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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 = ({(- .250433 + .149912*ii)x1  + (.194448 + .217495*ii)x1*x2 + (- .14737
     ------------------------------------------------------------------------
                     2                                             
     + .0723755*ii)x2  + (.278556 - .254257*ii)x1*x3 + (- .569094 -
     ------------------------------------------------------------------------
                                                   2             
     .511976*ii)x2*x3 + (- .0921775 + .234511*ii)x3 , (.0962689 +
     ------------------------------------------------------------------------
                  3                           2                
     .063265*ii)x1  + (.163857 - .193328*ii)x1 x2 + (.0482014 +
     ------------------------------------------------------------------------
                     2                            3            
     .110531*ii)x1*x2  + (.0698874 - .110677*ii)x2  + (.31979 -
     ------------------------------------------------------------------------
                 2                                                 
     .59646*ii)x1 x3 + (.0270385 - .102027*ii)x1*x2*x3 + (.203236 -
     ------------------------------------------------------------------------
                  2                                  2                 
     .135874*ii)x2 x3 + (- .370119 - .119423*ii)x1*x3  + (- .00601817 -
     ------------------------------------------------------------------------
                      2                             3
     .0626109*ii)x2*x3  + (- .114213 - .023795*ii)x3 },
     ------------------------------------------------------------------------
     {{-.794384+.195637*ii, .074602+.558638*ii, .0899437-.0703427*ii}})

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

o3 = {{-.413566+.805163*ii, -.317807+.0381832*ii, -.055038+.274203*ii}}

o3 : List

See also

Ways to use randomInitialPair :