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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 = ({(- .0752167 - .0143308*ii)x1  + (.0628183 + .27742*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                             
     .213748 - .0287405*ii)x2  + (.109767 - .354149*ii)x1*x3 + (- .282451 +
     ------------------------------------------------------------------------
                                                2              
     .16794*ii)x2*x3 + (.0686193 + .175434*ii)x3 , (- .136484 +
     ------------------------------------------------------------------------
                   3                         2                
     .0141073*ii)x1  + (.1198 + .317117*ii)x1 x2 + (- .23108 -
     ------------------------------------------------------------------------
                     2                            3               
     .460921*ii)x1*x2  + (.0251423 + .107293*ii)x2  + (- .288739 +
     ------------------------------------------------------------------------
                  2                                                 
     .144131*ii)x1 x3 + (- .11703 + .690302*ii)x1*x2*x3 + (.566708 -
     ------------------------------------------------------------------------
                  2                                2              
     .696289*ii)x2 x3 + (.161142 - .385471*ii)x1*x3  + (.0283035 +
     ------------------------------------------------------------------------
                      2                           3
     .0570833*ii)x2*x3  + (.126453 + .161966*ii)x3 }, {{-.474441-.443503*ii,
     ------------------------------------------------------------------------
     .379621+.429115*ii, .463519-.187377*ii}})

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

o3 = {{-.552251-.620274*ii, .33624+.227778*ii, .367094-.10286*ii}}

o3 : List

See also

Ways to use randomInitialPair :