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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 = ({(.179863 + .0796081*ii)x1  + (- .231102 + .219463*ii)x1*x2 + (.0452759
     ------------------------------------------------------------------------
                     2                                          
     + .0428706*ii)x2  + (.17877 - .174551*ii)x1*x3 + (.211653 -
     ------------------------------------------------------------------------
                                                   2            
     .186045*ii)x2*x3 + (- .292542 + .0615556*ii)x3 , (.188612 -
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                    3                             2                 
     .00657483*ii)x1  + (.0274215 - .0993358*ii)x1 x2 + (- .434325 +
     ------------------------------------------------------------------------
                     2                            3             
     .298729*ii)x1*x2  + (.167087 + .0233561*ii)x2  + (.161638 -
     ------------------------------------------------------------------------
                  2                                                   
     .355265*ii)x1 x3 + (- .40306 - .205436*ii)x1*x2*x3 + (- .580009 +
     ------------------------------------------------------------------------
                  2                                  2             
     .337592*ii)x2 x3 + (- .137403 + .354465*ii)x1*x3  + (.557673 -
     ------------------------------------------------------------------------
                     2                           3
     .157889*ii)x2*x3  + (.331115 - .106578*ii)x3 }, {{.476875+.031299*ii,
     ------------------------------------------------------------------------
     .5759+.088531*ii, .656534+.032795*ii}})

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

o3 = {{.836794-.330804*ii, .335138+.0451065*ii, .267594+.0662214*ii}}

o3 : List

See also

Ways to use randomInitialPair :