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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 = ({(.0765112 + .0463764*ii)x1  + (.284192 - .39537*ii)x1*x2 + (- .174556
     ------------------------------------------------------------------------
                    2                                            
     - .389296*ii)x2  + (.20606 + .446625*ii)x1*x3 + (- .225765 +
     ------------------------------------------------------------------------
                                                 2              
     .117085*ii)x2*x3 + (.250556 - .0324426*ii)x3 , (- .117506 -
     ------------------------------------------------------------------------
                  3                              2               
     .269122*ii)x1  + (- .0488788 - .102063*ii)x1 x2 + (.104003 +
     ------------------------------------------------------------------------
                     2                               3                
     .219264*ii)x1*x2  + (- .0346264 - .0606724*ii)x2  + (- .0268897 +
     ------------------------------------------------------------------------
                  2                                                  
     .339004*ii)x1 x3 + (.181669 + .176536*ii)x1*x2*x3 + (- .411874 +
     ------------------------------------------------------------------------
                  2                                  2             
     .174544*ii)x2 x3 + (- .491562 + .181161*ii)x1*x3  + (.223401 +
     ------------------------------------------------------------------------
                      2                             3
     .0123566*ii)x2*x3  + (- .201192 + .332325*ii)x3 },
     ------------------------------------------------------------------------
     {{-.347196+.753072*ii, .298525-.385829*ii, .210856+.172906*ii}})

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

o3 = {{-.422705+.318811*ii, -.0569076-.168655*ii, .733328-.387593*ii}}

o3 : List

See also

Ways to use randomInitialPair :