endGameCauchy -- Cauchy end game for getting a better approximation of a singular solution

Synopsis

• Usage:

  endGameCauchy(H,t'end,p0)

  endGameCauchy(H,t'end,points)

• Inputs:
  • H, an instance of the type GateHomotopy
  • t'end, a number
  • p0, a point
  • points, a mutable matrix
• Optional inputs:
  • backtrack factor
  • CorrectorTolerance => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • EndZoneFactor => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • InfinityThreshold => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • maxCorrSteps => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • number of vertices
  • numberSuccessesBeforeIncrease => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • stepIncreaseFactor => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • tStep => ..., default value null, options for core functions of Numerical Algebraic Geometry
  • tStepMin => ..., default value null, options for core functions of Numerical Algebraic Geometry

Description

i1 : CC[x,y]

o1 = CC  [x..y]
       53

o1 : PolynomialRing

i2 : T = {(x-2)^3,y-x+x^2-x^3}

       3     2               3    2
o2 = {x  - 6x  + 12x - 8, - x  + x  - x + y}

o2 : List

i3 : sols = solveSystem(T,PostProcess=>false);

i4 : p0 = first sols;

i5 : peek p0

o5 = Point{Coordinates => {2.01079-.011783*ii, 434.14+1247.66*ii}}
           H => GateHomotopy{...12...}
           LastIncrement => 5.72205e-7
           LastT => .999999
           NumberOfSteps => 26
           SolutionStatus => MinStepFailure

i6 : t'end = 1

o6 = 1

i7 : p = endGameCauchy(p0#"H",t'end,p0)

o7 = p

o7 : Point

See also

• refine -- refine numerical solutions to a system of polynomial equations