goodInitialPair(List) -- make an initial pair conjectured to be good by Shub and Smale

• Function: goodInitialPair

• Usage:

  (S,sol) = goodInitialPair T

• Inputs:
  • T, a list, contains homogeneous polynomials
• Optional inputs:
  • GeneralPosition => ..., default value false, make a random unitary change of coordinates
• Outputs:
  • S, contains homogeneous polynomials
  • sol, contains one solution of S

i1 : T = randomSd {2,3};

i2 : (S,solsS) = goodInitialPair T

                                 2
o2 = ({1.41421x1*x3, 1.73205x2*x3 }, {{0, 0, 1}})

o2 : Sequence

i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{.751732+.463283*ii, .284351-.0717164*ii, .348144-.114302*ii}}

o3 : List