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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an 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 = ({(- .0794154 + .0475764*ii)x1  + (- .0325463 - .0583483*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                           
     .139361 + .0575381*ii)x2  + (.319125 - .216426*ii)x1*x3 + (.101924 -
     ------------------------------------------------------------------------
                                                2                           3
     .132953*ii)x2*x3 + (.108958 + .417913*ii)x3 , (.192874 + .0117552*ii)x1 
     ------------------------------------------------------------------------
                                 2                                    2     
     + (- .218055 - .260193*ii)x1 x2 + (- .0353835 - .0506952*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                              3                             2              
     .0536398 + .0353734*ii)x2  + (- .137123 - .401739*ii)x1 x3 + (.79702 -
     ------------------------------------------------------------------------
                                                    2                 
     .728373*ii)x1*x2*x3 + (- .36019 + .384596*ii)x2 x3 + (- .127174 -
     ------------------------------------------------------------------------
                     2                                2             
     .160823*ii)x1*x3  + (- .801857 - .134598*ii)x2*x3  + (.044372 -
     ------------------------------------------------------------------------
                    3
     .00958493*ii)x3 }, {{.879727+.269738*ii, -.0919888-.262255*ii,
     ------------------------------------------------------------------------
     .275161+.0192236*ii}})

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

o3 = {{.119626+.572193*ii, -.036461+.532028*ii, .507046-.341769*ii}}

o3 : List

Ways to use randomInitialPair :