bertiniZeroDimSolve -- a main method to solve a zero-dimensional system of equations

Synopsis

• Usage:

  S = bertiniZeroDimSolve F

  S = bertiniZeroDimSolve I

  S = bertiniZeroDimSolve(I, UseRegeneration=>1)

• Inputs:
  • F, a list, a list of ring elements (system need not be square)
  • I, an ideal, an ideal defining a variety
• Optional inputs:
  • AffVariableGroup => ..., default value {}, an option to group variables and use multihomogeneous homotopies
  • B'Constants => ..., default value {}, an option to designate the constants for a Bertini Input file
  • B'Functions (missing documentation) => ..., default value {},
  • BertiniInputConfiguration (missing documentation) => ..., default value {},
  • HomVariableGroup => ..., default value {}, an option to group variables and use multihomogeneous homotopies
  • IsProjective (missing documentation) => ..., default value -1,
  • M2Precision (missing documentation) => ..., default value 53,
  • NameMainDataFile (missing documentation) => ..., default value main_data,
  • NameSolutionsFile (missing documentation) => ..., default value raw_solutions,
  • OutputStyle (missing documentation) => ..., default value OutPoints,
  • RandomComplex => ..., default value {}, an option which designates symbols/strings/variables that will be set to be a random real number or random complex number
  • RandomReal => ..., default value {}, an option which designates symbols/strings/variables that will be set to be a random real number or random complex number
  • TopDirectory => ..., default value /tmp/M2-42289-0/0, Option to change directory for file storage.
  • UseRegeneration (missing documentation) => ..., default value -1,
  • Verbose => ..., default value false, Option to silence additional output
• Outputs:
  • S, a list, a list of points that are contained in the variety of F

Description

i1 : R = CC[x,y];

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

i3 : S = bertiniZeroDimSolve F

o3 = {{1, 1.41421}, {1, -1.41421}, {-1, 1.41421}, {-1, -1.41421}}

o3 : List

i4 : peek S_0

o4 = Point{AccuracyEst => 3.4703e-13         }
           AccuracyEstInternal => 5.71549e-14
           ConditionNumber => 2.40039
           Coordinates => {1, 1.41421}
           CycleNumber => 1
           FinalTValue => .000390625
           FunctionResidual => 7.85046e-17
           MaxPrecisionUtilized => 52
           Multiplicity => 1
           NewtonResidual => 2.48129e-18
           PathNumber => 0
           PathsWithSameEndpoint => {}
           PrecisionIncreased => 0
           SolutionNumber => 0

i5 : R = CC[x];

i6 : F = {x^2*(x-1)};

i7 : S = bertiniZeroDimSolve F

o7 = {{1}, {4.30297e-15+1.81764e-15*ii}}

o7 : List

i8 : B = bertiniZeroDimSolve(F,UseRegeneration=>1)

o8 = {{1}}

o8 : List