monodromySolve(System,AbstractPoint,List) -- the main function of the MonodromySolver package

Synopsis

• Function: monodromySolve

• Usage:

  (N, npaths) = monodromySolve(PS,p0,L)

• Inputs:
  • PS, an instance of the type System, with parametric coefficients
  • p0, a point, representing a parametrized system
  • L, a list, containing solutions associated to p0, each represented as a AbstractPoint.
• Optional inputs:
  • AugmentEdgeCount => ..., default value 0,
  • AugmentGraphFunction => ..., default value null,
  • AugmentNodeCount => ..., default value 0,
  • AugmentNumberOfRepeats => ..., default value null,
  • BatchSize => ..., default value infinity,
  • EdgesSaturated => ..., default value false,
  • Equivalencer (missing documentation) => ..., default value null,
  • FilterCondition (missing documentation) => ..., default value null,
  • GraphInitFunction => ..., default value completeGraphInit,
  • new tracking routine
  • NumberOfEdges => ..., default value null,
  • NumberOfNodes => ..., default value null,
  • NumberOfRepeats => ..., default value 10,
  • PointArrayTol (missing documentation) => ..., default value .0001,
  • Potential => ..., default value null,
  • Randomizer (missing documentation) => ..., default value null,
  • SelectEdgeAndDirection => ..., default value selectFirstEdgeAndDirection,
  • StoppingCriterion => ..., default value null,
  • TargetSolutionCount => ..., default value null,
  • Verbose => ..., default value false,
• Outputs:
  • N, an instance of the type HomotopyNode,
  • npaths, an integer, reporting the number of paths tracked.

Description

i1 : setRandomSeed 0;

i2 : S = CC[a,b,c];

i3 : R = S[x,w];

i4 : (h, f) = (a*x+b*w+c, 3*x^2 - w + 1);

i5 : x0 = point {{ii_CC,-2}}; -- clearly a zero of f

i6 : l = apply(2,i->random CC);

i7 : p0 = point({append(l,- sum apply(l, x0.Coordinates,(i,x)->i*x))});

i8 : (N, npaths) = monodromySolve(polySystem {h,f},p0,{x0},NumberOfNodes=>3);