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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 = ({(.201958 - .0116736*ii)x1  + (- .497118 + .0361805*ii)x1*x2 + (.100678
     ------------------------------------------------------------------------
                    2                                             
     - .265199*ii)x2  + (- .654277 - .108092*ii)x1*x3 + (.300866 -
     ------------------------------------------------------------------------
                                                    2               
     .106129*ii)x2*x3 + (- .0261075 - .0361137*ii)x3 , (- .0724662 +
     ------------------------------------------------------------------------
                  3                            2                 
     .170418*ii)x1  + (- .316113 - .08561*ii)x1 x2 + (- .932723 +
     ------------------------------------------------------------------------
                     2                             3             
     .104732*ii)x1*x2  + (- .106886 + .058227*ii)x2  + (.192536 -
     ------------------------------------------------------------------------
                  2                                                  
     .191908*ii)x1 x3 + (.186521 + .130085*ii)x1*x2*x3 + (- .159924 +
     ------------------------------------------------------------------------
                   2                                2             
     .0868857*ii)x2 x3 + (.275807 + .378164*ii)x1*x3  + (.322486 -
     ------------------------------------------------------------------------
                     2                           3
     .233122*ii)x2*x3  + (.165381 - .113199*ii)x3 }, {{-.186461+.0556621*ii,
     ------------------------------------------------------------------------
     .297918-.784589*ii, .235596+.44977*ii}})

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

o3 = {{{-.428253-.19686*ii, .457082-.749613*ii, -.0421705+.0722748*ii},
     ------------------------------------------------------------------------
     #steps => 18, status  => REGULAR, last t => 1, cond#^{-1} => .432536}}

o3 : List

Ways to use randomInitialPair :