doc/// Key BertiniInputConfiguration SecurityLevel ScreenOut OutputLevel StepsForIncrease MaxNewtonIts MaxStepSize MaxNumberSteps MaxCycleNum RegenStartLevel AccuracyEst MPType PRECISION ODEPredictor TrackTolBeforeEG TrackTolDuringEG FinalTol MaxNorm MinStepSizeBeforeEG MinStepSizeDuringEG ImagThreshold CoeffBound DegreeBound CondNumThreshold RandomSeed SingValZeroTol EndGameNum Headline a key to designate a configuration in a Bertini input file Description Text These are some of the configurations that can be set in Bertini. Bertini ignores configurations that are not needed for a computation. ///; ------------------------------------------------------ ------FUNCTIONS BERTINI VERSION 2------------ ------------------------------------------------------ ------------------------------------------------------------------ ------SUPPORTING FUNCTIONS ------------ ------------------------------------------------------------------ doc /// Key replaceFirstLine (replaceFirstLine,String,String,Thing) Headline Replaces the first line of a file with a string. Usage replaceFirstLine(filesGoHere,fileName,aString) Inputs filesGoHere:String The directory where the files are stored. fileName:String The file whose first line we will replace with aString. aString:Thing The string which we write in the first line. Description Text replaceFirstLine replaces the first line of a file with a string. This function is used in the trace test functions. Example writeStartFile(storeBM2Files,{{2,3},{4,5}}); replaceFirstLine(storeBM2Files,"start","1") ///; doc /// Key runBertini (runBertini,String) Headline Calls Bertini. Usage runBertini(s) Inputs s:String The directory where Bertini will store files. Description Text To run bertini we need to say where we want to output the files, which is given by s. Additional options include speciifying the location of the input file (the default is that the input file is located where we output the files) B'Exe is how we call Bertini. The default option is how Bertini is usually called in M2 in the init file. InputFileName has its default as "input". Example makeB'InputFile(storeBM2Files, AffVariableGroup=>{x,y}, B'Polynomials=>{"x^2-1","y^2-4"}); runBertini(storeBM2Files) readFile(storeBM2Files) Example makeB'InputFile(storeBM2Files, AffVariableGroup=>{x,y}, B'Polynomials=>{"x^2-1","y^2-4"}); runBertini(storeBM2Files,StorageFolder=>"StoreMyFiles") readFile(storeBM2Files|"/StoreMyFiles") ///; doc /// Key readFile (readFile,String,String,Number) (readFile,String,Number) (readFile,String) Headline Read the first lines of a file. Usage readFile(filesGoHere,fileName,numCharacters) readFile(filesGoHere,numCharacters) Inputs filesGoHere:String The directory where the files are stored. fileName:String The file whose lines we will read. numCharacters:Number The number of lines we read. Description Text Read the first characters of a file. When fileName is omitted "bertini_session.log" is read. Example makeB'InputFile(storeBM2Files,AffVariableGroup=>{x,y},B'Polynomials=>{"x^2+2","y^2+3"}); runBertini(storeBM2Files) readFile(storeBM2Files,"nonsingular_solutions",1) readFile(storeBM2Files,10000) readFile(storeBM2Files) ///; doc /// Key makeMembershipFile (makeMembershipFile,String) Headline Creates a Bertini incidence_matrix file using Tracktype 3.. Usage makeMembershipFile(s) Inputs s:String The directory where the input file, witness_data, and member_points is stored. Description Text After doing a positive dimensional solve with Bertini a witness data file is produced. This function requires an input file, member_points file and witness_data file. It appends "TrackType: 3" to the configurations in the input file and calls Bertini to produce and incidence_matrix file with respect to the member_points file. Text The option NameWitnessPointFile has "member_points" set as its default. Text The option TestSolutions can be set to a list of coordinates of points which will be written to a file. Example makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{TrackType,1}}, AffVariableGroup=>{x,y,z}, B'Polynomials=>{"z*((x+y+z)^3-1)","z*(y^2-3+z)"} ); runBertini(storeBM2Files) makeSampleSolutionsFile(storeBM2Files,2,SpecifyComponent=>{1,0}) makeMembershipFile(storeBM2Files,NameSolutionsFile=>"sample_solutions_file") makeMembershipFile(storeBM2Files,TestSolutions=>{{1,2,0},{3,2,1}}) importIncidenceMatrix(storeBM2Files) ///; doc /// Key makeSampleSolutionsFile (makeSampleSolutionsFile,String,Number) Headline This function samples points from a component by performing a Bertini TrackType 2. Usage makeSampleSolutionsFile(theDir,s) Inputs theDir:String The directory where Bertini will store files and the witness_data file and input file are located. s:Number The number of sample points we want. Description Text This function does a track type 2 Bertini run creating "sample_solutions_file" that contains a list of witness points in the standard Bertini format. Example makeB'InputFile(storeBM2Files, AffVariableGroup=>{x,y,z}, BertiniInputConfiguration=>{{TrackType,1}}, B'Polynomials=>{"(x^2+y^2+z^2-1)*y"}); runBertini(storeBM2Files) makeSampleSolutionsFile(storeBM2Files,4,SpecifyComponent=>{2,0})--creates a witness point file with 4 sample points for the 0th component in dimension 2. theSols=importSolutionsFile(storeBM2Files,NameSolutionsFile=>"sample_solutions_file") ///; doc /// Key writeParameterFile (writeParameterFile,String,List) Headline Writes the list of parameter values to a file that Bertini can read. Usage writeParameterFile(s,v) Inputs s:String The directory where the Bertini file will be written. v:List A list of numbers that will be written to the file. Description Text To do a parameter homotopy one must have a start_parameters file and a final_parameters file. Example R=QQ[x,y,t] makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{"PARAMETERHOMOTOPY",1}}, ParameterGroup=>{t}, AffVariableGroup=>{{x,y}}, B'Polynomials=>{x^2-1,y^2-t}); runBertini(storeBM2Files) copyFile(storeBM2Files|"/nonsingular_solutions",storeBM2Files|"/start") makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{"PARAMETERHOMOTOPY",2}}, ParameterGroup=>{t}, AffVariableGroup=>{{x,y}}, B'Polynomials=>{x^2-1,y^2-t}); writeParameterFile(storeBM2Files,{1}); runBertini(storeBM2Files) ///; doc /// Key sortMainDataComponents (sortMainDataComponents,List) Headline Sorts imported main data into components. Usage sortMainDataComponents(l) Inputs l:List A list of points imported from a main_data file. Description Text After importing a main_data file we have a list of points. This function organizes the components by irreducible component. Example F={"x*(x+2*y+3*z^2)","(y^3-x+z)*(z)*(x+2*y+3*z^2)"} makeB'InputFile(storeBM2Files,BertiniInputConfiguration=>{{TrackType,1}},AffVariableGroup=>{x,y,z},B'Polynomials=>F); runBertini(storeBM2Files) listPoints=importMainDataFile(storeBM2Files) #listPoints theComponents=sortMainDataComponents(listPoints) for i in theComponents_0 list (i#ComponentNumber,i#Dimension) for i in theComponents_1 list (i#ComponentNumber,i#Dimension) for i in theComponents_2 list (i#ComponentNumber,i#Dimension) ///; doc /// Key OutputStyle [bertiniParameterHomotopy, OutputStyle] [bertiniZeroDimSolve,OutputStyle] Headline Used to change the output style. Usage bertiniParameterHomotopy(...,OutputStyle=>String) bertiniZeroDimSolve(...,OutputStyle=>String) Description Text Use OutputStyle to change the style of output. ///; ------------------- -----OPTIONS------- ------------------- undocumented { "Bertini options", NameMainDataFile, NameIncidenceMatrixFile, NameB'Slice, NameFunctionFile, NameSampleSolutionsFile, NameIncidenceMatrixFile, NameStartFile, NameWitnessSliceFile, NameWitnessSolutionsFile, OrderPaths, PathNumber, PreparePH2, RandomComplex, RandomReal, SaveData, SpecifyComponent, SpecifyDim, StartParameterFileDirectory, TestSolutions, TextScripts, PathVariable, PathsWithSameEndpoint, FunctionResidual, ParameterValues, VariableList, CycleNumber, UseRegeneration, PrecisionIncreased, AccuracyEstInternal, ComponentNumber, B'Exe, DeflationsNeeded, Dimension, MaxPrecisionUtilized, FinalTValue, SolutionType, B'Homogenization, ContainsPoint, RandomCoefficientGenerator, NameB'Section, B'NumberCoefficients, SpecifyVariables, RandomGamma, StorageFolder, SubFolder, StartPoints, StartParameters, SubIntoCC, storeBM2Files, MultiplicityTol, SetParameterGroup, ReturnPoints, ConditionNumTol, ContainsMultiProjectivePoint, HomVariableGroup, importSliceFile, InputFileDirectory, ListB'Sections, makeB'TraceInput, MoveToDirectory } end doc /// Key M2Precision [bertiniParameterHomotopy,M2Precision] [bertiniZeroDimSolve,M2Precision] Headline Option to change the precision Macaulay2 uses to import the files. Usage bertiniParameterHomotopy(...,M2Precision=>ZZ) bertiniZeroDimSolve(...,TopDirectory=>ZZ) Description Text When importing solutions, they are first converted to an external string where precision is set. The default is 53. ///; doc/// Key ParameterGroup [makeB'InputFile, ParameterGroup] Headline An option which designates the parameters for a Parameter Homotopy. Description Text This option should be set to a list of parameters. Example R=QQ[x,y,u] makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{"PARAMETERHOMOTOPY",1}}, AffVariableGroup=>{{x,y}}, ParameterGroup=>{u}, B'Polynomials=>{y-(x^2-1),y-u}); ///; doc/// Key [makeB'InputFile, BertiniInputConfiguration] [bertiniParameterHomotopy,BertiniInputConfiguration] [bertiniZeroDimSolve,BertiniInputConfiguration] Headline An option to designate the CONFIG part of a Bertini Input file. Description Text This option should be set to a list of lists of 2 elements. The first element is the name of the Bertini option, e.g. "MPType" and the second element is what the Bertini option will be set to e.g. "2". Example R=QQ[x0,x1,y0,y1,z] makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{"MPTYPE"=>2}, HomVariableGroup=>{{x0,x1},{y0,y1}}, AffVariableGroup=>{{z}}, B'Polynomials=>{z*x1^2+x0^2,y0*z+y1,y0-2*z^2*y1}); ///; doc/// Key B'Polynomials [makeB'InputFile, B'Polynomials] Headline An option which designates the polynomials that we want to solve. Description Text The user should specify the polynomial system they want to solve with the B'Polynomials option or B'Functions option. If B'Polynomials is not used then the user should use the NamePolynomials option. Example R=QQ[x,y] makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{"MPTYPE",2}}, AffVariableGroup=>{{x,y}}, B'Polynomials=>{x+y-1,x^2-2}); Text B'Polynomials can be in combination with B'Functions. B'Functions allows the user to define subfunctions. Example R=QQ[x,y,A] makeB'InputFile(storeBM2Files, AffVariableGroup=>{{x,y}}, B'Functions=>{{A,x^2-1}}, B'Polynomials=>{A+y,x+y-2}); ///; doc/// Key B'Functions [makeB'InputFile, B'Functions] [bertiniZeroDimSolve,B'Functions] [bertiniParameterHomotopy,B'Functions] Headline An option which designates sub-functions or a polynomial system as a straight line program. Description Text The user should specify the polynomial system they want to solve with the B'Polynomials option or the B'Functions option. The user should use the NamePolynomials option in conjunction with B'Functions whenever B'Polynomials is not used. Example R=QQ[x,y] makeB'InputFile(storeBM2Files, AffVariableGroup=>{{x,y}}, NamePolynomials=>{f1,f2}, B'Functions=>{{f1,x+y-1},f2=>x^2-2}); --f1=x+y+1,f2=x^2-2 is written to the input file Text B'Polynomials can be in combination with B'Functions. B'Functions allows the user to define subfunctions. Example R=QQ[x,y,A] makeB'InputFile(storeBM2Files, AffVariableGroup=>{{x,y}}, B'Functions=>{{A,x^2-1}},--A=x^2-1 is written to the input file B'Polynomials=>{A+y,x+y-2}); ///; doc/// Key NamePolynomials [makeB'InputFile, NamePolynomials] Headline An option which designates the names of the polynomials we want to solve. Description Text The user should specify the polynomial system they want to solve with the B'Polynomials option or the B'Functions option. The user should use the NamePolynomials option in conjunction with B'Functions whenever B'Polynomials is not used. Example R=QQ[x,y] makeB'InputFile(storeBM2Files, AffVariableGroup=>{{x,y}}, NamePolynomials=>{f1,f2}, B'Functions=>{{f1,x+y-1},{f2,x^2-2}}); --f1=x+y+1,f2=x^2-2 is written to the input file ///; doc/// Key NameB'InputFile [makeB'InputFile, NameB'InputFile] Headline This option names the input file. Description Text Set this option to a string to name the input file. Example R=QQ[x,y] makeB'InputFile(storeBM2Files, AffVariableGroup=>{{x,y}}, B'Polynomials=>{x+y-1,x^2-2}, NameB'InputFile=>"testInput"); --the input file will be named "testInput" rather than the default "input". ///; doc/// Key NameParameterFile [writeParameterFile, NameParameterFile] Headline This option names the parameter file. Description Text Set this option to a string to name the parameter file. Example writeParameterFile(storeBM2Files,{.1,.2,.5},NameParameterFile=>"testParameters"); --this function writes a parameter file named testParameters ///; doc/// Key SolutionFileStyle [b'PHSequence, SolutionFileStyle] Headline This is to adjust to the different ways Bertini stores solutions. Description Text The option can be set to the "simple" style (coordinates only), "raw_solutions" style (path number and coordinates), and "main_data" style (detailed information). ///; doc/// Key NameSolutionsFile [importSolutionsFile, NameSolutionsFile] NameFunctionFile NameWitnessSliceFile NameWitnessSolutionsFile NameMainDataFile NameSampleSolutionsFile [b'PHGaloisGroup,NameB'InputFile] [b'PHMonodromyCollect,NameB'InputFile] [b'PHSequence,NameB'InputFile] [calculateB'Trace,NameB'InputFile] [makeB'TraceInput,NameB'InputFile] [makeSampleSolutionsFile,NameB'InputFile] [makeWitnessSetFiles,NameB'InputFile] [runBertini,NameB'InputFile] [runBertini,B'Exe] [b'PHGaloisGroup,NameParameterFile] [b'PHMonodromyCollect,NameParameterFile] [b'PHSequence,NameParameterFile] [importParameterFile,NameParameterFile] [b'PHGaloisGroup,NameSolutionsFile] [b'PHMonodromyCollect,NameSolutionsFile] [b'PHSequence,NameSolutionsFile] [makeMembershipFile,NameSolutionsFile] [makeSampleSolutionsFile,NameSolutionsFile] [makeWitnessSetFiles,NameSolutionsFile] [b'PHGaloisGroup,NameStartFile] [calculateB'Trace,NameStartFile] [makeWitnessSetFiles,NameWitnessSliceFile] [importMainDataFile,NameMainDataFile] NameGaloisGroupGeneratorFile [b'TraceTestImage,NameB'InputFile] [b'PHGaloisGroup,NameGaloisGroupGeneratorFile] [makeMembershipFile,NameB'InputFile] [b'PHMonodromyCollect,NameStartFile] [b'PHSequence,NameStartFile] NameIncidenceMatrixFile NameStartFile [writeStartFile,NameStartFile] [importIncidenceMatrix, NameIncidenceMatrixFile] [bertiniZeroDimSolve,NameSolutionsFile] [bertiniZeroDimSolve,NameMainDataFile] Headline options determine the name of a file to be imported or written. Description Text Set this option to a string to name the file to be imported or written. Example makeB'InputFile(storeBM2Files,AffVariableGroup=>{x},B'Polynomials=>{"x^2-2"}); runBertini(storeBM2Files); importSolutionsFile(storeBM2Files,NameSolutionsFile=>"nonsingular_solutions"); importSolutionsFile(storeBM2Files,NameSolutionsFile=>"real_finite_solutions"); Example writeStartFile(storeBM2Files,{{2},{ -2}},NameStartFile=>"start"); writeParameterFile(storeBM2Files,{4},NameParameterFile=>"start_parameters"); writeParameterFile(storeBM2Files,{3},NameParameterFile=>"final_parameters"); makeB'InputFile(storeBM2Files,B'Polynomials=>{"x^2-t"},ParameterGroup=>{t},BertiniInputConfiguration=>{{ParameterHomotopy,2}},AffVariableGroup=>{x},NameB'InputFile=>"inputWin"); runBertini(storeBM2Files,NameB'InputFile=>"inputWin"); importSolutionsFile(storeBM2Files,NameSolutionsFile=>"nonsingular_solutions") importSolutionsFile(storeBM2Files,NameSolutionsFile=>"real_finite_solutions") ///; [bertiniComponentMemberTest, MPType] [bertiniComponentMemberTest, PRECISION] [bertiniComponentMemberTest, ODEPredictor] [bertiniComponentMemberTest, TrackTolBeforeEG] [bertiniComponentMemberTest, TrackTolDuringEG] [bertiniComponentMemberTest, FinalTol] [bertiniComponentMemberTest, MaxNorm] [bertiniComponentMemberTest, MinStepSizeBeforeEG] [bertiniComponentMemberTest, MinStepSizeDuringEG] [bertiniComponentMemberTest, ImagThreshold] [bertiniComponentMemberTest, CoeffBound] [bertiniComponentMemberTest, DegreeBound] [bertiniComponentMemberTest, CondNumThreshold] [bertiniComponentMemberTest, RandomSeed] [bertiniComponentMemberTest, SingValZeroTol] [bertiniComponentMemberTest, EndGameNum] [bertiniComponentMemberTest, UseRegeneration] [bertiniComponentMemberTest, SecurityLevel] [bertiniComponentMemberTest, ScreenOut] [bertiniComponentMemberTest, OutputLevel] [bertiniComponentMemberTest, StepsForIncrease] [bertiniComponentMemberTest, MaxNewtonIts] [bertiniComponentMemberTest, MaxStepSize] [bertiniComponentMemberTest, MaxNumberSteps] [bertiniComponentMemberTest, MaxCycleNum] [bertiniComponentMemberTest, RegenStartLevel] [bertiniPosDimSolve, MPType] [bertiniPosDimSolve, PRECISION] [bertiniPosDimSolve, ODEPredictor] [bertiniPosDimSolve, TrackTolBeforeEG] [bertiniPosDimSolve, TrackTolDuringEG] [bertiniPosDimSolve, FinalTol] [bertiniPosDimSolve, MaxNorm] [bertiniPosDimSolve, MinStepSizeBeforeEG] [bertiniPosDimSolve, MinStepSizeDuringEG] [bertiniPosDimSolve, ImagThreshold] [bertiniPosDimSolve, CoeffBound] [bertiniPosDimSolve, DegreeBound] [bertiniPosDimSolve, CondNumThreshold] [bertiniPosDimSolve, RandomSeed] [bertiniPosDimSolve, SingValZeroTol] [bertiniPosDimSolve, EndGameNum] [bertiniPosDimSolve, UseRegeneration] [bertiniPosDimSolve, SecurityLevel] [bertiniPosDimSolve, ScreenOut] [bertiniPosDimSolve, OutputLevel] [bertiniPosDimSolve, StepsForIncrease] [bertiniPosDimSolve, MaxNewtonIts] [bertiniPosDimSolve, MaxStepSize] [bertiniPosDimSolve, MaxNumberSteps] [bertiniPosDimSolve, MaxCycleNum] [bertiniPosDimSolve, RegenStartLevel] [bertiniRefineSols, MPType] [bertiniRefineSols, PRECISION] [bertiniRefineSols, ODEPredictor] [bertiniRefineSols, TrackTolBeforeEG] [bertiniRefineSols, TrackTolDuringEG] [bertiniRefineSols, FinalTol] [bertiniRefineSols, MaxNorm] [bertiniRefineSols, MinStepSizeBeforeEG] [bertiniRefineSols, MinStepSizeDuringEG] [bertiniRefineSols, ImagThreshold] [bertiniRefineSols, CoeffBound] [bertiniRefineSols, DegreeBound] [bertiniRefineSols, CondNumThreshold] [bertiniRefineSols, RandomSeed] [bertiniRefineSols, SingValZeroTol] [bertiniRefineSols, EndGameNum] [bertiniRefineSols, UseRegeneration] [bertiniRefineSols, SecurityLevel] [bertiniRefineSols, ScreenOut] [bertiniRefineSols, OutputLevel] [bertiniRefineSols, StepsForIncrease] [bertiniRefineSols, MaxNewtonIts] [bertiniRefineSols, MaxStepSize] [bertiniRefineSols, MaxNumberSteps] [bertiniRefineSols, MaxCycleNum] [bertiniRefineSols, RegenStartLevel] [bertiniSample, MPType] [bertiniSample, PRECISION] [bertiniSample, ODEPredictor] [bertiniSample, TrackTolBeforeEG] [bertiniSample, TrackTolDuringEG] [bertiniSample, FinalTol] [bertiniSample, MaxNorm] [bertiniSample, MinStepSizeBeforeEG] [bertiniSample, MinStepSizeDuringEG] [bertiniSample, ImagThreshold] [bertiniSample, CoeffBound] [bertiniSample, DegreeBound] [bertiniSample, CondNumThreshold] [bertiniSample, RandomSeed] [bertiniSample, SingValZeroTol] [bertiniSample, EndGameNum] [bertiniSample, UseRegeneration] [bertiniSample, SecurityLevel] [bertiniSample, ScreenOut] [bertiniSample, OutputLevel] [bertiniSample, StepsForIncrease] [bertiniSample, MaxNewtonIts] [bertiniSample, MaxStepSize] [bertiniSample, MaxNumberSteps] [bertiniSample, MaxCycleNum] [bertiniSample, RegenStartLevel] [bertiniTrackHomotopy, MPType] [bertiniTrackHomotopy, PRECISION] [bertiniTrackHomotopy, ODEPredictor] [bertiniTrackHomotopy, TrackTolBeforeEG] [bertiniTrackHomotopy, TrackTolDuringEG] [bertiniTrackHomotopy, FinalTol] [bertiniTrackHomotopy, MaxNorm] [bertiniTrackHomotopy, MinStepSizeBeforeEG] [bertiniTrackHomotopy, MinStepSizeDuringEG] [bertiniTrackHomotopy, ImagThreshold] [bertiniTrackHomotopy, CoeffBound] [bertiniTrackHomotopy, DegreeBound] [bertiniTrackHomotopy, CondNumThreshold] [bertiniTrackHomotopy, RandomSeed] [bertiniTrackHomotopy, SingValZeroTol] [bertiniTrackHomotopy, EndGameNum] [bertiniTrackHomotopy, UseRegeneration] [bertiniTrackHomotopy, SecurityLevel] [bertiniTrackHomotopy, ScreenOut] [bertiniTrackHomotopy, OutputLevel] [bertiniTrackHomotopy, StepsForIncrease] [bertiniTrackHomotopy, MaxNewtonIts] [bertiniTrackHomotopy, MaxStepSize] [bertiniTrackHomotopy, MaxNumberSteps] [bertiniTrackHomotopy, MaxCycleNum] [bertiniTrackHomotopy, RegenStartLevel] [bertiniUserHomotopy,CoeffBound] [bertiniUserHomotopy,CondNumThreshold] [bertiniUserHomotopy,DegreeBound] [bertiniUserHomotopy,EndGameNum] [bertiniUserHomotopy,FinalTol] [bertiniUserHomotopy,ImagThreshold] [bertiniUserHomotopy,MaxCycleNum] [bertiniUserHomotopy,MaxNewtonIts] [bertiniUserHomotopy,MaxNorm] [bertiniUserHomotopy,MaxNumberSteps] [bertiniUserHomotopy,MaxStepSize] [bertiniUserHomotopy,MinStepSizeBeforeEG] [bertiniUserHomotopy,MinStepSizeDuringEG] [bertiniUserHomotopy,MPType] [bertiniUserHomotopy,ODEPredictor] [bertiniUserHomotopy,OutputLevel] [bertiniUserHomotopy,PRECISION] [bertiniUserHomotopy,RandomSeed] [bertiniUserHomotopy,RegenStartLevel] [bertiniUserHomotopy,ScreenOut] [bertiniUserHomotopy,SecurityLevel] [bertiniUserHomotopy,SingValZeroTol] [bertiniUserHomotopy,StepsForIncrease] [bertiniUserHomotopy,TrackTolBeforeEG] [bertiniUserHomotopy,TrackTolDuringEG] [bertiniUserHomotopy,UseRegeneration] [bertiniZeroDimSolve, MPType] [bertiniZeroDimSolve, PRECISION] [bertiniZeroDimSolve, ODEPredictor] [bertiniZeroDimSolve, TrackTolBeforeEG] [bertiniZeroDimSolve, TrackTolDuringEG] [bertiniZeroDimSolve, FinalTol] [bertiniZeroDimSolve, MaxNorm] [bertiniZeroDimSolve, MinStepSizeBeforeEG] [bertiniZeroDimSolve, MinStepSizeDuringEG] [bertiniZeroDimSolve, ImagThreshold] [bertiniZeroDimSolve, CoeffBound] [bertiniZeroDimSolve, DegreeBound] [bertiniZeroDimSolve, CondNumThreshold] [bertiniZeroDimSolve, RandomSeed] [bertiniZeroDimSolve, SingValZeroTol] [bertiniZeroDimSolve, EndGameNum] [bertiniZeroDimSolve, UseRegeneration] [bertiniZeroDimSolve, SecurityLevel] [bertiniZeroDimSolve, ScreenOut] [bertiniZeroDimSolve, OutputLevel] [bertiniZeroDimSolve, StepsForIncrease] [bertiniZeroDimSolve, MaxNewtonIts] [bertiniZeroDimSolve, MaxStepSize] [bertiniZeroDimSolve, MaxNumberSteps] [bertiniZeroDimSolve, MaxCycleNum] [bertiniZeroDimSolve, RegenStartLevel] ------------------- -------Types------- ------------------- ------------------- ---EXPERIMENTAL------ ------------------- doc /// Key StartFileDirectory InputFileDirectory StartParameterFileDirectory NumSolBound OrderPaths NumberOfLoops BranchPoints SpecifyLoops SaveData ListB'Sections TextScripts PreparePH2 SpecifyDim MonodromyStartPoints PathNumber TestSolutions SpecifyComponent ContainsMultiProjectivePoint UseStartPointsFirst MonodromyStartParameters B'Exe calculateB'Trace makeB'TraceInput importSliceFile (calculateB'Trace,String) (importSliceFile,String) -- storeBM2Files [b'PHMonodromyCollect,NumSolBound] (makeB'TraceInput,String,Number,Number) [makeB'InputFile,PathVariable] [makeB'InputFile,VariableList] [makeMembershipFile,TestSolutions] [makeMembershipFile,M2Precision] [valueBM2,M2Precision] [NumberToB'String,M2Precision] [makeSampleSolutionsFile,SpecifyComponent] [b'PHMonodromyCollect,B'Exe] [b'PHMonodromyCollect,MonodromyStartParameters] [b'PHMonodromyCollect,MonodromyStartPoints] [b'PHMonodromyCollect,NumberOfLoops] [b'PHMonodromyCollect,SaveData] [b'PHMonodromyCollect,SpecifyLoops] [runBertini,PreparePH2] [runBertini,TextScripts] [importSolutionsFile,OrderPaths] [importSolutionsFile,M2Precision] [importParameterFile,M2Precision] [writeParameterFile,M2Precision] [importMainDataFile,SpecifyDim] [importMainDataFile,M2Precision] [b'PHSequence,B'Exe] [b'PHSequence,SaveData] [makeWitnessSetFiles,SpecifyComponent] [writeStartFile,M2Precision] [b'PHGaloisGroup,LoopRadius] [b'TraceTestImage,MapPoints] [moveB'File,MoveToDirectory] [b'TraceTestImage,OnlyCalculateTrace] [b'TraceTestImage,RandomGamma] [b'PHGaloisGroup,ReturnGaloisGroupGeneratorFile] [subPoint,SpecifyVariables] [b'TraceTestImage,StartParameters] [b'TraceTestImage,StartPoints] [b'TraceTestImage,StopBeforeTest] [b'PHGaloisGroup,StorageFolder] [b'PHMonodromyCollect,StorageFolder] [b'PHSequence,StorageFolder] [importIncidenceMatrix,StorageFolder] [importParameterFile,StorageFolder] [importSolutionsFile,StorageFolder] [makeB'InputFile,StorageFolder] [makeMembershipFile,StorageFolder] [makeSampleSolutionsFile,StorageFolder] [makeWitnessSetFiles,StorageFolder] [runBertini,StorageFolder] [writeParameterFile,StorageFolder] [writeStartFile,StorageFolder] [b'TraceTestImage,SubFolder] [moveB'File,SubFolder] [b'TraceTestImage,SubIntoCC] [subPoint,SubIntoCC] [subPoint,M2Precision] [b'TraceTestImage,B'Exe] [b'TraceTestImage,M2Precision] [b'PHGaloisGroup,B'Exe] [b'PHGaloisGroup,BranchPoints] [b'PHGaloisGroup,MonodromyStartParameters] [b'PHGaloisGroup,MonodromyStartPoints] [b'PHGaloisGroup,NumberOfLoops] [b'PHGaloisGroup,SaveData] [b'PHGaloisGroup,M2Precision] [bertiniImageMonodromyCollect,AffVariableGroup] [bertiniUserHomotopy,AffVariableGroup] [bertiniUserHomotopy,BertiniInputConfiguration] [bertiniImageMonodromyCollect,B'Constants] [bertiniUserHomotopy,B'Constants] [bertiniImageMonodromyCollect,B'Functions] [bertiniUserHomotopy,B'Functions] [bertiniImageMonodromyCollect,ContinueLoop] [bertiniImageMonodromyCollect,EquivalentCoordinates] [bertiniImageMonodromyCollect,GeneralCoordinate] [bertiniImageMonodromyCollect,ImageCoordinates] [bertiniImageMonodromyCollect,M2Precision] [bertiniUserHomotopy,M2Precision] [bertiniImageMonodromyCollect,NameB'InputFile] [bertiniImageMonodromyCollect,NameParameterFile] [bertiniImageMonodromyCollect,NameSolutionsFile] [bertiniImageMonodromyCollect,OnlyMoveParameters] [bertiniUserHomotopy,OutputStyle] [bertiniImageMonodromyCollect,PrintMidStatus] [bertiniUserHomotopy,RandomReal] [bertiniImageMonodromyCollect,ReturnPoints] [makeB'InputFile,SetParameterGroup] [bertiniUserHomotopy,TopDirectory] [bertiniImageMonodromyCollect,B'Exe] [bertiniImageMonodromyCollect,MonodromyStartParameters] [bertiniImageMonodromyCollect,MonodromyStartPoints] [bertiniImageMonodromyCollect,NameStartFile] [bertiniImageMonodromyCollect,NumberOfLoops] [bertiniImageMonodromyCollect,NumSolBound] [bertiniImageMonodromyCollect,SaveData] [bertiniImageMonodromyCollect,SpecifyLoops] [bertiniImageMonodromyCollect,StorageFolder] [bertiniImageMonodromyCollect,Verbose] [bertiniUserHomotopy,HomVariableGroup] [bertiniUserHomotopy,RandomComplex] Headline This option or key is for a function that is in active development. Description Text The Bertini.m2 package is in active development for version 2 to provide additional functionality. This option is for a function in version 2. For more information contact Jose Israel Rodriguez at JoIsRo[AT]UChicago.edu. ///; end--ENDFILE -- to be added in another version doc /// Key bertiniSegmentHomotopy (bertiniSegmentHomotopy,List, List, List) Headline constructs and tracks a straight-line homotopy Usage S0 = bertiniSegmentHomotopy() Inputs start:List start system, list of polynomial equations tar:List target system, list of polynomial equations S1:List start solutions (solutions of start system when t=1) Outputs S0:List target solutions (solutions of target system when t=0) Description Text Constructs and tracks a straight line homotopy from the start system to the target system. Example R=CC[x,y] start={x^3-1, y^3-1} tar={x^3+y^3-4,x^3+2*y-1} --input start system, target system, list of start points bertiniSegmentHomotopy( start,tar,{{1,1},{-.5-0.86603*ii,1},{1,-0.5+0.86603*ii}}) ///; doc /// Key importPoints (importPoints,String,ZZ) Headline importPoints reads solutions from a Bertini solution file to store as points in M2 Usage S=importPoints(l,n) Inputs l: String A string giving the location of a Bertini solution file. n: ZZ Number of coordinates for each solution. Outputs S: List of solutions of type Point Description Text This method imports points from a solution file that Bertini created while solving a zero-dimensional system. The string l is a path which gives the location of the solution file and n is an integer stating the desired number of coordinates for each solution. When solving a zero-dimensional system, Bertini creates several solution files; @TO importPoints@ works with the following Bertini solution files: "finite_solutions", "nonsingular-solutions", "real_finite_solutions", "singular_solutions". -- The output is a list of points. The user can specify which solutions to read from the file using the @TO SpecifyPoints@ option or which coordinates to select using the @TO SpecifyCoordinates@ option. -- Example --locationOfSolutionFile="/Users/.../YourFolder/solution_file"; -- A=importPoints(locationOfSolutionFile,4) --The output would be a list of points that have 4 coordinates. -- Example -- locationOfSolutionFile="/Users/.../YourFolder/solution_file"; -- B=importPoints(locationOfSolutionFile,4,SpecifyPoints=>{0,2}) --The output would be the first and third solutions of the file. -- Example -- locationOfSolutionFile="/Users/.../YourFolder/solution_file"; -- C=importPoints(locationOfSolutionFile,4,SpecifyCoordinates=>{0,1}) --The output would be the first and second coordinate of each solution of the file. --Caveat --The method importPoints will not --For importPoints to be successful, the Bertini solution file must have a particular format. --The first line is an integer, the number of solutions in the. --The next lines consist of a blank line followed by a line for each coordinate; --these lines consist of: RR|"e"|ZZ" "RR|"e"|ZZ for scientific notation of the real and imaginary parts of the coordinate. ///; doc /// Key phPostProcess (phPostProcess,String,List,ZZ) Headline Does post processing parameter homotopy. Usage S=phPostProcess(sIn,L,n) Inputs sIn: String A string giving the directory of the input files. L: List A list of parameters. n: ZZ Number of coordinates in a solution. Description Text The purpose of this function is to allow a person to share their Bertini computations with a second user, who can then analyze the data easily with the Bertini.M2 interface. Instead of doing a parameter run by calling Bertini, the PrintNotes option prints a file titled "notes" located in the input file's directory. If the "notes" file does not exist it returns an error. The output will be a list of points that have 3 coordinates, that are solutions to a parameterized system of equations evaluated at L, found by doing a parameter homotopy. -- Example -- inputFileLocation="/Users/.../YourFolderA"; -- L={.8234+ii*8,9}--A list of two parameter values. -- n=3--A solution has n coordinates. -- phPostProcess(inputFileLocation,L,n) -- Example -- inputFileLocation="/Users/.../YourFolderA"; -- phPostProcess(inputFileLocation,"",{},0,PrintNotes=>1) Caveat Even if Bertini is called but does not run, an error may not be reported if previous solution files were already in the outputDirectory. ///; doc /// Key phMonodromy (phMonodromy,String,ZZ,ZZ) Headline Does a sequence of parameter homotopies. Usage S=phMonodromy(sIn,p,n) Inputs sIn: String A string giving the directory of start files: input, start, start_parameters p: ZZ Number of parameters. n: ZZ Number of coordinates of a point. ///; --ref{} need to add about the option ParameterValues doc /// Key SpecifyPoints [importPoints, SpecifyPoints] Headline optional argument to specify which solutions to import Usage importPoints(...,SpecifyPoints=>List) ///; doc/// Key AffVariableGroup [makeB'InputFile, AffVariableGroup] Headline An option which designates the Affine Variable Groups. Description Text We can group variables together when using zero-dimensional runs in Bertini. Example R=QQ[x1,x2,y] makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{{"MPTYPE",2}}, AffVariableGroup=>{{x1,x2},{y}}, B'Polynomials=>{y*(x1+x2+1)^2+1,x1-x2+1,y-2}); ///; doc /// Key NameIncidenceMatrixFile [importIncidenceMatrix, NameIncidenceMatrixFile] Headline An optional argument to import an incidence matrix that has a different name than "incidence_matrix". Description Text When this option is set to "another_incidence_matrix", a file named "another_incidence_matrix" is imported. The default is "incidence_matrix". ///; doc /// Key NameStartFile [writeStartFile, NameStartFile] Headline An optional argument to write a start file that has a different name than "start". Description Text When this option is set to "another_start_file", a file named "another_start_file" is written. The default is "start". ///; [bertiniComponentMemberTest, MPType], [bertiniComponentMemberTest, PRECISION], [bertiniComponentMemberTest, ODEPredictor], [bertiniComponentMemberTest, TrackTolBeforeEG], [bertiniComponentMemberTest, TrackTolDuringEG], [bertiniComponentMemberTest, FinalTol], [bertiniComponentMemberTest, MaxNorm], [bertiniComponentMemberTest, MinStepSizeBeforeEG], [bertiniComponentMemberTest, MinStepSizeDuringEG], [bertiniComponentMemberTest, ImagThreshold], [bertiniComponentMemberTest, CoeffBound], [bertiniComponentMemberTest, DegreeBound], [bertiniComponentMemberTest, CondNumThreshold], [bertiniComponentMemberTest, RandomSeed], [bertiniComponentMemberTest, SingValZeroTol], [bertiniComponentMemberTest, EndGameNum], [bertiniComponentMemberTest, UseRegeneration], [bertiniComponentMemberTest, SecurityLevel], [bertiniComponentMemberTest, ScreenOut], [bertiniComponentMemberTest, OutputLevel], [bertiniComponentMemberTest, StepsForIncrease], [bertiniComponentMemberTest, MaxNewtonIts], [bertiniComponentMemberTest, MaxStepSize], [bertiniComponentMemberTest, MaxNumberSteps], [bertiniComponentMemberTest, MaxCycleNum], [bertiniComponentMemberTest, RegenStartLevel], [bertiniPosDimSolve, MPType], [bertiniPosDimSolve, PRECISION], [bertiniPosDimSolve, ODEPredictor], [bertiniPosDimSolve, TrackTolBeforeEG], [bertiniPosDimSolve, TrackTolDuringEG], [bertiniPosDimSolve, FinalTol], [bertiniPosDimSolve, MaxNorm], [bertiniPosDimSolve, MinStepSizeBeforeEG], [bertiniPosDimSolve, MinStepSizeDuringEG], [bertiniPosDimSolve, ImagThreshold], [bertiniPosDimSolve, CoeffBound], [bertiniPosDimSolve, DegreeBound], [bertiniPosDimSolve, CondNumThreshold], [bertiniPosDimSolve, RandomSeed], [bertiniPosDimSolve, SingValZeroTol], [bertiniPosDimSolve, EndGameNum], [bertiniPosDimSolve, UseRegeneration], [bertiniPosDimSolve, SecurityLevel], [bertiniPosDimSolve, ScreenOut], [bertiniPosDimSolve, OutputLevel], [bertiniPosDimSolve, StepsForIncrease], [bertiniPosDimSolve, MaxNewtonIts], [bertiniPosDimSolve, MaxStepSize], [bertiniPosDimSolve, MaxNumberSteps], [bertiniPosDimSolve, MaxCycleNum], [bertiniPosDimSolve, RegenStartLevel], [bertiniRefineSols, MPType], [bertiniRefineSols, PRECISION], [bertiniRefineSols, ODEPredictor], [bertiniRefineSols, TrackTolBeforeEG], [bertiniRefineSols, TrackTolDuringEG], [bertiniRefineSols, FinalTol], [bertiniRefineSols, MaxNorm], [bertiniRefineSols, MinStepSizeBeforeEG], [bertiniRefineSols, MinStepSizeDuringEG], [bertiniRefineSols, ImagThreshold], [bertiniRefineSols, CoeffBound], [bertiniRefineSols, DegreeBound], [bertiniRefineSols, CondNumThreshold], [bertiniRefineSols, RandomSeed], [bertiniRefineSols, SingValZeroTol], [bertiniRefineSols, EndGameNum], [bertiniRefineSols, UseRegeneration], [bertiniRefineSols, SecurityLevel], [bertiniRefineSols, ScreenOut], [bertiniRefineSols, OutputLevel], [bertiniRefineSols, StepsForIncrease], [bertiniRefineSols, MaxNewtonIts], [bertiniRefineSols, MaxStepSize], [bertiniRefineSols, MaxNumberSteps], [bertiniRefineSols, MaxCycleNum], [bertiniRefineSols, RegenStartLevel], [bertiniSample, MPType], [bertiniSample, PRECISION], [bertiniSample, ODEPredictor], [bertiniSample, TrackTolBeforeEG], [bertiniSample, TrackTolDuringEG], [bertiniSample, FinalTol], [bertiniSample, MaxNorm], [bertiniSample, MinStepSizeBeforeEG], [bertiniSample, MinStepSizeDuringEG], [bertiniSample, ImagThreshold], [bertiniSample, CoeffBound], [bertiniSample, DegreeBound], [bertiniSample, CondNumThreshold], [bertiniSample, RandomSeed], [bertiniSample, SingValZeroTol], [bertiniSample, EndGameNum], [bertiniSample, UseRegeneration], [bertiniSample, SecurityLevel], [bertiniSample, ScreenOut], [bertiniSample, OutputLevel], [bertiniSample, StepsForIncrease], [bertiniSample, MaxNewtonIts], [bertiniSample, MaxStepSize], [bertiniSample, MaxNumberSteps], [bertiniSample, MaxCycleNum], [bertiniSample, RegenStartLevel], [bertiniTrackHomotopy, MPType], [bertiniTrackHomotopy, PRECISION], [bertiniTrackHomotopy, ODEPredictor], [bertiniTrackHomotopy, TrackTolBeforeEG], [bertiniTrackHomotopy, TrackTolDuringEG], [bertiniTrackHomotopy, FinalTol], [bertiniTrackHomotopy, MaxNorm], [bertiniTrackHomotopy, MinStepSizeBeforeEG], [bertiniTrackHomotopy, MinStepSizeDuringEG], [bertiniTrackHomotopy, ImagThreshold], [bertiniTrackHomotopy, CoeffBound], [bertiniTrackHomotopy, DegreeBound], [bertiniTrackHomotopy, CondNumThreshold], [bertiniTrackHomotopy, RandomSeed], [bertiniTrackHomotopy, SingValZeroTol], [bertiniTrackHomotopy, EndGameNum], [bertiniTrackHomotopy, UseRegeneration], [bertiniTrackHomotopy, SecurityLevel], [bertiniTrackHomotopy, ScreenOut], [bertiniTrackHomotopy, OutputLevel], [bertiniTrackHomotopy, StepsForIncrease], [bertiniTrackHomotopy, MaxNewtonIts], [bertiniTrackHomotopy, MaxStepSize], [bertiniTrackHomotopy, MaxNumberSteps], [bertiniTrackHomotopy, MaxCycleNum], [bertiniTrackHomotopy, RegenStartLevel], [bertiniUserHomotopy,CoeffBound], [bertiniUserHomotopy,CondNumThreshold], [bertiniUserHomotopy,DegreeBound], [bertiniUserHomotopy,EndGameNum], [bertiniUserHomotopy,FinalTol], [bertiniUserHomotopy,ImagThreshold], [bertiniUserHomotopy,MaxCycleNum], [bertiniUserHomotopy,MaxNewtonIts], [bertiniUserHomotopy,MaxNorm], [bertiniUserHomotopy,MaxNumberSteps], [bertiniUserHomotopy,MaxStepSize], [bertiniUserHomotopy,MinStepSizeBeforeEG], [bertiniUserHomotopy,MinStepSizeDuringEG], [bertiniUserHomotopy,MPType], [bertiniUserHomotopy,ODEPredictor], [bertiniUserHomotopy,OutputLevel], [bertiniUserHomotopy,PRECISION], [bertiniUserHomotopy,RandomSeed], [bertiniUserHomotopy,RegenStartLevel], [bertiniUserHomotopy,ScreenOut], [bertiniUserHomotopy,SecurityLevel], [bertiniUserHomotopy,SingValZeroTol], [bertiniUserHomotopy,StepsForIncrease], [bertiniUserHomotopy,TrackTolBeforeEG], [bertiniUserHomotopy,TrackTolDuringEG], [bertiniUserHomotopy,UseRegeneration], [bertiniZeroDimSolve, MPType], [bertiniZeroDimSolve, PRECISION], [bertiniZeroDimSolve, ODEPredictor], [bertiniZeroDimSolve, TrackTolBeforeEG], [bertiniZeroDimSolve, TrackTolDuringEG], [bertiniZeroDimSolve, FinalTol], [bertiniZeroDimSolve, MaxNorm], [bertiniZeroDimSolve, MinStepSizeBeforeEG], [bertiniZeroDimSolve, MinStepSizeDuringEG], [bertiniZeroDimSolve, ImagThreshold], [bertiniZeroDimSolve, CoeffBound], [bertiniZeroDimSolve, DegreeBound], [bertiniZeroDimSolve, CondNumThreshold], [bertiniZeroDimSolve, RandomSeed], [bertiniZeroDimSolve, SingValZeroTol], [bertiniZeroDimSolve, EndGameNum], [bertiniZeroDimSolve, UseRegeneration], [bertiniZeroDimSolve, SecurityLevel], [bertiniZeroDimSolve, ScreenOut], [bertiniZeroDimSolve, OutputLevel], [bertiniZeroDimSolve, StepsForIncrease], [bertiniZeroDimSolve, MaxNewtonIts], [bertiniZeroDimSolve, MaxStepSize], [bertiniZeroDimSolve, MaxNumberSteps], [bertiniZeroDimSolve, MaxCycleNum], [bertiniZeroDimSolve, RegenStartLevel] doc /// Key makeWitnessSetFiles (makeWitnessSetFiles,String,Number) Headline This function creates a witness point file and a slice file. Usage makeWitnessSetFiles(theDir,d) Inputs theDir:String The directory where Bertini will store files and the witness_data file and input file are located. d:Number The dimension of the variety that we intersect with the slice defined by the linear system of equations. Description Text This function does a track type 4 Bertini run creating a linear system file. The slice information for a positive dimensional run can be recovered from such a file. Example makeB'InputFile(storeBM2Files, AffVariableGroup=>{x,y,z}, BertiniInputConfiguration=>{{TrackType,1}}, B'Polynomials=>{"(x^2+y^2+z^2-1)*y"}); runBertini(storeBM2Files) makeWitnessSetFiles(storeBM2Files,2)--creats a witness point file for all dimension 2 components and a linear slice file for dimension 2 components. L=importSliceFile(storeBM2Files) -- makeWitnessSetFiles(storeBM2Files,2, NameSolutionsFile=>"custom_name_witness_points",--creates a witness point file with a custom name. SpecifyComponent=>0) --Component indexing begins at 0. The function creates a witness point file for only a particular component. L1=importSliceFile(storeBM2Files) S0=importSolutionsFile(storeBM2Files,NameSolutionsFile=>"custom_name_witness_points") -- makeWitnessSetFiles(storeBM2Files,2, NameSolutionsFile=>"custom_name_witness_points") S=importSolutionsFile(storeBM2Files,NameSolutionsFile=>"custom_name_witness_points") ///;

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