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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 = ({(- .213967 - .0724305*ii)x1  + (.261998 - .0932691*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                              2                                           
     .0646985 - .0172967*ii)x2  + (.156496 + .089077*ii)x1*x3 + (.465441 -
     ------------------------------------------------------------------------
                                                  2            
     .117078*ii)x2*x3 + (.0610031 + .0398019*ii)x3 , (.148239 +
     ------------------------------------------------------------------------
                  3                               2               
     .323578*ii)x1  + (- .0802008 + .0490396*ii)x1 x2 + (.114803 +
     ------------------------------------------------------------------------
                       2                              3             
     .00422193*ii)x1*x2  + (- .373254 - .0901837*ii)x2  + (.238672 +
     ------------------------------------------------------------------------
                  2                                                     
     .399095*ii)x1 x3 + (- .551775 - .0428611*ii)x1*x2*x3 + (- .625959 +
     ------------------------------------------------------------------------
                   2                                   2             
     .0367723*ii)x2 x3 + (- .0196733 - .606836*ii)x1*x3  + (.452935 -
     ------------------------------------------------------------------------
                     2                            3
     .186698*ii)x2*x3  + (.0333247 - .298505*ii)x3 }, {{-.479573+.0872607*ii,
     ------------------------------------------------------------------------
     .618189+.030055*ii, .6153+.027209*ii}})

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

o3 = {{-.350139+.25552*ii, .52519-.036915*ii, .690088+.242288*ii}}

o3 : List

See also

Ways to use randomInitialPair :