monodromySolve(System) -- the main function of the MonodromySolver package

Synopsis

• Function: monodromySolve
• 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,

Description

i1 : R = CC[a,b,c,d][A,B]

o1 = R

o1 : PolynomialRing

i2 : polys = polySystem {A^2*a+B^2*b,A*B*c+d}

o2 = polys

o2 : PolySystem

i3 : setRandomSeed 0;

i4 : (V,npaths) = monodromySolve(polys, NumberOfNodes => 3);

i5 : peek V

o5 = HomotopyNode{BasePoint => {-.78761-.616174*ii, .976163-.21704*ii, -.416188-.909278*ii, .85817-.513365*ii}                                                                                                                               }
                  Edges => MutableList{...8...}
                  Graph => HomotopyGraph{...12...}
                  PartialSolBins => {PointArray( 4 points: 3 0 2 1 ), {.48801-.872838*ii, .814076-.580758*ii}, {-.872838-.48801*ii, .580758+.814076*ii}, {-.48801+.872838*ii, -.814076+.580758*ii}, {.872838+.48801*ii, -.580758-.814076*ii}}

                  PartialSols => {PointArray( 4 points: 0 1 3 2 ), {.48801-.872838*ii, .814076-.580758*ii}, {-.872838-.48801*ii, .580758+.814076*ii}, {-.48801+.872838*ii, -.814076+.580758*ii}, {.872838+.48801*ii, -.580758-.814076*ii}}

                  Position => 2
                                                                2                         2
                  SpecializedSystem => {(- .78761 - .616174*ii)A  + (.976163 - .21704*ii)B , (- .416188 - .909278*ii)A*B + .85817 - .513365*ii}