next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Bertini :: Bertini

Bertini -- software for numerical algebraic geometry

Description

Interfaces the functionality of the software Bertini to solve polynomial systems and perform calculations in numerical algebraic geometry. The software is available at http://bertini.nd.edu/. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.

The user may place the executable program bertini in the executation path. Alternatively, the path to the executable needs to be specified, for instance,

i1 : needsPackage("Bertini", Configuration=>{"BERTINIexecutable"=>"/folder/subfolder/bertini"})

o1 = Bertini

o1 : Package

Below is a simple example using the most popular function, a basic zero-dimensional solve with no special options.

i2 : R = CC[x,y]

o2 = R

o2 : PolynomialRing
i3 : F = {x^2-1,y^2-1}

       2       2
o3 = {x  - 1, y  - 1}

o3 : List
i4 : solns = bertiniZeroDimSolve(F)

o4 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}

o4 : List

Authors

Version

This documentation describes version 2.1.2.3 of Bertini.

Source code

The source code from which this documentation is derived is in the file Bertini.m2. The auxiliary files accompanying it are in the directory Bertini/.

Exports

  • Types
    • B'Section -- This is a mutable hash table that gives information about a hyperplane used to slice a numerical variety.
    • B'Slice -- This is a mutable hash table that gives information about a linear space used to slice a numerical variety.
  • Functions and commands
  • Symbols
    • AffVariableGroup -- See help for bertiniParameterHomotopy and/or makeB'InputFile.
    • HomVariableGroup, see AffVariableGroup -- See help for bertiniParameterHomotopy and/or makeB'InputFile.
    • B'Configs -- An option to designate the CONFIG part of a Bertini Input file.
    • B'Constants -- An option to designate the constants for a Bertini Input file.
    • B'Functions -- An option which designates sub-functions or a polynomial system as a straight line program.
    • B'Polynomials -- An option which designates the polynomials that we want to solve.
    • CoeffBound, see Bertini options -- options for methods of Bertini package
    • CondNumThreshold, see Bertini options -- options for methods of Bertini package
    • DegreeBound, see Bertini options -- options for methods of Bertini package
    • EndGameNum, see Bertini options -- options for methods of Bertini package
    • FinalTol, see Bertini options -- options for methods of Bertini package
    • ImagThreshold, see Bertini options -- options for methods of Bertini package
    • MaxCycleNum, see Bertini options -- options for methods of Bertini package
    • MaxNewtonIts, see Bertini options -- options for methods of Bertini package
    • MaxNorm, see Bertini options -- options for methods of Bertini package
    • MaxNumberSteps, see Bertini options -- options for methods of Bertini package
    • MaxStepSize, see Bertini options -- options for methods of Bertini package
    • MinStepSizeBeforeEG, see Bertini options -- options for methods of Bertini package
    • MinStepSizeDuringEG, see Bertini options -- options for methods of Bertini package
    • MPType, see Bertini options -- options for methods of Bertini package
    • ODEPredictor, see Bertini options -- options for methods of Bertini package
    • OutputLevel, see Bertini options -- options for methods of Bertini package
    • PRECISION, see Bertini options -- options for methods of Bertini package
    • RandomSeed, see Bertini options -- options for methods of Bertini package
    • RegenStartLevel, see Bertini options -- options for methods of Bertini package
    • ScreenOut, see Bertini options -- options for methods of Bertini package
    • SecurityLevel, see Bertini options -- options for methods of Bertini package
    • SingValZeroTol, see Bertini options -- options for methods of Bertini package
    • StepsForIncrease, see Bertini options -- options for methods of Bertini package
    • TrackTolBeforeEG, see Bertini options -- options for methods of Bertini package
    • TrackTolDuringEG, see Bertini options -- options for methods of Bertini package
    • UseRegeneration, see Bertini options -- options for methods of Bertini package
    • CopyB'File -- optional argument to specify whether make a copy of the file.
    • IsProjective -- optional argument to specify whether to use homogeneous coordinates
    • M2Precision -- Option to change the precision Macaulay2 uses to import the files.
    • NameB'Slice, see makeB'Slice -- makeB'Slice creates a hash table that represents a linear slice.
    • NameB'InputFile -- This option names the input file.
    • NameParameterFile -- This option names the parameter file.
    • NamePolynomials -- An option which designates the names of the polynomials we want to solve.
    • NameFunctionFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameGaloisGroupGeneratorFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameIncidenceMatrixFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameMainDataFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameSampleSolutionsFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameStartFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameWitnessSliceFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • NameWitnessSolutionsFile, see NameSolutionsFile -- options determine the name of a file to be imported or written.
    • OutputSyle -- Used to change the output style.
    • ParameterGroup -- An option which designates the parameters for a Parameter Homotopy.
    • PrintMidStatus -- Print outputs of intermediate computations.
    • RandomComplex, see RandomReal -- An option which designates symbols/strings/variables that will be set to be a random real number or random complex number.
    • RandomReal -- An option which designates symbols/strings/variables that will be set to be a random real number or random complex number.
    • SolutionFileStyle -- This is to adjust to the different ways Bertini stores solutions.
    • AccuracyEst, see StartFileDirectory -- This option or key is for a function that is in active development.
    • AccuracyEstInternal, see StartFileDirectory -- This option or key is for a function that is in active development.
    • B'Exe, see StartFileDirectory -- This option or key is for a function that is in active development.
    • B'Homogenization, see StartFileDirectory -- This option or key is for a function that is in active development.
    • B'NumberCoefficients, see StartFileDirectory -- This option or key is for a function that is in active development.
    • B'SectionString, see StartFileDirectory -- This option or key is for a function that is in active development.
    • BranchPoints, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ComponentNumber, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ConditionNumTol, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ContainsMultiProjectivePoint, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ContainsPoint, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ContinueLoop, see StartFileDirectory -- This option or key is for a function that is in active development.
    • CycleNumber, see StartFileDirectory -- This option or key is for a function that is in active development.
    • DeflationsNeeded, see StartFileDirectory -- This option or key is for a function that is in active development.
    • Dimension, see StartFileDirectory -- This option or key is for a function that is in active development.
    • EquivalentCoordinates, see StartFileDirectory -- This option or key is for a function that is in active development.
    • FinalTValue, see StartFileDirectory -- This option or key is for a function that is in active development.
    • FunctionResidual, see StartFileDirectory -- This option or key is for a function that is in active development.
    • GeneralCoordinate, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ImageCoordinates, see StartFileDirectory -- This option or key is for a function that is in active development.
    • InputFileDirectory, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ListB'Sections, see StartFileDirectory -- This option or key is for a function that is in active development.
    • LoopRadius, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MapPoints, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MaxPrecisionUtilized, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MonodromyStartParameters, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MonodromyStartPoints, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MoveToDirectory, see StartFileDirectory -- This option or key is for a function that is in active development.
    • MultiplicityTol, see StartFileDirectory -- This option or key is for a function that is in active development.
    • NameB'Section, see StartFileDirectory -- This option or key is for a function that is in active development.
    • NumberOfLoops, see StartFileDirectory -- This option or key is for a function that is in active development.
    • NumSolBound, see StartFileDirectory -- This option or key is for a function that is in active development.
    • OnlyCalculateTrace, see StartFileDirectory -- This option or key is for a function that is in active development.
    • OnlyMoveParameters, see StartFileDirectory -- This option or key is for a function that is in active development.
    • OrderPaths, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ParameterValues, see StartFileDirectory -- This option or key is for a function that is in active development.
    • PathNumber, see StartFileDirectory -- This option or key is for a function that is in active development.
    • PathsWithSameEndpoint, see StartFileDirectory -- This option or key is for a function that is in active development.
    • PathVariable, see StartFileDirectory -- This option or key is for a function that is in active development.
    • PrecisionIncreased, see StartFileDirectory -- This option or key is for a function that is in active development.
    • PreparePH2, see StartFileDirectory -- This option or key is for a function that is in active development.
    • RandomCoefficientGenerator, see StartFileDirectory -- This option or key is for a function that is in active development.
    • RandomGamma, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ReturnGaloisGroupGeneratorFile, see StartFileDirectory -- This option or key is for a function that is in active development.
    • ReturnPoints, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SaveData, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SetParameterGroup, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SolutionType, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SpecifyComponent, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SpecifyDim, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SpecifyLoops, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SpecifyVariables, see StartFileDirectory -- This option or key is for a function that is in active development.
    • StartFileDirectory -- This option or key is for a function that is in active development.
    • StartParameterFileDirectory, see StartFileDirectory -- This option or key is for a function that is in active development.
    • StartParameters, see StartFileDirectory -- This option or key is for a function that is in active development.
    • StartPoints, see StartFileDirectory -- This option or key is for a function that is in active development.
    • StopBeforeTest, see StartFileDirectory -- This option or key is for a function that is in active development.
    • StorageFolder, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SubFolder, see StartFileDirectory -- This option or key is for a function that is in active development.
    • SubIntoCC, see StartFileDirectory -- This option or key is for a function that is in active development.
    • TestSolutions, see StartFileDirectory -- This option or key is for a function that is in active development.
    • TextScripts, see StartFileDirectory -- This option or key is for a function that is in active development.
    • UseStartPointsFirst, see StartFileDirectory -- This option or key is for a function that is in active development.
    • VariableList, see StartFileDirectory -- This option or key is for a function that is in active development.
    • TopDirectory -- Option to change directory for file storage.
  • Other things
    • storeBM2Files (missing documentation)