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

Synopsis

• Usage:

  (S,sol) = goodInitialPair T

• Function: goodInitialPair
• 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

Description

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 = {{-.17574+.352468*ii, -.00349993+.0501918*ii, .906419+.144064*ii}}

o3 : List

See also

• Certified -- a value for the option Predictor that triggers certified tracking
• track -- track a user homotopy