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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 = ({(- .048518 - .025909*ii)x1  + (- .378598 + .0930385*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                             
     (.112162 + .0455527*ii)x2  + (- .101692 - .170458*ii)x1*x3 + (- .130187
     ------------------------------------------------------------------------
                                                       2               
     - .0679258*ii)x2*x3 + (- .00141551 - .308915*ii)x3 , (- .0245199 +
     ------------------------------------------------------------------------
                   3                               2                
     .0568123*ii)x1  + (- .493714 - .00906413*ii)x1 x2 + (.0491206 -
     ------------------------------------------------------------------------
                     2                            3               
     .284262*ii)x1*x2  + (- .065482 + .18079*ii)x2  + (- .130246 +
     ------------------------------------------------------------------------
                  2                                                 
     .133805*ii)x1 x3 + (.467152 + .0376825*ii)x1*x2*x3 + (.410357 -
     ------------------------------------------------------------------------
                  2                               2               
     .344626*ii)x2 x3 + (.51962 - .433806*ii)x1*x3  + (- .338115 -
     ------------------------------------------------------------------------
                    2                          3
     .37726*ii)x2*x3  + (.26423 - .255021*ii)x3 }, {{-.846272-.469076*ii,
     ------------------------------------------------------------------------
     .0193462+.0635375*ii, .239961-.0424034*ii}})

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

o3 = {{-.574904-.098912*ii, .296311+.138392*ii, -.383582-.636878*ii}}

o3 : List

See also

Ways to use randomInitialPair :