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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 = ({(.021463 + .0185816*ii)x1  + (.0109597 + .163016*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                             
     .0177182 - .267111*ii)x2  + (.541834 - .215719*ii)x1*x3 + (- .314879 -
     ------------------------------------------------------------------------
                                                   2              
     .168313*ii)x2*x3 + (- .308626 - .0708661*ii)x3 , (- .145192 +
     ------------------------------------------------------------------------
                    3                             2                 
     .00405644*ii)x1  + (- .621501 + .509679*ii)x1 x2 + (- .182009 +
     ------------------------------------------------------------------------
                     2                              3                
     .118786*ii)x1*x2  + (- .0358614 + .255063*ii)x2  + (- .0524596 +
     ------------------------------------------------------------------------
                  2                                                    
     .350237*ii)x1 x3 + (- .372745 + .114861*ii)x1*x2*x3 + (- .352278 +
     ------------------------------------------------------------------------
                 2                                2              
     .17966*ii)x2 x3 + (.109121 - .188388*ii)x1*x3  + (.0436855 +
     ------------------------------------------------------------------------
                     2                             3
     .583667*ii)x2*x3  + (.188372 - .00411834*ii)x3 }, {{.508779+.83953*ii,
     ------------------------------------------------------------------------
     .0636711-.158573*ii, -.0224978-.0814091*ii}})

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

o3 = {{{-.310643+.623026*ii, -.331153+.0280746*ii, .358325-.525826*ii},
     ------------------------------------------------------------------------
     #steps => 31, status  => REGULAR, last t => 1, cond#^{-1} => .368162}}

o3 : List

Ways to use randomInitialPair :