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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 = ({(- .231993 + .0201708*ii)x1  + (- .0329156 + .216085*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                             
     (.0150587 - .107634*ii)x2  + (.0669318 - .0630075*ii)x1*x3 + (- .331255
     ------------------------------------------------------------------------
                                                     2             
     + .0250421*ii)x2*x3 + (- .165427 + .206763*ii)x3 , (.0821183 -
     ------------------------------------------------------------------------
                  3                             2               
     .254454*ii)x1  + (.164091 - .00635747*ii)x1 x2 + (.349784 -
     ------------------------------------------------------------------------
                     2                           3               
     .255025*ii)x1*x2  + (.163422 - .104879*ii)x2  + (- .496034 +
     ------------------------------------------------------------------------
                  2                                                
     .228567*ii)x1 x3 + (.091945 - .335835*ii)x1*x2*x3 + (.796994 +
     ------------------------------------------------------------------------
                   2                                2               
     .0972229*ii)x2 x3 + (- .11967 - .34536*ii)x1*x3  + (- .329501 +
     ------------------------------------------------------------------------
                      2                              3
     .0782753*ii)x2*x3  + (- .269265 - .0418486*ii)x3 },
     ------------------------------------------------------------------------
     {{-.085318+.683555*ii, .265748+.31755*ii, .59343+.043069*ii}})

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

o3 = {{{-.1649+.664842*ii, -.0909859+.143421*ii, .509308-.492494*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .517576}}

o3 : List

Ways to use randomInitialPair :