solveFamily -- a solver for parametric families with simple output

Synopsis

• Usage:

  (p, sols) = solveFamily PS

  (p, sols) = solveFamily(p, P)

• Inputs:
  • PS, an instance of the type System, : a parametric polynomial system, represented as either a PolySystem whose underlying coefficient ring itself a polynomial ring in the parameters, or a GateSystem with parameters.
  • p, a point, consisting of target parameter values (optional.)
• 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 => ..., default value null,
  • FilterCondition => ..., 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 => ..., default value null,
  • SelectEdgeAndDirection => ..., default value selectFirstEdgeAndDirection,
  • StoppingCriterion => ..., default value null,
  • TargetSolutionCount => ..., default value null,
  • Verbose => ..., default value false,
• Outputs:
  • p, an instance of the type Point, parameter values. If not part of the input, they are chosen uniformly as complex numbers w/ modulus 1.
  • sols, an instance of the type PointArray, containing solutions to PS specialized at p.

Description

i1 : setRandomSeed 0

o1 = 0

i2 : R = CC[a,b,c,d,e,f][x,y];

i3 : q  = a*x^2+b*y+c;

i4 : l = d*x+e*y+f;

i5 : (sys, sols) = solveFamily(polySystem{q,l}, NumberOfNodes=>3)

o5 = (sys, {{1.7698-.292574*ii, 2.03236+1.25703*ii}, PointArray( 2 points: 1
     ------------------------------------------------------------------------
     0 ), {-.770087+.316588*ii, .35355-.743892*ii}})

o5 : Sequence

Caveat