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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 = ({(- .0323029 + .0166254*ii)x1  + (- .115568 + .112922*ii)x1*x2 +
     ------------------------------------------------------------------------
                             2                                               
     (.151087 + .111906*ii)x2  + (- .129349 + .0618405*ii)x1*x3 + (.0906911 +
     ------------------------------------------------------------------------
                                                2                          3
     .10317*ii)x2*x3 + (.0643216 - .130253*ii)x3 , (.188426 - .382371*ii)x1 
     ------------------------------------------------------------------------
                                 2                                   2     
     + (.316473 + .00435457*ii)x1 x2 + (- .200866 + .0286244*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                            3                            2                 
     .197651 - .244126*ii)x2  + (.326394 - .0299224*ii)x1 x3 + (- .259444 +
     ------------------------------------------------------------------------
                                                      2               
     1.00532*ii)x1*x2*x3 + (- .261428 - .0127223*ii)x2 x3 + (.234919 +
     ------------------------------------------------------------------------
                     2                               2             
     .309781*ii)x1*x3  + (- .489443 + .23324*ii)x2*x3  + (.312603 -
     ------------------------------------------------------------------------
                  3
     .223226*ii)x3 }, {{.420366-.479096*ii, -.512322-.119757*ii,
     ------------------------------------------------------------------------
     -.1118+.551765*ii}})

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

o3 = {{{.156365-.20712*ii, -.749304-.402282*ii, -.084643+.449667*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .49688}}

o3 : List

Ways to use randomInitialPair :