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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 = ({(- .243066 - .0184383*ii)x1  + (.0196543 - .101639*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                         
     .0379025 - .104999*ii)x2  + (.36982 + .294415*ii)x1*x3 + (.31574 -
     ------------------------------------------------------------------------
                                                2                          3
     .399014*ii)x2*x3 + (.257948 - .129934*ii)x3 , (.182053 + .163733*ii)x1 
     ------------------------------------------------------------------------
                               2                               2            
     + (.536859 - .848609*ii)x1 x2 + (.42722 + .060098*ii)x1*x2  + (.0624408
     ------------------------------------------------------------------------
                    3                            2               
     - .157256*ii)x2  + (.236272 + .0416087*ii)x1 x3 + (.191954 +
     ------------------------------------------------------------------------
                                                       2               
     .622444*ii)x1*x2*x3 + (- .0632773 + .0635249*ii)x2 x3 + (.107741 +
     ------------------------------------------------------------------------
                     2                               2                
     .179905*ii)x1*x3  + (.0773988 - .051493*ii)x2*x3  + (- .0726718 +
     ------------------------------------------------------------------------
                   3
     .0505003*ii)x3 }, {{.393963+.256917*ii, -.336711-.260492*ii,
     ------------------------------------------------------------------------
     .683027-.361982*ii}})

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

o3 = {{{.329432+.148937*ii, -.450566+.409953*ii, .516329+.481274*ii}, #steps
     ------------------------------------------------------------------------
     => 12, status  => REGULAR, last t => 1, cond#^{-1} => .237344}}

o3 : List

Ways to use randomInitialPair :