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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 = ({(.073791 + .0180165*ii)x1  + (.60294 - .240892*ii)x1*x2 + (.0656705 +
     ------------------------------------------------------------------------
                  2                                             
     .379961*ii)x2  + (- .456798 + .218485*ii)x1*x3 + (.222942 +
     ------------------------------------------------------------------------
                                                  2              
     .0693384*ii)x2*x3 + (.0324526 + .137237*ii)x3 , (- .115689 +
     ------------------------------------------------------------------------
                  3                             2                  
     .106309*ii)x1  + (.0140242 + .0994383*ii)x1 x2 + (- .0796662 -
     ------------------------------------------------------------------------
                      2                              3             
     .0370109*ii)x1*x2  + (- .0589522 - .353792*ii)x2  + (.291763 +
     ------------------------------------------------------------------------
                  2                                                 
     .443552*ii)x1 x3 + (- .218674 + .606905*ii)x1*x2*x3 + (.14254 -
     ------------------------------------------------------------------------
                  2                                   2               
     .266489*ii)x2 x3 + (- .380317 - .0861422*ii)x1*x3  + (- .676989 +
     ------------------------------------------------------------------------
                     2                              3
     .132933*ii)x2*x3  + (- .229649 + .0399079*ii)x3 },
     ------------------------------------------------------------------------
     {{-.122625-.954276*ii, -.168835+.102548*ii, -.1852+.0316263*ii}})

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

o3 = {{-.067726-.893716*ii, .294997-.014335*ii, .0294118-.329533*ii}}

o3 : List

See also

Ways to use randomInitialPair :