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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 = ({(- .307271 - .0379226*ii)x1  + (- .043455 - .0888861*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                             
     (.444877 - .0484954*ii)x2  + (- .109096 + .141172*ii)x1*x3 + (- .137407
     ------------------------------------------------------------------------
                                                    2              
     - .337683*ii)x2*x3 + (.0555325 - .0596388*ii)x3 , (- .330965 -
     ------------------------------------------------------------------------
                  3                          2               
     .212373*ii)x1  + (.10904 - .110142*ii)x1 x2 + (.409802 +
     ------------------------------------------------------------------------
                     2                            3              
     .361224*ii)x1*x2  + (- .11562 + .121656*ii)x2  + (.0242386 +
     ------------------------------------------------------------------------
                   2                                                  
     .0796359*ii)x1 x3 + (- .1348 - .167685*ii)x1*x2*x3 + (- .149029 +
     ------------------------------------------------------------------------
                  2                                  2                 
     .191459*ii)x2 x3 + (- .153663 + .144989*ii)x1*x3  + (- .00782926 +
     ------------------------------------------------------------------------
                     2                             3
     .680527*ii)x2*x3  + (.0929355 - .0524727*ii)x3 }, {{.34426-.0417665*ii,
     ------------------------------------------------------------------------
     -.0158158+.0474972*ii, .936604+.002599*ii}})

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

o3 = {{{.241947+.0669473*ii, -.383952+.0027175*ii, .861702+.216847*ii},
     ------------------------------------------------------------------------
     #steps => 11, status  => REGULAR, last t => 1, cond#^{-1} => .45479}}

o3 : List

Ways to use randomInitialPair :