createSeedPair -- create initial seed for the homotopy continuation

Synopsis

• Usage:

  (p0,x0) = createSeedPair PS

  (p0, x0) = createSeedPair(PS,x0)

• Inputs:
  • PS, an instance of the type System, a parametric polynomial system
  • x0, a point, an initial solution for some system
• Optional inputs:
  • affinity tolerance
  • initial parameters
  • Verbose (missing documentation) => ..., default value false,
• Outputs:
  • p0, an instance of the type Point, representing a random system
  • x0, an instance of the type Point, representing a solution to the system defined by p0

Description

i1 : setRandomSeed 0

o1 = 0

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

i3 : polys = polySystem {a*x+b*y^2,c*x*y+d};

i4 : (p0,x0) := createSeedPair polys;

i5 : polys0=specializeSystem(p0,polys);

i6 : apply(polys0,p->sub(p,{x=>first x0.Coordinates,y=>last x0.Coordinates}))

o6 = {-5.55112e-17, -5.55112e-17-1.66533e-16*ii}

o6 : List

See also

• monodromySolve(System,AbstractPoint,List) -- the main function of the MonodromySolver package