bertiniRefineSols -- sharpen solutions to a prescribed number of digits

Synopsis

• Usage:

  S = bertiniRefineSols(d, F, l)

• Inputs:
  • d, an integer, an integer specifying the number of digits of precision
  • F, a list, a list of polynomials (system need not be square)
  • l, a list, a list of points to be sharpened
• Optional inputs:
  • BertiniInputConfiguration (missing documentation) => ..., default value {},
  • IsProjective => ..., default value -1, optional argument to specify whether to use homogeneous coordinates
  • 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 : sols = 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, F, sols)

o4 = {[RF], [RF], [RF], [RF]}

o4 : List

i5 : coords = coordinates S_0

o5 = {-1.41421, -1.41421}

o5 : List

i6 : coords_0

o6 = -1.41421-2.22045e-16*ii

o6 : CC (of precision 333)