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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 = ({(- .157622 + .287706*ii)x1  + (- .0182223 - .287769*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                               
     .100204 - .0676682*ii)x2  + (- .254151 - .429457*ii)x1*x3 + (- .300706 -
     ------------------------------------------------------------------------
                                                   2            
     .122033*ii)x2*x3 + (.0229907 - .00906399*ii)x3 , (.158254 -
     ------------------------------------------------------------------------
                 3                           2               
     .12143*ii)x1  + (.170225 + .447722*ii)x1 x2 + (.529058 -
     ------------------------------------------------------------------------
                     2                              3                
     .293061*ii)x1*x2  + (- .301446 + .0473173*ii)x2  + (- .0254886 -
     ------------------------------------------------------------------------
                  2                                                  
     .460319*ii)x1 x3 + (- .516712 - .201851*ii)x1*x2*x3 + (.599107 +
     ------------------------------------------------------------------------
                  2                                  2                
     .129024*ii)x2 x3 + (- .126374 - .146249*ii)x1*x3  + (- .0337392 -
     ------------------------------------------------------------------------
                     2                              3
     .454139*ii)x2*x3  + (- .0476487 + .224299*ii)x3 }, {{.295441+.39947*ii,
     ------------------------------------------------------------------------
     .498473+.643984*ii, -.186872-.234578*ii}})

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

o3 = {{{.593383+.309464*ii, .58072+.275737*ii, .336868+.159314*ii}, #steps =>
     ------------------------------------------------------------------------
     11, status  => REGULAR, last t => 1, cond#^{-1} => .125828}}

o3 : List

Ways to use randomInitialPair :