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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 = ({(.118214 - .0527115*ii)x1  + (- .350432 + .126909*ii)x1*x2 + (.116477
     ------------------------------------------------------------------------
                    2                                                
     + .157647*ii)x2  + (- .00790339 - .132276*ii)x1*x3 + (.0480303 +
     ------------------------------------------------------------------------
                                                  2            
     .0988361*ii)x2*x3 + (.280086 - .0220089*ii)x3 , (.109614 +
     ------------------------------------------------------------------------
                  3                              2               
     .226163*ii)x1  + (- .270101 + .0331693*ii)x1 x2 + (.064674 +
     ------------------------------------------------------------------------
                     2                            3               
     .212675*ii)x1*x2  + (.0746381 + .340021*ii)x2  + (- .359966 -
     ------------------------------------------------------------------------
                  2                                                  
     .411364*ii)x1 x3 + (.768416 + .457056*ii)x1*x2*x3 + (- .736247 -
     ------------------------------------------------------------------------
                   2                                2             
     .0728862*ii)x2 x3 + (.259572 - .270281*ii)x1*x3  + (.122072 +
     ------------------------------------------------------------------------
                     2                            3
     .298303*ii)x2*x3  + (.277444 - .0294989*ii)x3 }, {{.524172-.154872*ii,
     ------------------------------------------------------------------------
     .465822+.234803*ii, .652438-.058829*ii}})

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

o3 = {{-.398566-.216862*ii, .312196-.1036*ii, .355612+.747968*ii}}

o3 : List

See also

Ways to use randomInitialPair :