bertiniRefineSols -- sharpen solutions to a prescribed number of digits

Synopsis

• Usage:

  S = bertiniRefineSols(d, F, l)

• Inputs:

  • d, an integer, number of digits
  • F, a list, whose entries are polynomials (system need not be square)
  • l, a list, whose entries are points to be sharpened
• Optional inputs:

  • 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
  • ImagThreshold => ..., -- options for methods of Bertini package
  • IsProjective => ..., -- optional argument to specify whether to use homogeneous coordinates
  • 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
  • ODEPredictor => ..., -- options for methods of Bertini package
  • OutputLevel => ..., -- options for methods of Bertini package
  • PRECISION => ..., -- options for methods of Bertini package
  • 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
  • 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^2-2,y^2-2};

i3 : sols = bertiniZeroDimSolve (F)
~/bertini

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

o3 : List

i4 : S = bertiniRefineSols (100, F, sols)
Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74635-0/1

The version of Bertini 
            you have installed on your computer 
            was used for this run. 
Bertini is under ongoing development by 
            D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.


o4 = {{-1.41421, -1.41421}, {-1.41421, 1.41421}, {1.41421, -1.41421},
     ------------------------------------------------------------------------
     {1.41421, 1.41421}}

o4 : List

i5 : coords = coordinates S_0

o5 = {-1.41421, -1.41421}

o5 : List

i6 : coords_0

o6 = -1.414213562373095048801688724209698078569671875376948073176679737990732
     478462107038850387534327641573+
     3.6293375664295463502309100705738928639868367720161625941979072156736995
     19815048438950614193310022977e-316*ii

o6 : CC (of precision 333)

Caveat