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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 = ({(- .231664 - .133823*ii)x1  + (.447796 - .349633*ii)x1*x2 + (.137934 +
     ------------------------------------------------------------------------
                  2                                            
     .151389*ii)x2  + (.629017 + .155016*ii)x1*x3 + (.0969896 -
     ------------------------------------------------------------------------
                                                     2              
     .0460032*ii)x2*x3 + (- .0673257 + .0665862*ii)x3 , (- .187237 -
     ------------------------------------------------------------------------
                  3                           2               
     .235905*ii)x1  + (.178175 - .254404*ii)x1 x2 + (.267557 -
     ------------------------------------------------------------------------
                     2                             3               
     .438724*ii)x1*x2  + (- .212959 - .142128*ii)x2  + (.00927764 -
     ------------------------------------------------------------------------
                  2                                                  
     .404273*ii)x1 x3 + (- .410917 + .367633*ii)x1*x2*x3 + (.212889 +
     ------------------------------------------------------------------------
                  2                                2           
     .123796*ii)x2 x3 + (.280868 + .347435*ii)x1*x3  + (.1238 +
     ------------------------------------------------------------------------
                     2                              3
     .202435*ii)x2*x3  + (- .0400456 - .334741*ii)x3 }, {{.144152-.396966*ii,
     ------------------------------------------------------------------------
     -.38189+.372279*ii, -.377795-.628075*ii}})

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

o3 = {{.294413-.449842*ii, -.266539+.794253*ii, .0727559-.0615539*ii}}

o3 : List

Ways to use randomInitialPair :