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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 = ({(- .129092 + .000656869*ii)x1  + (.0309471 + .490776*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                             
     .205302 - .286333*ii)x2  + (- .217376 - .294822*ii)x1*x3 + (.305512 -
     ------------------------------------------------------------------------
                                                 2                         3
     .052307*ii)x2*x3 + (.0344161 + .118463*ii)x3 , (.19404 - .110446*ii)x1 
     ------------------------------------------------------------------------
                                  2                                  2  
     + (- .0786636 - .345722*ii)x1 x2 + (- .338985 - .557624*ii)x1*x2  +
     ------------------------------------------------------------------------
                             3                               2               
     (.268735 - .102072*ii)x2  + (- .0354327 - .0241209*ii)x1 x3 + (- .153591
     ------------------------------------------------------------------------
                                                       2                
     - .419757*ii)x1*x2*x3 + (- .118152 + .496426*ii)x2 x3 + (.0521375 -
     ------------------------------------------------------------------------
                     2                              2             
     .308485*ii)x1*x3  + (.386682 - .480282*ii)x2*x3  + (.217901 -
     ------------------------------------------------------------------------
                 3
     .11592*ii)x3 }, {{.0527771+.138249*ii, -.302877-.123847*ii,
     ------------------------------------------------------------------------
     .933023-.022310*ii}})

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

o3 = {{-.099227+.107785*ii, .596485-.027981*ii, .787897-.034318*ii}}

o3 : List

See also

Ways to use randomInitialPair :