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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 = ({(- .116994 - .377399*ii)x1  + (.0747111 - .734185*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                                
     .303892 + .244136*ii)x2  + (- .135867 - .221365*ii)x1*x3 + (- .0443564 -
     ------------------------------------------------------------------------
                                                  2              
     .04649*ii)x2*x3 + (- .0514209 - .259575*ii)x3 , (.00900746 +
     ------------------------------------------------------------------------
                   3                              2                  
     .0128421*ii)x1  + (- .0413671 + .267988*ii)x1 x2 + (- .0579722 +
     ------------------------------------------------------------------------
                       2                            3              
     .00173973*ii)x1*x2  + (- .1099 + .0515514*ii)x2  + (- .11241 +
     ------------------------------------------------------------------------
                  2                                                    
     .105194*ii)x1 x3 + (.0326702 - .0103184*ii)x1*x2*x3 + (- .252725 +
     ------------------------------------------------------------------------
                  2                                2             
     .065171*ii)x2 x3 + (.161063 - .266455*ii)x1*x3  + (.760433 -
     ------------------------------------------------------------------------
                      2                             3
     .0664033*ii)x2*x3  + (.0414563 + .0355456*ii)x3 },
     ------------------------------------------------------------------------
     {{-.411388-.287419*ii, .249958-.128278*ii, .818037-.005534*ii}})

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

o3 = {{{-.828408-.080499*ii, .370988+.330131*ii, .245519+.0190271*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .300003}}

o3 : List

Ways to use randomInitialPair :