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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 = ({(- .000793733 - .137736*ii)x1  + (.416634 - .629545*ii)x1*x2 +
     ------------------------------------------------------------------------
                                2                                            
     (.0410921 + .00926089*ii)x2  + (.0689108 + .346266*ii)x1*x3 + (.425972 -
     ------------------------------------------------------------------------
                                                  2              
     .146879*ii)x2*x3 + (- .255913 - .179527*ii)x3 , (- .112665 +
     ------------------------------------------------------------------------
                   3                           2                 
     .0823839*ii)x1  + (- .2573 + .179199*ii)x1 x2 + (- .171909 +
     ------------------------------------------------------------------------
                     2                                3             
     .434211*ii)x1*x2  + (- .00739901 + .0494442*ii)x2  + (.460743 -
     ------------------------------------------------------------------------
                  2                                                      
     .367408*ii)x1 x3 + (- .395292 - .0748187*ii)x1*x2*x3 + (- .0895005 +
     ------------------------------------------------------------------------
                  2                                  2               
     .285141*ii)x2 x3 + (- .116354 - .517562*ii)x1*x3  + (- .199964 +
     ------------------------------------------------------------------------
                     2                            3
     .215576*ii)x2*x3  + (.145474 + .0198692*ii)x3 },
     ------------------------------------------------------------------------
     {{-.0478844-.0392327*ii, -.649557+.730924*ii, .193482-.050591*ii}})

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

o3 = {{-.209643+.104985*ii, -.607458+.733682*ii, .191133-.0346664*ii}}

o3 : List

See also

Ways to use randomInitialPair :