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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 = ({(- .21099 - .0904596*ii)x1  + (- .18017 - .0914052*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                             
     .221781 - .263245*ii)x2  + (- .517952 - .413107*ii)x1*x3 + (.267955 +
     ------------------------------------------------------------------------
                                                  2             
     .405577*ii)x2*x3 + (- .134145 - .345131*ii)x3 , (.0729563 +
     ------------------------------------------------------------------------
                  3                              2               
     .187384*ii)x1  + (- .152238 - .0212117*ii)x1 x2 + (.281629 -
     ------------------------------------------------------------------------
                      2                               3              
     .0115192*ii)x1*x2  + (- .0913641 - .0975737*ii)x2  + (.0664778 +
     ------------------------------------------------------------------------
                  2                                                 
     .110438*ii)x1 x3 + (.460859 + .0503454*ii)x1*x2*x3 + (.176453 +
     ------------------------------------------------------------------------
                  2                                    2              
     .516644*ii)x2 x3 + (- .0918709 + .0590868*ii)x1*x3  + (.0469952 -
     ------------------------------------------------------------------------
                      2                            3
     .0355927*ii)x2*x3  + (- .164643 + .21897*ii)x3 }, {{-.608112-.198227*ii,
     ------------------------------------------------------------------------
     -.159295+.127294*ii, .6806+.293447*ii}})

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

o3 = {{{-.590015-.339419*ii, -.490559-.207664*ii, .499381-.0593579*ii},
     ------------------------------------------------------------------------
     #steps => 11, status  => REGULAR, last t => 1, cond#^{-1} => .396513}}

o3 : List

Ways to use randomInitialPair :