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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 = ({(- .340033 - .299124*ii)x1  + (- .136008 + .207007*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                                
     .110603 - .172433*ii)x2  + (- .0464938 + .212453*ii)x1*x3 + (- .126508 -
     ------------------------------------------------------------------------
                                               2                            3
     .357534*ii)x2*x3 + (.15835 - .241803*ii)x3 , (.00786774 - .310924*ii)x1 
     ------------------------------------------------------------------------
                                  2                                2  
     + (- .382209 + .0755602*ii)x1 x2 + (.265024 - .047458*ii)x1*x2  +
     ------------------------------------------------------------------------
                             3                            2                 
     (.151093 + .168427*ii)x2  + (.131296 + .0819674*ii)x1 x3 + (- .534816 +
     ------------------------------------------------------------------------
                                                   2                 
     .351181*ii)x1*x2*x3 + (.314353 - .309368*ii)x2 x3 + (- .147665 +
     ------------------------------------------------------------------------
                     2                              2              
     .179916*ii)x1*x3  + (.406216 - .185017*ii)x2*x3  + (.0540882 -
     ------------------------------------------------------------------------
                   3
     .0438828*ii)x3 }, {{.290475-.257015*ii, .0212004-.418529*ii,
     ------------------------------------------------------------------------
     .817873-.070957*ii}})

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

o3 = {{{.281914+.12939*ii, .0700852-.440868*ii, .795103-.268918*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .418269}}

o3 : List

Ways to use randomInitialPair :