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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 = ({(- .230953 - .352444*ii)x1  + (.210046 - .0343487*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                           
     .0406256 + .263025*ii)x2  + (.414069 + .19418*ii)x1*x3 + (.0590925 +
     ------------------------------------------------------------------------
                                                   2            
     .168296*ii)x2*x3 + (- .287439 + .0711919*ii)x3 , (.296179 +
     ------------------------------------------------------------------------
                   3                             2                  
     .0594019*ii)x1  + (- .126704 - .566498*ii)x1 x2 + (- .0494842 +
     ------------------------------------------------------------------------
                      2                           3             
     .0716423*ii)x1*x2  + (.142521 + .146401*ii)x2  + (.112675 +
     ------------------------------------------------------------------------
                  2                                                    
     .262791*ii)x1 x3 + (- .811971 - .675382*ii)x1*x2*x3 + (- .138761 -
     ------------------------------------------------------------------------
                  2                                  2              
     .217798*ii)x2 x3 + (.0822708 - .0924173*ii)x1*x3  + (.0507865 -
     ------------------------------------------------------------------------
                     2                             3
     .305677*ii)x2*x3  + (.0430511 + .0180983*ii)x3 }, {{.619928-.092398*ii,
     ------------------------------------------------------------------------
     .142552-.136926*ii, .739801-.144139*ii}})

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

o3 = {{.916131-.138131*ii, .0500859-.123672*ii, .34686-.0592305*ii}}

o3 : List

See also

Ways to use randomInitialPair :