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randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has and equal chance of reaching any of the solutions of the target system T.
i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                 2                                           
o2 = ({(- .050754 + .171528*ii)x1  + (- .191599 + .135717*ii)x1*x2 + (.257344
     ------------------------------------------------------------------------
                     2                                             
     + .0540958*ii)x2  + (.241259 - .245949*ii)x1*x3 + (- .084161 +
     ------------------------------------------------------------------------
                                                2                          3
     .0877642*ii)x2*x3 + (.142751 + .11536*ii)x3 , (.118933 + .178191*ii)x1 
     ------------------------------------------------------------------------
                                 2                                  2     
     + (- .483821 - .322924*ii)x1 x2 + (- .125842 + .254709*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                              3                             2               
     .0171403 - .0729154*ii)x2  + (- .331622 - .467784*ii)x1 x3 + (- .514888
     ------------------------------------------------------------------------
                                                     2                 
     + .702033*ii)x1*x2*x3 + (.449525 + .337749*ii)x2 x3 + (- .142618 -
     ------------------------------------------------------------------------
                     2                              2               
     .870347*ii)x1*x3  + (.238762 - .317843*ii)x2*x3  + (.00465552 +
     ------------------------------------------------------------------------
                  3
     .186521*ii)x3 }, {{.121096+.403116*ii, -.154378-.696869*ii,
     ------------------------------------------------------------------------
     .42649-.362601*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{{-.437304+.737424*ii, .328431-.323029*ii, -.225233+.0450173*ii},
     ------------------------------------------------------------------------
     #steps => 13, status  => REGULAR, last t => 1, cond#^{-1} => .308716}}

o3 : List

Ways to use randomInitialPair :