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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 = ({(- .0305154 + .192419*ii)x1  + (- .221734 + .245473*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                           
     (.0240293 - .0798377*ii)x2  + (.483873 - .181356*ii)x1*x3 + (.174208 -
     ------------------------------------------------------------------------
                                                  2            
     .0463874*ii)x2*x3 + (.330543 - .0312316*ii)x3 , (.115936 -
     ------------------------------------------------------------------------
                  3                              2               
     .198367*ii)x1  + (- .0999147 + .184209*ii)x1 x2 + (.560488 -
     ------------------------------------------------------------------------
                     2                           3               
     .350465*ii)x1*x2  + (.103036 + .146248*ii)x2  + (- .376435 -
     ------------------------------------------------------------------------
                   2                                                
     .0447309*ii)x1 x3 + (.646166 - .424092*ii)x1*x2*x3 + (.198624 +
     ------------------------------------------------------------------------
                  2                                 2              
     .265841*ii)x2 x3 + (.0556653 - .283212*ii)x1*x3  + (.0586294 -
     ------------------------------------------------------------------------
                     2                            3
     .627676*ii)x2*x3  + (.0186748 + .167876*ii)x3 }, {{.903478+.192218*ii,
     ------------------------------------------------------------------------
     -.0247608-.175131*ii, .204936-.271105*ii}})

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

o3 = {{.944406+.05003*ii, -.206386-.0724078*ii, -.204403+.126393*ii}}

o3 : List

See also

Ways to use randomInitialPair :