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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 = ({(.0178649 + .142914*ii)x1  + (- .427432 - .0463751*ii)x1*x2 + (.243964
     ------------------------------------------------------------------------
                     2                                             
     + .0287349*ii)x2  + (.350886 - .0775722*ii)x1*x3 + (- .51384 +
     ------------------------------------------------------------------------
                                                 2             
     .0598602*ii)x2*x3 + (.14954 + .0958574*ii)x3 , (.0596405 +
     ------------------------------------------------------------------------
                  3                              2                
     .106965*ii)x1  + (- .0174011 + .224789*ii)x1 x2 + (.0711846 +
     ------------------------------------------------------------------------
                     2                              3             
     .232132*ii)x1*x2  + (- .0505458 - .188261*ii)x2  + (.183998 +
     ------------------------------------------------------------------------
                  2                                                    
     .535767*ii)x1 x3 + (- .345579 + .819249*ii)x1*x2*x3 + (- .043278 +
     ------------------------------------------------------------------------
                   2                                 2             
     .0851409*ii)x2 x3 + (.312019 + .0668871*ii)x1*x3  + (.240126 +
     ------------------------------------------------------------------------
                     2                             3
     .611765*ii)x2*x3  + (- .158519 + .290554*ii)x3 }, {{.530842+.763282*ii,
     ------------------------------------------------------------------------
     -.330565+.106326*ii, -.0486246-.112537*ii}})

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

o3 = {{{.304294+.599514*ii, -.354258+.61977*ii, .152757+.122634*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .439448}}

o3 : List

Ways to use randomInitialPair :