(************** 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: 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[ 18833, 453]*) (*NotebookOutlinePosition[ 19498, 476]*) (* CellTagsIndexPosition[ 19454, 472]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Mathematica Interface for POLSYS_GLP", "Title"], Cell["\<\ Summary: the purpose of this notebook is to facilate the prepartion of input \ data file for POLSYS_GLP. POLSYS_GLP is a genearl purpose homotopy solver for \ large polynomial systems and accepts generalized linear product start \ systems. It supports parallel computer systems based on Message Passing \ Interface (MPI). Author: Hai-Jun Su, haijunsu@iastate.edu Reference: Su,H.-J.,McCarthy,J.M.,Sosonkina,M.and Watson,L.T.,\"Algorithm \ xxx: POLSYS_GLP: A Parallel General Linear Product Homotopy Code for Solving \ Polynomial Systems of Equations,\" (in press) ACM Transactions on \ Mathematical Software, to appear in September 2006.\ \>", "Text"], Cell[CellGroupData[{ Cell["Export Data For GLP(generalized linear product)", "Section"], Cell[BoxData[ \(CheckGLP[PolSys_?ListQ, Partition_?ListQ, \ SetDeg_?ListQ] := Module[{NN = Length[PolSys], StartSystem, ValidFlag}, \[IndentingNewLine]If[ Length[Partition] \[NotEqual] NN\ || \ Length[SetDeg] \[NotEqual] NN, \[IndentingNewLine]Print["\<\n\ Length[PolSys]!=Length[Partition] or Length[PolSys]!=Length[SetDeg]\>"]; \ \[IndentingNewLine]Return[ False];\[IndentingNewLine]]; \[IndentingNewLine]ValidFlag = Table[CheckGLPOneEqn[PolSys[\([i]\)], Partition[\([i]\)], SetDeg[\([i]\)]], {i, 1, NN}]; \[IndentingNewLine]Print[ ValidFlag]; \[IndentingNewLine]If[ MemberQ[ValidFlag, False], \[IndentingNewLine]Return[False], Return[True]]\[IndentingNewLine]]\)], "Input"], Cell[BoxData[ \(CheckGLPOneEqn[Pol_, Partition_?ListQ, \ SetDeg_?ListQ] := Module[{StartSystem, MonListAll, MonListPol, PL, ValidFlag}, \[IndentingNewLine]If[ Length[Partition] \[NotEqual] \ Length[SetDeg], \ \[IndentingNewLine]Print["\"]; \ \[IndentingNewLine]Return[ False];\[IndentingNewLine]]; \[IndentingNewLine]StartSystem = 1; \[IndentingNewLine]Do[\[IndentingNewLine]Do[\[IndentingNewLine]\ Coef = Table[Random[Real, {\(-1\), 1}, 20], {k, Length[Partition[\([i]\)]]}]; \ \[IndentingNewLine]StartSystem = StartSystem*\((Coef . Partition[\([i]\)] - 1)\);\[IndentingNewLine], {j, 1, SetDeg[\([i]\)]}]\[IndentingNewLine], {i, 1, Length[Partition]}\[IndentingNewLine]]; \[IndentingNewLine]\ \[IndentingNewLine]StartSystem = Expand[StartSystem]; \[IndentingNewLine]MonListAll = Table[StartSystem[\([i]\)], {i, Length[StartSystem]}] /. {_Real \[Rule] 1}; \[IndentingNewLine]\[IndentingNewLine]PL = N[Expand[Pol], 20]; \[IndentingNewLine]MonListPol = Table[PL[\([i]\)], {i, Length[PL]}] /. {_Real \[Rule] 1, _Complex \[Rule] 1}; \[IndentingNewLine]\[IndentingNewLine]ValidFlag = Table[MemberQ[MonListAll, MonListPol[\([i]\)]], {i, Length[MonListPol]}]; \[IndentingNewLine]If[ MemberQ[ValidFlag, False], \[IndentingNewLine]Return[False], Return[True]]\[IndentingNewLine]]\)], "Input"], Cell[BoxData[ \(\(ExportGLP[PolSys_?ListQ] := ExportGLP[PolSys, "\"];\)\)], "Input"], Cell[BoxData[ \(ExportGLP[PolSys_?ListQ, FileName_?StringQ\ ] := Module[{Partition, SetDeg, Vars, \ PL, maxDeg}, \[IndentingNewLine]Vars = Variables[PolSys]; \[IndentingNewLine]Partition = \ Table[{Vars}, {i, Length[PolSys]}]; \[IndentingNewLine]PL = Expand[PolSys]; \[IndentingNewLine]maxDeg = Table[Max[ Table[Sum[ Exponent[PL[\([k, i]\)], Vars[\([j]\)]], {j, 1, Length[Vars]}], {i, 1, Length[PL[\([1]\)]]}]], {k, 1, Length[PL]}]; \[IndentingNewLine]SetDeg = Table[{maxDeg[\([i]\)]}, {i, 1, Length[Partition]}]; \[IndentingNewLine]ExportGLP[PolSys, Partition, SetDeg, \ FileName];]\)], "Input"], Cell[BoxData[ \(\(ExportGLP[PolSys_?ListQ, Partition_?ListQ] := ExportGLP[PolSys, \ Partition, "\"];\)\)], "Input"], Cell[BoxData[ \(\(ExportGLP[PolSys_?ListQ, Partition_?ListQ, \ SetDeg_?ListQ] := ExportGLP[PolSys, \ Partition, SetDeg, "\"];\)\)], "Input"], Cell[BoxData[ \(ExportGLP[PolSys_?ListQ, Partition_?ListQ, FileName_?StringQ] := Module[{SetDeg}, \[IndentingNewLine]SetDeg = Table[Table[1, {j, 1, Length[Partition[\([i]\)]]}], {i, 1, Length[Partition]}]; \[IndentingNewLine]Print[ SetDeg]; \[IndentingNewLine]ExportGLP[PolSys, \ Partition, SetDeg, "\"];]\)], "Input"], Cell[BoxData[ \(ExportGLP[PolSys_?ListQ, Partition_?ListQ, \ SetDeg_?ListQ, FileName_?StringQ] := \[IndentingNewLine]Module[{OldDir, outputFile, vars, NumEQ, SYSPARTITION, PROBLEM, TITLE, TRACKTOL, FINALTOL, SINGTOL, SSPAR5, NUMRR, AllTerms, CoeffAllTerms, TotalDEGs, TOTDG, MAXT}, \[IndentingNewLine]OldDir = Directory[]; \[IndentingNewLine]CurrentDir = ToFileName[ Extract["\" /. NotebookInformation[EvaluationNotebook[]], {1}, FrontEnd`FileName]]; \[IndentingNewLine]SetDirectory[ CurrentDir]; \[IndentingNewLine]\[IndentingNewLine]outputFile = OpenWrite[FileName]; \[IndentingNewLine]vars = Variables[PolSys]; \[IndentingNewLine]NumEQ = Length[PolSys]; \[IndentingNewLine]\[IndentingNewLine]PROBLEM = \ "\<&PROBLEM NEW_PROBLEM = .TRUE. \n\>"; \[IndentingNewLine]TITLE = "\"; \[IndentingNewLine]TRACKTOL = "\<TRACKTOL = 1.D-04\n\>"; \ \[IndentingNewLine]FINALTOL = "\<FINALTOL = 1.D-12\n\>"; \ \[IndentingNewLine]SINGTOL = "\<SINGTOL = 0.0\n\>"; \[IndentingNewLine]SSPAR5 \ = "\<SSPAR(5) = 1.D+00\n\>"; \[IndentingNewLine]NUMRR = 1; \[IndentingNewLine]\[IndentingNewLine]SYSPARTITION = \ "\<&SYSGLPSET ROOT_COUNT_ONLY = .FALSE.\n\>"; \[IndentingNewLine]\ \[IndentingNewLine]AllTerms = Table[Table[PolSys[\([i, j]\)], {j, Length[PolSys[\([i]\)]]}], {i, Length[PolSys]}]; \[IndentingNewLine]CoeffAllTerms = AllTerms /. Table[vars[\([i]\)] \[Rule] 1, {i, Length[vars]}]; \ \[IndentingNewLine]\[IndentingNewLine]TotalDEGs = Table[Max[ Table[Sum[ Exponent[AllTerms[\([i, j]\)], vars[\([k]\)]], {k, Length[vars]}], {j, Length[AllTerms[\([i]\)]]}]], {i, Length[AllTerms]}]; \[IndentingNewLine]TOTDG = Product[TotalDEGs[\([i]\)], {i, Length[TotalDEGs]}]; \n\ \ \ \ \ MAXT = Max[Table[ Length[PolSys[\([i]\)]], {i, Length[PolSys]}]]; \ \[IndentingNewLine]\[IndentingNewLine]WriteString[outputFile, PROBLEM]; \[IndentingNewLine]WriteString[outputFile, TITLE]; \[IndentingNewLine]WriteString[ outputFile, "\<\n\>"]; \[IndentingNewLine]WriteString[outputFile, TRACKTOL]; \[IndentingNewLine]WriteString[outputFile, FINALTOL]; \[IndentingNewLine]WriteString[outputFile, SINGTOL]; \[IndentingNewLine]WriteString[outputFile, SSPAR5]; \[IndentingNewLine]WriteString[ outputFile, "\<NUMRR = \>", \ NUMRR, "\<\n\>"]; \[IndentingNewLine]WriteString[ outputFile, "\<N = \>", \ NumEQ, "\<\n\>"]; \[IndentingNewLine]\[IndentingNewLine]WriteString[ outputFile, "\<\n\>"]; \ \[IndentingNewLine]Do[\[IndentingNewLine]WriteString[ outputFile, \ \ "\<NUM_TERMS(\>", i, "\<) = \>", Length[AllTerms[\([i]\)]], "\<\n\>"]; \[IndentingNewLine]Do[\ \[IndentingNewLine]Do[\[IndentingNewLine]WriteString[ outputFile, \ "\< DEG(\>", i, "\<,\>", j, "\<,\>", k, "\<) = \>", \ Exponent[AllTerms[\([i, j]\)], vars[\([k]\)]], "\<\n\>"], \[IndentingNewLine]{k, Length[vars]}]; \[IndentingNewLine]WriteString[ outputFile, "\< COEF(\>", i, "\<,\>", j, "\<) = (\>", FortranForm[Re[CoeffAllTerms[\([i, j]\)]]], "\<, \>", FortranForm[ Im[CoeffAllTerms[\([i, j]\)]]], "\<)\>", \ "\<\n\>"], \[IndentingNewLine]{j, Length[AllTerms[\([i]\)]]}]; \[IndentingNewLine]WriteString[ outputFile, "\<\n\>"];\[IndentingNewLine], {i, Length[AllTerms]}]; \[IndentingNewLine]WriteString[ outputFile, "\</\n\n\>"]; \ \[IndentingNewLine]\[IndentingNewLine]WriteString[outputFile, SYSPARTITION]; \[IndentingNewLine]\[IndentingNewLine]Do[\ \[IndentingNewLine]WriteString[outputFile, "\<P(\>", i, "\<) = '\>", Partition[\([i]\)], \ "\<'\n\>"], \[IndentingNewLine]{i, 1, Length[Partition]}]; \ \[IndentingNewLine]Do[\[IndentingNewLine]WriteString[outputFile, "\<DG(\>", i, "\<) = '\>", SetDeg[\([i]\)], "\<'\n\>"], \[IndentingNewLine]{i, 1, Length[SetDeg]}]; \ \[IndentingNewLine]\[IndentingNewLine]WriteString[ outputFile, "\<\n\>"]; \ \[IndentingNewLine]Do[\[IndentingNewLine]WriteString[ outputFile, "\<NUM_SETS(\>", i, "\<) = \>", Length[Partition[\([i]\)]], \ "\<\n\>"]; \[IndentingNewLine]Do[\ \[IndentingNewLine]WriteString[outputFile, "\< NUM_INDICES(\>", i, "\<,\>", j, "\<) = \>", Length[Partition[\([i, j]\)]], \ "\<\n\>"]; \[IndentingNewLine]WriteString[ outputFile, "\< SET_DEG(\>", i, "\<,\>", j, "\<) = \>", SetDeg[\([i, j]\)], \ "\<\n\>"]; \[IndentingNewLine]Do[\ \[IndentingNewLine]WriteString[outputFile, "\< INDEX(\>", i, "\<,\>", j, "\<,\>", k, "\<) = \>", \((Position[vars, Partition[\([i, j, k]\)]])\)[\([1, 1]\)], \ "\<\n\>"], \[IndentingNewLine]{k, Length[Partition[\([i, j]\)]]}];\[IndentingNewLine], {j, Length[Partition[\([i]\)]]}];\[IndentingNewLine], {i, 1, NumEQ}]; \[IndentingNewLine]WriteString[ outputFile, "\</\n\>"]; \ \[IndentingNewLine]\[IndentingNewLine]Print["\<FILE = \>", \ FileName, "\<\nNumber of Equations = \>", \ NumEQ, "\<\nNumber of Variables = \>", \ Length[vars], "\< \>", \ vars, \[IndentingNewLine]"\<\nWarnning: Total Degree = \>", \ TOTDG, \[IndentingNewLine]"\<\nWarnning: Maximun Number of Terms = \ \>", \ MAXT, "\<\nPARTITION = \n\>", Partition]; \[IndentingNewLine]\[IndentingNewLine]Close[ outputFile]; \[IndentingNewLine]SetDirectory[ OldDir];\[IndentingNewLine]]\)], "Input"], Cell[TextData[StyleBox["Note: INPUT.TXT must be converted to UNIX format that \ is replaceing CR+LR with LR. In hexidecimal format, replace 0d0a with 0a. We \ can use fromdos.exe to convert dos format to unix format. and use todos.exe \ to convert unix format to dos format.", FontColor->RGBColor[1, 0, 0]]], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["GLP example", "Section"], Cell[CellGroupData[{ Cell["Two Quadratic Equations", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[{ \(P1 = \((\(-9.80000000000000\)*10^\(-04\))\)* x^2 + \((9.78000000000000*10^\(+05\))\)* y^2 + \((\(-9.80000000000000\)*10^\(+00\))\)*x* y + \((\(-2.35000000000000\)*10^\(+02\))\)* x + \((8.89000000000000*10^\(+04\))\)* y + \((\(-1.00000000000000\)*10^\(+00\))\)\), "\n", \(P2 = \((\(-1.00000000000000\)*10^\(-02\))\)* x^2 + \((\(-9.84000000000000\)*10^\(-01\))\)* y^2 + \((\(-2.97000000000000\)*10^\(+01\))\)*x* y + \((9.87000000000000*10^\(-03\))\)* x + \((\(-1.24000000000000\)*10^\(-01\))\)* y + \((\(-2.50000000000000\)*10^\(-01\))\)\)}], "Input"], Cell[BoxData[ \(\(-1.`\) - 235.`\ x - 0.0009800000000000002`\ x\^2 + 88900.`\ y - 9.8`\ x\ y + 977999.9999999999`\ y\^2\)], "Output"], Cell[BoxData[ \(\(-0.25`\) + 0.009869999999999999`\ x - 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