sparseMonodromySolve -- an "out of the box" polynomial system solver

Synopsis

• Usage:

  sols = sparseMonodromySolve PS

• Inputs:
  • PS, an instance of the type System, whose coefficients are complex numbers
• 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:
  • sols, a list, containing solutions to sys, each represented as a Point.

Description

i1 : setRandomSeed 2021;

i2 : R=CC[x,y,z];

i3 : F=random(3,R);
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)

i4 : P=sum apply(gens R,g->diff(g,F)*random CC);

i5 : PS = polySystem {F,P,random(1,R)-1};

i6 : sols = sparseMonodromySolve PS;

i7 : length points sols

o7 = 6

i8 : for i from 0 to 5 list norm evaluate(PS, sols#i)

o8 = {3.87307e-15, 1.06167e-14, 2.22045e-16, 9.15513e-16, 2.78384e-13,
     ------------------------------------------------------------------------
     2.83052e-16}

o8 : List