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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 = ({(- .259445 - .116131*ii)x1  + (- .0490867 - .325223*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                               
     .112885 + .0753414*ii)x2  + (- .238296 + .467349*ii)x1*x3 + (- .128088 +
     ------------------------------------------------------------------------
                                                   2               
     .0423758*ii)x2*x3 + (- .142423 + .253658*ii)x3 , (- .0928266 +
     ------------------------------------------------------------------------
                  3                             2               
     .208936*ii)x1  + (- .260765 + .221999*ii)x1 x2 + (.329684 -
     ------------------------------------------------------------------------
                     2                            3             
     .196908*ii)x1*x2  + (.0886961 + .359421*ii)x2  + (.261723 +
     ------------------------------------------------------------------------
                  2                                                    
     .241452*ii)x1 x3 + (- .678685 + .586777*ii)x1*x2*x3 + (- .112081 -
     ------------------------------------------------------------------------
                  2                                2               
     .303318*ii)x2 x3 + (.129203 + .530946*ii)x1*x3  + (- .288217 -
     ------------------------------------------------------------------------
                     2                           3
     .223844*ii)x2*x3  + (.190108 - .132698*ii)x3 }, {{-.125393-.522419*ii,
     ------------------------------------------------------------------------
     .709645-.170993*ii, -.0405266-.420568*ii}})

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

o3 = {{-.324199-.326146*ii, .727901-.196699*ii, .281664-.375045*ii}}

o3 : List

See also

Ways to use randomInitialPair :