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

Synopsis

Function: monodromySolve
Optional inputs:
- AugmentEdgeCount => ...,
- AugmentGraphFunction => ...,
- AugmentNodeCount => ...,
- AugmentNumberOfRepeats => ...,
- BatchSize => ...,
- EdgesSaturated => ...,
- GraphInitFunction => ...,
- new tracking routine
- NumberOfEdges => ...,
- NumberOfNodes => ...,
- NumberOfRepeats => ...,
- Potential => ...,
- SelectEdgeAndDirection => ...,
- StoppingCriterion => ...,
- TargetSolutionCount => ...,
- Verbose => ...,

Description

This blackbox solver is similar in usage to sparseMonodromySolve, but with "technical" output.

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 => {-.971549+.236839*ii, .157598-.987503*ii, .841103-.540875*ii, -.396553+.918012*ii}                                                                                                                         }
                  Edges => MutableList{...8...}
                  Graph => HomotopyGraph{...5...}
                  PartialSols => {PointArray( 4 points: 0 3 1 2 ), {-.555644-.83142*ii, .002423+.999997*ii}, {.83142-.555644*ii, .999997-.002423*ii}, {.555644+.83142*ii, -.002423-.999997*ii}, {-.83142+.555644*ii, -.999997+.002423*ii}}

                                                                 2                          2
                  SpecializedSystem => {(- .971549 + .236839*ii)A  + (.157598 - .987503*ii)B , (.841103 - .540875*ii)A*B - .396553 + .918012*ii}