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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 = ({(- .169938 - .170536*ii)x1  + (.0723547 - .71226*ii)x1*x2 + (.219375 +
     ------------------------------------------------------------------------
                   2                                               
     .0274122*ii)x2  + (.0121406 + .156085*ii)x1*x3 + (- .0260659 -
     ------------------------------------------------------------------------
                                                 2             
     .331293*ii)x2*x3 + (.0101965 + .188011*ii)x3 , (.0208863 -
     ------------------------------------------------------------------------
                   3                             2               
     .0332547*ii)x1  + (- .154007 + .154023*ii)x1 x2 + (.472769 -
     ------------------------------------------------------------------------
                     2                             3             
     .290412*ii)x1*x2  + (- .243745 - .151276*ii)x2  + (.220883 +
     ------------------------------------------------------------------------
                  2                                                  
     .188912*ii)x1 x3 + (.244449 - .584939*ii)x1*x2*x3 + (- .117232 +
     ------------------------------------------------------------------------
                 2                                   2               
     .28999*ii)x2 x3 + (- .642727 + .0512133*ii)x1*x3  + (- .227124 -
     ------------------------------------------------------------------------
                     2                              3
     .292362*ii)x2*x3  + (- .0110236 - .178855*ii)x3 }, {{.816213+.059098*ii,
     ------------------------------------------------------------------------
     .005578+.234219*ii, .47546+.222151*ii}})

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

o3 = {{{.739463+.136677*ii, .253024+.406473*ii, .39761+.217206*ii}, #steps =>
     ------------------------------------------------------------------------
     11, status  => REGULAR, last t => 1, cond#^{-1} => .35558}}

o3 : List

Ways to use randomInitialPair :