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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 = ({(- .0845358 + .171018*ii)x1  + (- .331242 - .119553*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                            
     .155159 + .143514*ii)x2  + (.0403919 - .193196*ii)x1*x3 + (.197998 -
     ------------------------------------------------------------------------
                                               2                            3
     .29517*ii)x2*x3 + (.192294 + .295201*ii)x3 , (.0999906 - .0489532*ii)x1 
     ------------------------------------------------------------------------
                                  2                                2     
     + (- .554641 - .0255643*ii)x1 x2 + (.202006 + .843565*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                            3                            2               
     .13489 + .0173871*ii)x2  + (.380694 - .0902273*ii)x1 x3 + (.423427 +
     ------------------------------------------------------------------------
                                                     2               
     .565913*ii)x1*x2*x3 + (- .198551 + .378628*ii)x2 x3 + (.192552 +
     ------------------------------------------------------------------------
                    2                                2               
     .26988*ii)x1*x3  + (.606222 + .00572373*ii)x2*x3  + (- .117422 -
     ------------------------------------------------------------------------
                  3
     .104505*ii)x3 }, {{-.117603-.585355*ii, -.644437+.351369*ii,
     ------------------------------------------------------------------------
     .295109-.13297*ii}})

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

o3 = {{-.013301-.776009*ii, -.374523+.176238*ii, .199479-.431872*ii}}

o3 : List

See also

Ways to use randomInitialPair :