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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 = ({(- .205072 - .0775383*ii)x1  + (.0484168 + .0472869*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                            
     (.0360614 + .0222324*ii)x2  + (.135086 - .0958896*ii)x1*x3 + (.229042 +
     ------------------------------------------------------------------------
                                                     2              
     .339736*ii)x2*x3 + (- .00979572 - .0214085*ii)x3 , (- .129072 -
     ------------------------------------------------------------------------
                   3                             2               
     .0690919*ii)x1  + (- .211095 + .628482*ii)x1 x2 + (.050261 +
     ------------------------------------------------------------------------
                     2                              3               
     .277024*ii)x1*x2  + (- .0139499 - .160887*ii)x2  + (- .999777 -
     ------------------------------------------------------------------------
                   2                                                  
     .0219377*ii)x1 x3 + (.364574 + .754251*ii)x1*x2*x3 + (- .338627 +
     ------------------------------------------------------------------------
                  2                                  2               
     .169316*ii)x2 x3 + (- .155936 + .102981*ii)x1*x3  + (- .159334 +
     ------------------------------------------------------------------------
                     2                              3
     .243657*ii)x2*x3  + (- .173469 + .0507655*ii)x3 },
     ------------------------------------------------------------------------
     {{-.423156+.363183*ii, -.402499-.467412*ii, .55349+.046982*ii}})

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

o3 = {{-.793949-.136131*ii, -.315522-.312878*ii, -.163976-.35606*ii}}

o3 : List

See also

Ways to use randomInitialPair :