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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 = ({(.113279 - .101914*ii)x1  + (- .286646 - .209719*ii)x1*x2 + (- .360685
     ------------------------------------------------------------------------
                    2                                             
     - .196753*ii)x2  + (.408228 + .0246767*ii)x1*x3 + (.0911896 -
     ------------------------------------------------------------------------
                                                     2               
     .0919216*ii)x2*x3 + (- .00402678 - .240403*ii)x3 , (- .0338762 -
     ------------------------------------------------------------------------
                  3                           2               
     .235607*ii)x1  + (.685466 - .392045*ii)x1 x2 + (.168549 +
     ------------------------------------------------------------------------
                     2                              3             
     .337393*ii)x1*x2  + (- .299259 + .0812951*ii)x2  + (.157878 -
     ------------------------------------------------------------------------
                  2                                                  
     .472408*ii)x1 x3 + (.359544 + .0947412*ii)x1*x2*x3 + (.0817982 -
     ------------------------------------------------------------------------
                  2                                2              
     .349223*ii)x2 x3 + (.223342 + .204419*ii)x1*x3  + (.0231964 -
     ------------------------------------------------------------------------
                    2                             3
     .50743*ii)x2*x3  + (.0203017 - .0197299*ii)x3 }, {{-.164865+.328577*ii,
     ------------------------------------------------------------------------
     .0326997+.325241*ii, .870436-.018625*ii}})

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

o3 = {{-.336602-.343157*ii, -.0239332+.329575*ii, .787181-.200241*ii}}

o3 : List

See also

Ways to use randomInitialPair :