bertiniRefineSols -- sharpen solutions to a prescribed number of digits

Synopsis

• Usage:

  S = bertiniRefineSols(IFD, d, W, OFD)

  S = bertiniRefineSols(d, W, OFD)

  S = bertiniRefineSols(d, W)

• Inputs:
  • IFD, a string, a directory where the input file of a bertiniZeroDim solve is stored along with that runs output files
  • d, an integer, an integer specifying the number of digits of precision
  • W, a list, a list of points to be sharpened
  • OFD, a string, a directory where the output files of the refinement are stored
• Optional inputs:
  • AdditionalFiles (missing documentation) => ..., default value {},
  • IsProjective => ..., default value -1, optional argument to specify whether to use homogeneous coordinates
  • NameB'InputFile (missing documentation) => ..., default value "input",
  • Verbose => ..., default value false, Option to silence additional output
• Outputs:
  • S, a list, a list of solutions of type Point

Description

i1 : R = CC[x,y];

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

i3 : W = bertiniZeroDimSolve (F)

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

o3 : List

i4 : S = bertiniRefineSols (100,W)

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 = 1.4142135623730950488016887242096980785696718753769480731766797379907324
     78462107038850387534327641573

o6 : CC (of precision 333)