bertiniZeroDimSolve -- solve zero-dimensional system of equations

Synopsis

• Usage:

  S = bertiniZeroDimSolve F

• Inputs:

  • F, a list, whose entries are polynomials (system need not be square)
• Optional inputs:

  • 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.
  • CoeffBound => ..., -- options for methods of Bertini package
  • CondNumThreshold => ..., -- options for methods of Bertini package
  • DegreeBound => ..., -- options for methods of Bertini package
  • EndGameNum => ..., -- options for methods of Bertini package
  • FinalTol => ..., -- options for methods of Bertini package
  • HomVariableGroup => ..., -- See help for bertiniParameterHomotopy and/or makeB'InputFile.
  • ImagThreshold => ..., -- options for methods of Bertini package
  • M2Precision => ..., -- Option to change the precision Macaulay2 uses to import the files.
  • MaxCycleNum => ..., -- options for methods of Bertini package
  • MaxNewtonIts => ..., -- options for methods of Bertini package
  • MaxNorm => ..., -- options for methods of Bertini package
  • MaxNumberSteps => ..., -- options for methods of Bertini package
  • MaxStepSize => ..., -- options for methods of Bertini package
  • MinStepSizeBeforeEG => ..., -- options for methods of Bertini package
  • MinStepSizeDuringEG => ..., -- options for methods of Bertini package
  • MPType => ..., -- options for methods of Bertini package
  • NameMainDataFile => ..., -- 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.
  • ODEPredictor => ..., -- options for methods of Bertini package
  • OutputLevel => ..., -- options for methods of Bertini package
  • OutputSyle => ..., -- Used to change the output style.
  • PRECISION => ..., -- options for methods of Bertini package
  • RandomComplex => ..., -- 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.
  • RandomSeed => ..., -- options for methods of Bertini package
  • RegenStartLevel => ..., -- options for methods of Bertini package
  • ScreenOut => ..., -- options for methods of Bertini package
  • SecurityLevel => ..., -- options for methods of Bertini package
  • SingValZeroTol => ..., -- options for methods of Bertini package
  • StepsForIncrease => ..., -- options for methods of Bertini package
  • TopDirectory => ..., -- Option to change directory for file storage.
  • TrackTolBeforeEG => ..., -- options for methods of Bertini package
  • TrackTolDuringEG => ..., -- options for methods of Bertini package
  • UseRegeneration => ..., -- options for methods of Bertini package
  • Verbose => ..., -- Option to silence additional output
• Outputs:

  • S, a list, of solutions of type Point

Description

i1 : R = CC[x,y];

i2 : F = {x^2-1,y^2-1};

i3 : S = bertiniZeroDimSolve F
~/bertini

o3 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}

o3 : List

i4 : peek S_0

o4 = Point{AccuracyEst => 3.09883e-16     }
           AccuracyEstInternal => 0
           ConditionNumber => 2.80882
           Coordinates => {1, 1}
           CycleNumber => 1
           FinalTValue => .0015625
           FunctionResidual => 5.55112e-17
           MaxPrecisionUtilized => 52
           Multiplicity => 1
           NewtonResidual => 3.58271e-17
           PathNumber => 0
           PathsWithSameEndpoint => {}
           PrecisionIncreased => 0
           SolutionNumber => 1

Caveat