Certified -- a value for the option Predictor that triggers certified tracking

Description

Tells basic functions, e.g., track, to use soft certification described in

The code for robust certification is not incorporated in this package at the moment; the location of this stand-alone code is in the references of

The functions related to this paper are:

• randomInitialPair -- a random initial pair
• goodInitialPair -- make an initial pair conjectured to be good by Shub and Smale
• randomSd -- a random homogeneous system of polynomial equations

i1 : R = CC[x,y,z];

i2 : S = {x^2-z^2,y^2-z^2};

i3 : T = {x^2+y^2-z^2, x*y};

i4 : solsS = {(1,-1,1),(1,1,1)};

i5 : track(S,T,solsS,Predictor=>Certified,Normalize=>true)

o5 = {{.00000107266, -.70712, .70712}, {.707125, -1.48993e-7, .707107}}

o5 : List