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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 = ({(- .0883247 - .321477*ii)x1  + (- .0482145 - .0569195*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                           
     (.0433999 + .0741562*ii)x2  + (.333688 + .114459*ii)x1*x3 + (.213209 +
     ------------------------------------------------------------------------
                                                   2             
     .0137345*ii)x2*x3 + (- .292721 - .182504*ii)x3 , (- .06492 -
     ------------------------------------------------------------------------
                  3                           2                  
     .202162*ii)x1  + (.361082 - .694493*ii)x1 x2 + (- .0232409 +
     ------------------------------------------------------------------------
                      2                             3                
     .0571069*ii)x1*x2  + (.0413197 + .0161713*ii)x2  + (- .0372825 +
     ------------------------------------------------------------------------
                  2                                                 
     .272107*ii)x1 x3 + (.0107782 - .191505*ii)x1*x2*x3 + (.181959 -
     ------------------------------------------------------------------------
                  2                               2               
     .481295*ii)x2 x3 + (.266946 - .54999*ii)x1*x3  + (- .533135 -
     ------------------------------------------------------------------------
                      2                          3
     .0763706*ii)x2*x3  + (.165527 + .13548*ii)x3 }, {{-.197504-.312681*ii,
     ------------------------------------------------------------------------
     .710941+.313719*ii, .509266+.003846*ii}})

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

o3 = {{.108289+.0516402*ii, .374519+.619188*ii, .634677-.243175*ii}}

o3 : List

See also

Ways to use randomInitialPair :