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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 = ({(- .0783056 + .244314*ii)x1  + (- .0685529 + .508916*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                            
     .0497164 - .137267*ii)x2  + (- .47013 - .197684*ii)x1*x3 + (.200583 +
     ------------------------------------------------------------------------
                                                 2                
     .144989*ii)x2*x3 + (.0997622 + .132362*ii)x3 , (- .00925831 -
     ------------------------------------------------------------------------
                   3                            2                 
     .0416659*ii)x1  + (.319398 - .0147878*ii)x1 x2 + (- .179754 -
     ------------------------------------------------------------------------
                      2                             3               
     .0516566*ii)x1*x2  + (.0293527 + .0286244*ii)x2  + (- .264567 -
     ------------------------------------------------------------------------
                   2                                                     
     .0176713*ii)x1 x3 + (.0358912 + .0887277*ii)x1*x2*x3 + (- .0827134 -
     ------------------------------------------------------------------------
                  2                                  2             
     .483077*ii)x2 x3 + (- .187328 + .317857*ii)x1*x3  + (.613762 +
     ------------------------------------------------------------------------
                     2                                3
     .323547*ii)x2*x3  + (- .0599389 + .00953872*ii)x3 },
     ------------------------------------------------------------------------
     {{.387168+.278816*ii, .172418-.50697*ii, .672801-.181534*ii}})

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

o3 = {{-.494071+.334301*ii, -.255804-.406858*ii, .633372+.10958*ii}}

o3 : List

See also

Ways to use randomInitialPair :