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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 = ({(- .372568 - .0229169*ii)x1  + (- .274746 - .306496*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                            
     (.201642 + .0693445*ii)x2  + (.0744623 + .130774*ii)x1*x3 + (.355369 -
     ------------------------------------------------------------------------
                                               2                            3
     .148623*ii)x2*x3 + (.30395 + .100556*ii)x3 , (.0324819 - .0107265*ii)x1 
     ------------------------------------------------------------------------
                              2                                  2           
     + (.210268 - .13221*ii)x1 x2 + (- .236792 - .059399*ii)x1*x2  + (.125676
     ------------------------------------------------------------------------
                    3                             2                 
     - .157745*ii)x2  + (- .188829 + .119674*ii)x1 x3 + (- .350931 -
     ------------------------------------------------------------------------
                                                      2              
     .0414688*ii)x1*x2*x3 + (- .376321 + .763325*ii)x2 x3 + (.42046 -
     ------------------------------------------------------------------------
                      2                              2             
     .0880076*ii)x1*x3  + (- .3244 - .382855*ii)x2*x3  + (.247417 -
     ------------------------------------------------------------------------
                  3
     .138631*ii)x3 }, {{-.697492+.398955*ii, .318853-.297438*ii,
     ------------------------------------------------------------------------
     .357178-.191384*ii}})

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

o3 = {{-.521885+.345858*ii, .253271+.151025*ii, -.136419-.708839*ii}}

o3 : List

See also

Ways to use randomInitialPair :