bertiniComponentMemberTest -- test whether points lie on a given variety

Synopsis

• Usage:

  L = bertiniComponentMemberTest (pts, NV)

• Inputs:

  • pts, a list, points to test
  • NV, a numerical variety
• Optional inputs:

  • CoeffBound => ...,
  • CondNumThreshold => ...,
  • DegreeBound => ...,
  • EndGameNum => ...,
  • FinalTol => ...,
  • ImagThreshold => ...,
  • IsProjective => ...,
  • MaxCycleNum => ...,
  • MaxNewtonIts => ...,
  • MaxNorm => ...,
  • MaxNumberSteps => ...,
  • MaxStepSize => ...,
  • MinStepSizeBeforeEG => ...,
  • MinStepSizeDuringEG => ...,
  • MPType => ...,
  • ODEPredictor => ...,
  • OutputLevel => ...,
  • PRECISION => ...,
  • RandomSeed => ...,
  • RegenStartLevel => ...,
  • ScreenOut => ...,
  • SecurityLevel => ...,
  • SingValZeroTol => ...,
  • StepsForIncrease => ...,
  • TrackTolBeforeEG => ...,
  • TrackTolDuringEG => ...,
  • UseRegeneration => ...,
  • Verbose => ...,
• Outputs:

  • L, a list, entries are lists of witness sets containing the test point
• Consequences:

  • Writes the witness set information of NV and the test points to temporary files

  • Invokes Bertini’s solver with option TRACKTYPE: 3

  • Stores output of Bertini in temporary file

  • Parses and outputs the solutions

Description

i1 : R = CC[x,y,z];

i2 : F = {(y^2+x^2+z^2-1)*x,(y^2+x^2+z^2-1)*y};

i3 : NV = bertiniPosDimSolve(F)

o3 = NV

o3 : NumericalVariety

i4 : pts = {{0,0,0}} --z-axis

o4 = {{0, 0, 0}}

o4 : List

i5 : bertiniComponentMemberTest(pts, NV)

o5 = {{[dim=1,deg=1]}}

o5 : List

Caveat