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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 = ({(.128627 - .0712154*ii)x1  + (.0797411 + .150698*ii)x1*x2 + (.220924 -
     ------------------------------------------------------------------------
                   2                                               
     .0789312*ii)x2  + (- .153129 + .100128*ii)x1*x3 + (- .020821 +
     ------------------------------------------------------------------------
                                                    2             
     .0410025*ii)x2*x3 + (- .0308665 - .126002*ii)x3 , (.0156975 +
     ------------------------------------------------------------------------
                  3                           2               
     .245063*ii)x1  + (.320902 + .398022*ii)x1 x2 + (.250501 +
     ------------------------------------------------------------------------
                     2                          3             
     .319115*ii)x1*x2  + (.15544 + .367198*ii)x2  + (.291235 -
     ------------------------------------------------------------------------
                  2                                                   
     .287461*ii)x1 x3 + (.129347 - .616536*ii)x1*x2*x3 + (- .0508479 -
     ------------------------------------------------------------------------
                 2                               2             
     .19141*ii)x2 x3 + (.371484 - .88244*ii)x1*x3  + (.154074 +
     ------------------------------------------------------------------------
                      2                            3
     .0323608*ii)x2*x3  + (.0757395 + .157423*ii)x3 }, {{.068936+.637191*ii,
     ------------------------------------------------------------------------
     -.577036-.085623*ii, .344601-.36081*ii}})

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

o3 = {{{.480548+.283714*ii, -.261334-.047766*ii, .498362-.607979*ii}, #steps
     ------------------------------------------------------------------------
     => 13, status  => REGULAR, last t => 1, cond#^{-1} => .283946}}

o3 : List

Ways to use randomInitialPair :