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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. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                2                                           
o2 = ({(.190796 + .0922511*ii)x1  + (.290714 - .506741*ii)x1*x2 + (- .121118
     ------------------------------------------------------------------------
                    2                                                
     + .174559*ii)x2  + (- .0330241 - .347288*ii)x1*x3 + (- .189615 +
     ------------------------------------------------------------------------
                                                  2              
     .105789*ii)x2*x3 + (- .172315 + .175364*ii)x3 , (.00811142 +
     ------------------------------------------------------------------------
                  3                               2               
     .312426*ii)x1  + (- .00344181 - .130185*ii)x1 x2 + (.152354 +
     ------------------------------------------------------------------------
                    2                            3             
     .15815*ii)x1*x2  + (.0639089 + .120489*ii)x2  + (.364869 +
     ------------------------------------------------------------------------
                  2                                                     
     .201614*ii)x1 x3 + (- .100574 - .342297*ii)x1*x2*x3 + (- .0649516 -
     ------------------------------------------------------------------------
                 2                                  2               
     .87689*ii)x2 x3 + (- .351891 - .209625*ii)x1*x3  + (- .426275 +
     ------------------------------------------------------------------------
                     2                             3
     .446682*ii)x2*x3  + (- .108799 + .146282*ii)x3 }, {{.604172-.105786*ii,
     ------------------------------------------------------------------------
     -.204403+.168271*ii, .743006+.040387*ii}})

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

o3 = {{.377598-.256635*ii, -.175097+.4005*ii, -.377705+.676637*ii}}

o3 : List

See also

Ways to use randomInitialPair :