(************** 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). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 39701, 1072]*) (*NotebookOutlinePosition[ 40614, 1103]*) (* CellTagsIndexPosition[ 40525, 1097]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[{ \(\(\(SetAttributes[Swap23, HoldAll]\)\(\n\) \)\), "\[IndentingNewLine]", \(Swap23[L_] := Module[{temp}, temp = L[\([2]\)]; \[IndentingNewLine]L[\([2]\)] = L[\([3]\)]; \[IndentingNewLine]L[\([3]\)] = temp; \[IndentingNewLine]L]\)}], "Input"], Cell[BoxData[{ \(SetAttributes[InitializeMatrix, HoldFirst]\), "\[IndentingNewLine]", \(\(InitializeMatrix[M_, n_] := \(M = Table[If[i \[Equal] j, Infinity, \(-Infinity\)], {i, 1, n}, {j, 1, n}]\);\)\), "\[IndentingNewLine]", \(\(SetAttributes[SetToLambda, HoldFirst];\)\), "\[IndentingNewLine]", \(\(SetToLambda[M_, i_, j_] := \ If[i > j, SetToLambda[M, j, i], M[\([i, j]\)]\ = \ \(M[\([j, i]\)]\ = \ \[Lambda]\_\(i\[InvisibleComma]j\)\)];\)\), "\ \[IndentingNewLine]", \(\(SetAttributes[RecoverFromRowSum, HoldFirst];\)\), "\[IndentingNewLine]", \(\(\(RecoverFromRowSum[M_, i_, j_]\ := \ \((M[\([i, j]\)]\ = \ 0; \ M[\([i, j]\)]\ = \ \(M[\([j, i]\)]\ = \ \(-Total[ M[\([i]\)]]\)\))\);\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(SetAttributes[SolveDet, HoldFirst];\)\), "\[IndentingNewLine]", \(\(\(SolveDet[M_, i_, j_, rows_, cols_, \ sieveFunction_: \((True &)\)]\ := \ Module[{submat, x, soln, eqn}, \ \[IndentingNewLine]M[\([i, j]\)] = \(M[\([j, i]\)] = x\); \ (*\ Double\ assignment\ important\ for\ the\ square - root\ trick\ *) \[IndentingNewLine]submat = M[\([rows]\)]; \ submat = Transpose[\ \((Transpose[ submat])\)[\([cols]\)]]; \[IndentingNewLine] (*\ Maxe\ soln\ the\ list\ of\ solutions*) \[IndentingNewLine]eqn = \ \((Det[submat] \[Equal] 0)\); \[IndentingNewLine]soln\ = \ x /. 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the\ relations\ are\ now\ \ R\_\(\(L[\([1]\)]\)[\([1]\)]\)\%\(\(L[\([1]\)]\)[\([2]\)]\) + R\_\(\(L[\([3]\)]\)[\([1]\)]\)\%\(\(L[\([3]\)]\)[\([2]\)]\)\ \ == \ R\_\(\(L[\([2]\)]\)[\([1]\)]\)\%\(\(L[\([2]\)]\)[\([2]\)]\) . \ Imagine\ this\ as\ R\_12\%14 + R\_15\%16\ \[Equal] \ R\_12\%16*) \[IndentingNewLine]infinities = 0; loToFind = 0; hiToFind = 0; \[IndentingNewLine]Scan[ Function[\[IndentingNewLine]\[IndentingNewLine]If[\(\(R[#[\([1]\)], \ #[\([2]\)]]\)[\([i]\)]\)[\([j]\)] \[Equal] Infinity, \ \((\(++infinities\); loToFind\ = \ #[\([1]\)]; \ hiToFind\ = \ #[\([2]\)]; \ Print[loToFind, "\< \>", \ hiToFind])\)]\[IndentingNewLine]], \ l]; \[IndentingNewLine]Print[loToFind, \ "\< \>", \ hiToFind, \ "\< \>", \ i, \ "\< \>", \ j]; \[IndentingNewLine]If[ infinities\ \[Equal] \ 1, \[IndentingNewLine]\(\(R[loToFind, hiToFind]\)[\([i]\)]\)[\([j]\)]\ \ = x; \[IndentingNewLine]R1\ := \ R[\(l[\([1]\)]\)[\([1]\)], \ \(l[\([1]\)]\)[\([2]\)]]; \ R2 := R[\(l[\([3]\)]\)[\([1]\)], \ 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