}}, {{0,
1}, {1}}, {{1, 2}, {0}}, {{0, 0}, {3}}, {{1, 1}, {2}}, {{2, 2}, {
1}}, {{3, 3}, {0}}, {{2, 1}, {3}}, {{3, 2}, {2}}, {{4, 3}, {1}}, {{4,
2}, {3}}, {{5, 3}, {2}}, {{0, 1}, {2}}, {{1, 2}, {1}}, {{2, 3}, {
0}}, {{0, 0}, {4}}, {{1, 1}, {3}}, {{2, 2}, {2}}, {{3, 3}, {1}}, {{2,
1}, {4}}, {{3, 2}, {3}}, {{4, 3}, {2}}, {{5, 3}, {3}}, {{0, 2}, {
1}}, {{0, 1}, {3}}, {{1, 2}, {2}}, {{2, 3}, {1}}, {{0, 0}, {5}}, {{1,
1}, {4}}, {{2, 2}, {3}}, {{3, 3}, {2}}, {{3, 2}, {4}}, {{4, 3}, {
3}}, {{0, 2}, {2}}, {{1, 3}, {1}}, {{0, 1}, {4}}, {{1, 2}, {3}}, {{2,
3}, {2}}, {{1, 1}, {5}}, {{2, 2}, {4}}, {{3, 3}, {3}}, {{4, 3}, {
4}}, {{0, 2}, {3}}, {{1, 3}, {2}}, {{0, 1}, {5}}, {{1, 2}, {4}}, {{2,
3}, {3}}, {{2, 2}, {5}}, {{3, 3}, {4}}, {{0, 3}, {2}}, {{0, 2}, {
4}}, {{1, 3}, {3}}, {{1, 2}, {5}}, {{2, 3}, {4}}, {{3, 3}, {5}}, {{0,
3}, {3}}, {{0, 2}, {5}}, {{1, 3}, {4}}, {{2, 3}, {5}}, {{0, 3}, {
4}}, {{1, 3}, {5}}, {{0, 3}, {5}}}, {{{0, 0}, {1}}, {{1, 0}, {2}}, {{
2, 0}, {3}}, {{3, 0}, {4}}, {{0, 0}, {2}}, {{1, 1}, {1}}, {{1, 0}, {
3}}, {{2, 1}, {2}}, {{2, 0}, {4}}, {{3, 1}, {3}}, {{3, 0}, {5}}, {{1,
2}, {0}}, {{0, 0}, {3}}, {{1, 1}, {2}}, {{2, 2}, {1}}, {{1, 0}, {
4}}, {{2, 1}, {3}}, {{3, 2}, {2}}, {{2, 0}, {5}}, {{3, 1}, {4}}, {{3,
0}, {6}}, {{1, 2}, {1}}, {{2, 3}, {0}}, {{0, 0}, {4}}, {{1, 1}, {
3}}, {{2, 2}, {2}}, {{3, 3}, {1}}, {{1, 0}, {5}}, {{2, 1}, {4}}, {{3,
2}, {3}}, {{2, 0}, {6}}, {{3, 1}, {5}}, {{1, 2}, {2}}, {{2, 3}, {
1}}, {{3, 4}, {0}}, {{0, 0}, {5}}, {{1, 1}, {4}}, {{2, 2}, {3}}, {{3,
3}, {2}}, {{1, 0}, {6}}, {{2, 1}, {5}}, {{3, 2}, {4}}, {{3, 1}, {
6}}, {{2, 4}, {0}}, {{1, 2}, {3}}, {{2, 3}, {2}}, {{3, 4}, {1}}, {{0,
0}, {6}}, {{1, 1}, {5}}, {{2, 2}, {4}}, {{3, 3}, {3}}, {{2, 1}, {
6}}, {{3, 2}, {5}}, {{2, 4}, {1}}, {{3, 5}, {0}}, {{1, 2}, {4}}, {{2,
3}, {3}}, {{3, 4}, {2}}, {{1, 1}, {6}}, {{2, 2}, {5}}, {{3, 3}, {
4}}, {{3, 2}, {6}}, {{2, 4}, {2}}, {{3, 5}, {1}}, {{1, 2}, {5}}, {{2,
3}, {4}}, {{3, 4}, {3}}, {{2, 2}, {6}}, {{3, 3}, {5}}, {{3, 6}, {
0}}, {{2, 4}, {3}}, {{3, 5}, {2}}, {{2, 3}, {5}}, {{3, 4}, {4}}, {{3,
3}, {6}}, {{3, 6}, {1}}, {{2, 4}, {4}}, {{3, 5}, {3}}, {{3, 4}, {
5}}, {{3, 6}, {2}}, {{3, 5}, {4}}, {{3, 6}, {3}}}, {{0, 1}, {0, 4}, {
0, 7}, {0, 10}, {1, 2}, {1, 2}, {1, 5}, {1, 5}, {1, 8}, {1, 8}, {1,
11}, {2, 0}, {2, 3}, {2, 3}, {2, 3}, {2, 6}, {2, 6}, {2, 6}, {2, 9}, {2,
9}, {2, 12}, {3, 1}, {3, 1}, {3, 4}, {3, 4}, {3, 4}, {3, 4}, {3, 7}, {
3, 7}, {3, 7}, {3, 10}, {3, 10}, {4, 2}, {4, 2}, {4, 2}, {4, 5}, {4,
5}, {4, 5}, {4, 5}, {4, 8}, {4, 8}, {4, 8}, {4, 11}, {5, 0}, {5, 3}, {5,
3}, {5, 3}, {5, 6}, {5, 6}, {5, 6}, {5, 6}, {5, 9}, {5, 9}, {6, 1}, {6,
1}, {6, 4}, {6, 4}, {6, 4}, {6, 7}, {6, 7}, {6, 7}, {6, 10}, {7, 2}, {
7, 2}, {7, 5}, {7, 5}, {7, 5}, {7, 8}, {7, 8}, {8, 0}, {8, 3}, {8, 3}, {
8, 6}, {8, 6}, {8, 9}, {9, 1}, {9, 4}, {9, 4}, {9, 7}, {10, 2}, {10,
5}, {11, 3}}}, Private`componentsEdgesAndnuc[{
Pattern[Private`lam$,
BlankSequence[]]}, {
Pattern[Private`mu$,
BlankSequence[]]}] := (
Private`componentsEdgesAndnuc[{Private`lam$}, {Private`mu$}] =
Module[{Private`redsol$, Private`locrules$, Private`nuclist$,
Private`fundcompval$, Private`edgesEWValues$,
Private`edgesNESWValues$, Private`edgesNWSEValues$},
Private`redsol$ = Reduce[
And[
ReplaceAll[Private`lambdaequations,
Private`buildlambdainput[{Private`lam$}, {Private`mu$}]],
Private`positivityconstraints], Private`fundamentalcomponents,
Integers]; Private`locrules$ = ToRules[Private`redsol$];
Private`fundcompval$ =
ReplaceAll[Private`fundamentalcomponents, {Private`locrules$}];
Private`nuclist$ = ReplaceAll[
Table[
Private`lambda[0, 0, Private`p], {Private`p, 1, 3 - 1}], {
Private`locrules$}]; Private`edgesEWValues$ = Table[
ReplaceAll[
Private`edgesEW[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; Private`edgesNESWValues$ = Table[
ReplaceAll[
Private`edgesNESW[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; Private`edgesNWSEValues$ = Table[
ReplaceAll[
Private`edgesNWSE[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; {
Private`fundcompval$, Private`edgesEWValues$,
Private`edgesNESWValues$, Private`edgesNWSEValues$,
Private`nuclist$}]), Private`componentsEdgesAndnuc[{
Pattern[Private`lam$,
BlankSequence[]]}, {
Pattern[Private`mu$,
BlankSequence[]]}, {
Pattern[Private`nuc$,
BlankSequence[]]}] := (
Private`componentsEdgesAndnuc[{Private`lam$}, {Private`mu$}, {
Private`nuc$}] =
Module[{Private`redsol$, Private`locrules$, Private`nuclist$,
Private`fundcompval$, Private`edgesEWValues$,
Private`edgesNESWValues$, Private`edgesNWSEValues$},
Private`redsol$ = Reduce[
And[
ReplaceAll[Private`lambdaequations,
Private`buildlambdainput[{Private`lam$}, {Private`mu$}, {
Private`nuc$}]], Private`positivityconstraints],
Private`fundamentalcomponents, Integers];
Private`redsol$ = And[Private`redsol$,
Apply[And,
Table[
Private`lambda[0, 0, Private`p] ==
Part[{Private`nuc$}, Private`p], {Private`p, 1, 3 - 1}]]];
If[Private`redsol$ =!= False, Private`locrules$ =
ToRules[Private`redsol$],
Return[{0, 0, 0, 0, 0}]];
Private`fundcompval$ =
ReplaceAll[Private`fundamentalcomponents, {Private`locrules$}];
Private`nuclist$ = ReplaceAll[
Table[
Private`lambda[0, 0, Private`p], {Private`p, 1, 3 - 1}], {
Private`locrules$}]; Private`edgesEWValues$ = Table[
ReplaceAll[
Private`edgesEW[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; Private`edgesNESWValues$ = Table[
ReplaceAll[
Private`edgesNESW[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; Private`edgesNWSEValues$ = Table[
ReplaceAll[
Private`edgesNWSE[3],
MapThread[Rule, {Private`fundamentalcomponents,
Part[Private`fundcompval$, Private`s]}]], {Private`s, 1,
Length[Private`fundcompval$]}]; {
Private`fundcompval$, Private`edgesEWValues$,
Private`edgesNESWValues$, Private`edgesNWSEValues$,
Private`nuclist$}]), Attributes[Private`lam$] = {Temporary},
Attributes[Private`mu$] = {Temporary},
Attributes[Private`redsol$] = {Temporary},
Attributes[Private`locrules$] = {Temporary},
Attributes[Private`nuclist$] = {Temporary},
Attributes[Private`fundcompval$] = {Temporary},
Attributes[Private`edgesEWValues$] = {Temporary},
Attributes[Private`edgesNESWValues$] = {Temporary},
Attributes[Private`edgesNWSEValues$] = {Temporary},
Attributes[Private`nuc$] = {Temporary},
Private`AdjMatbis = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0,
0, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 0, 0,
0}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 0}, {0,
0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0,
1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}},
adjmatPackageIOS`adjmatfct[3] = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1,
1, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0,
1, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 1,
0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 0}, {0,
0, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}},
adjmatPackageIOS`adjmatfct[
Pattern[Private`NN,
Blank[]]] := (adjmatPackageIOS`adjmatfct[Private`NN] =
Module[{Private`levelplus, Private`rk, Private`One, Private`iii,
Private`SparseAdjTens, Private`normalAdjTens, Private`lab,
Private`partlab, Private`adjacencyMatrices},
Private`levelplus = Private`NN + 1;
Private`rk = (Private`NN + 1) ((Private`NN + 2)/2);
Private`One = IdentityMatrix[Private`rk];
Private`SparseAdjTens = SparseArray[{Condition[{
Pattern[Private`a,
Blank[]],
Pattern[Private`b,
Blank[]],
Pattern[Private`c,
Blank[]],
Pattern[Private`d,
Blank[]]},
Or[
And[Private`c == Private`a + 1, Private`d == Private`b],
And[Private`c == Private`a, Private`d == Private`b - 1],
And[Private`c == Private`a - 1, Private`d == Private`b + 1]]] ->
1}, {Private`levelplus, Private`levelplus, Private`levelplus,
Private`levelplus}];
Private`normalAdjTens = Normal[Private`SparseAdjTens];
Private`lab = {{0, 0}, {1, 0}, {0, 1}};
Do[Do[Private`iii = Private`i + 1;
Private`partlab[Private`iii] = {
Private`j - Private`i, Private`i}, {Private`i, 0, Private`j}];
Do[Private`lab = Append[Private`lab,
Private`partlab[Private`i]], {Private`i, 1, Private`j + 1}], {
Private`j, 2, Private`levelplus - 1}];
Private`adjacencyMatrices =
Module[{Private`v, Private`crit0, Private`crit1, Private`crit2,
Private`indices0, Private`indices1, Private`indices2,
Private`indices, Private`orderedindices, Private`smallAdjTens,
Private`matbid, Private`trisort, Private`tritolab,
Private`permutritolab, Private`permutritolabinverse,
Private`AdjMatTriality, Private`AdjMatLevel},
Private`indices = Flatten[
Table[
Private`v[Private`i, Private`j], {
Private`i, 1, Private`levelplus}, {
Private`j, 1, Private`levelplus - Private`i + 1}]];
Private`crit0[
Private`v[
Pattern[Private`p,
Blank[]],
Pattern[Private`q,
Blank[]]]] := Mod[Private`p + 2 Private`q - 3, 3] == 0;
Private`crit1[
Private`v[
Pattern[Private`p,
Blank[]],
Pattern[Private`q,
Blank[]]]] := Mod[Private`p + 2 Private`q - 3, 3] == 1;
Private`crit2[
Private`v[
Pattern[Private`p,
Blank[]],
Pattern[Private`q,
Blank[]]]] := Mod[Private`p + 2 Private`q - 3, 3] == 2;
Private`indices0 = Select[Private`indices, Private`crit0];
Private`indices1 = Select[Private`indices, Private`crit1];
Private`indices2 = Select[Private`indices, Private`crit2];
Private`orderedindices =
Join[Private`indices0, Private`indices1, Private`indices2];
Private`smallAdjTens = Table[
Part[
Private`normalAdjTens, Private`i, Private`j, Private`k,
Private`l], {Private`i, 1, Private`levelplus}, {
Private`j, 1, Private`levelplus - Private`i + 1}, {
Private`k, 1, Private`levelplus}, {
Private`l, 1, Private`levelplus - Private`k + 1}]; Private`matbid[
Private`v[
Pattern[Private`a,
Blank[]],
Pattern[Private`b,
Blank[]]],
Private`v[
Pattern[Private`c,
Blank[]],
Pattern[Private`d,
Blank[]]]] :=
Part[Private`smallAdjTens, Private`a, Private`b, Private`c,
Private`d]; Private`AdjMatTriality = Table[
Private`matbid[
Part[Private`orderedindices, Private`i],
Part[Private`orderedindices, Private`j]], {
Private`i, 1, Private`rk}, {Private`j, 1, Private`rk}];
Private`trisort =
ReplaceAll[Private`orderedindices, {Private`v -> List}] -
ConstantArray[{1, 1}, Private`rk]; Private`tritolab = Table[
Flatten[{Private`s,
Position[Private`lab,
Part[Private`trisort, Private`s]]}], {
Private`s, 1, Private`rk}]; Private`permutritolab = SparseArray[
MapThread[Rule, {Private`tritolab,
ConstantArray[1, Private`rk]}], {Private`rk, Private`rk}];
Private`permutritolabinverse = SparseArray[
Inverse[Private`permutritolab]];
Private`AdjMatLevel =
Dot[Private`permutritolabinverse, Private`AdjMatTriality,
Private`permutritolab]; {
Private`AdjMatTriality, Private`AdjMatLevel}];
Part[Private`adjacencyMatrices, 2]]),
TagSet[adjmatPackageIOS`adjmatfct,
MessageName[adjmatPackageIOS`adjmatfct, "usage"],
"adjmatfct[n] returns the adjacency matrix of SU(3) at level n"],
Private`rs = 4, adjmatPackageIOS`nntoseed =
Association[
1 -> 22, 2 -> 8, 3 -> 4, 4 -> 3, 5 -> 6, 6 -> 19, 7 -> 11, 8 -> 34, 9 ->
3, 10 -> 12, 11 -> 18, 12 -> 9],
TagSet[adjmatPackageIOS`nntoseed,
MessageName[adjmatPackageIOS`nntoseed, "usage"],
"nntoseedIOS is an association list and nntoseed[NN] gives the \
RandomSeed to be used in GraphPlot in order to display correctly \
(orientation) the graph of adjacency matrices. The list nntoseedIOS should be \
completed manually. Tested with IOS version 2017 on iPad."],
Private`plotSUNoblade[
Pattern[Private`mytripleofweights$,
Blank[]],
Pattern[Private`loccoupling$,
Blank[]]] :=
Module[{Private`adj$, Private`vert$ = Private`mytripleofweights$,
Private`grid$, Private`gr2$, Private`grla$, Private`grmu$,
Private`grnu$, Private`grEW$, Private`grNESW$, Private`grNWSE$},
Private`adj$ = Private`AdjMatbis;
Private`fullinfo = Private`componentsEdgesAndnuc[
Part[Private`mytripleofweights$, 1],
Part[Private`mytripleofweights$, 2],
Reverse[
Part[Private`mytripleofweights$, 3]]];
Private`grid$ =