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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 = ({(.0533705 + .169623*ii)x1  + (- .203836 - .167978*ii)x1*x2 + (.0434496
     ------------------------------------------------------------------------
                  2                                           
     + .2282*ii)x2  + (.52982 - .430844*ii)x1*x3 + (.0476169 -
     ------------------------------------------------------------------------
                                               2               
     .139654*ii)x2*x3 + (.184846 + .14793*ii)x3 , (- .0795637 -
     ------------------------------------------------------------------------
                   3                              2                
     .0168722*ii)x1  + (- .681336 - .0726232*ii)x1 x2 + (.0257102 +
     ------------------------------------------------------------------------
                     2                              3               
     .079852*ii)x1*x2  + (- .127366 + .0763973*ii)x2  + (- .547983 +
     ------------------------------------------------------------------------
                 2                                                 
     .12259*ii)x1 x3 + (.273454 - .245496*ii)x1*x2*x3 + (.0784881 +
     ------------------------------------------------------------------------
                  2                                2               
     .583474*ii)x2 x3 + (.133943 - .369651*ii)x1*x3  + (- .236512 -
     ------------------------------------------------------------------------
                     2                             3
     .191225*ii)x2*x3  + (- .280925 + .255127*ii)x3 }, {{-.195906-.376015*ii,
     ------------------------------------------------------------------------
     .548217-.425979*ii, .576679-.075329*ii}})

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

o3 = {{-.549714-.373493*ii, .333345-.430458*ii, -.240619-.451671*ii}}

o3 : List

See also

Ways to use randomInitialPair :