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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 = ({(.331935 + .167892*ii)x1  + (.0739411 - .155614*ii)x1*x2 + (.168295 -
     ------------------------------------------------------------------------
                  2                                                
     .126221*ii)x2  + (- .0288817 - .186931*ii)x1*x3 + (- .266635 +
     ------------------------------------------------------------------------
                                                  2              
     .238695*ii)x2*x3 + (- .023958 - .169766*ii)x3 , (- .027215 +
     ------------------------------------------------------------------------
                 3                             2               
     .21642*ii)x1  + (- .107574 - .148373*ii)x1 x2 + (.527934 -
     ------------------------------------------------------------------------
                     2                           3               
     .215815*ii)x1*x2  + (.222607 + .419228*ii)x2  + (- .256898 +
     ------------------------------------------------------------------------
                   2                                                   
     .0765696*ii)x1 x3 + (- .0247345 + .598495*ii)x1*x2*x3 + (.504216 +
     ------------------------------------------------------------------------
                   2                                 2               
     .0204941*ii)x2 x3 + (- .356905 + .25814*ii)x1*x3  + (.00406804 -
     ------------------------------------------------------------------------
                     2                              3
     .149256*ii)x2*x3  + (- .0563377 + .244869*ii)x3 },
     ------------------------------------------------------------------------
     {{-.103505-.413672*ii, -.173425+.367095*ii, -.114847+.800086*ii}})

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

o3 = {{{.443718-.429124*ii, .360706-.11537*ii, .017030+.68939*ii}, #steps =>
     ------------------------------------------------------------------------
     25, status  => REGULAR, last t => 1, cond#^{-1} => .615668}}

o3 : List

Ways to use randomInitialPair :