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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 = ({(- .0113481 - .0436128*ii)x1  + (- .264519 + .245511*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                              2                                            
     .410028 - .00803318*ii)x2  + (.0869894 - .172492*ii)x1*x3 + (.271909 +
     ------------------------------------------------------------------------
                                                 2               
     .0283388*ii)x2*x3 + (.140725 + .114866*ii)x3 , (- .0705827 -
     ------------------------------------------------------------------------
                  3                          2                 
     .185607*ii)x1  + (.096303 - .89471*ii)x1 x2 + (.00233764 -
     ------------------------------------------------------------------------
                       2                           3                
     .00195666*ii)x1*x2  + (- .39354 + .20187*ii)x2  + (- .0877033 -
     ------------------------------------------------------------------------
                  2                                                  
     .139213*ii)x1 x3 + (.246712 + .563942*ii)x1*x2*x3 + (- .348001 -
     ------------------------------------------------------------------------
                  2                                2                
     .132926*ii)x2 x3 + (.200674 - .335539*ii)x1*x3  + (- .0562719 +
     ------------------------------------------------------------------------
                    2                             3
     .34694*ii)x2*x3  + (- .065479 + .115505*ii)x3 },
     ------------------------------------------------------------------------
     {{-.0547747-.0182628*ii, -.328062-.179071*ii, .925611-.014813*ii}})

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

o3 = {{{-.030567+.605626*ii, -.502047-.073844*ii, .555729+.256794*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .592683}}

o3 : List

Ways to use randomInitialPair :