dynamicFlowerSolve -- a naive dynamic strategy

Synopsis

• Usage:

  (L, npaths) = dynamicFlowerSolve(M,p0,L)

• Inputs:
  • M, a matrix, defining polynomial system
  • p0, a point, associated to a specialized system
  • L, a list, containing partial solutions associated to p0
• Optional inputs:
  • RandomPointFunction (missing documentation) => ..., default value null,
  • StoppingCriterion => ..., default value FunctionClosure[../../../../../Macaulay2/packages/MonodromySolver/solveViaMonodromy.m2:110:110-110:120],
  • TargetSolutionCount (missing documentation) => ..., default value null,
• Outputs:
  • L, a list,
  • npaths, an integer,

Description

i1 : R = CC[a,b,c,d][x,y];

i2 : polys = polySystem {a*x+b*y^2,c*x*y+d};

i3 : (p0, x0) = createSeedPair polys;

i4 : (L, npaths) = dynamicFlowerSolve(polys.PolyMap,p0,{x0})
 -- .00246968s elapsed
 -- .00258483s elapsed
 -- .000337096s elapsed
 -- .00274274s elapsed
 -- .0182799s elapsed
 -- .000271589s elapsed
 -- .00274029s elapsed
 -- .00297943s elapsed
 -- .00027106s elapsed
 -- .00276883s elapsed
 -- .00304103s elapsed
 -- .000272905s elapsed
--backup directory created: /tmp/M2-2653117-0/1
  H01: 1
  H10: 1
number of paths tracked: 2
found 1 points in the fiber so far
  H01: 1
  H10: 1
number of paths tracked: 4
found 1 points in the fiber so far
  H01: 1
  H10: 1
number of paths tracked: 6
found 1 points in the fiber so far
  H01: 1
  H10: 1
number of paths tracked: 8
found 1 points in the fiber so far

o4 = ({{.892712+.673395*ii, .29398+.632944*ii}}, 8)

o4 : Sequence