next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = ({(- .027878 + .13024*ii)x1  + (- .233814 - .212029*ii)x1*x2 + (.268557
     ------------------------------------------------------------------------
                     2                                                     
     - .0831536*ii)x2  + (- .00857797 - .000924731*ii)x1*x3 + (- .0613706 +
     ------------------------------------------------------------------------
                                                  2              
     .00629238*ii)x2*x3 + (.107927 + .235938*ii)x3 , (- .078095 -
     ------------------------------------------------------------------------
                   3                             2               
     .0181345*ii)x1  + (- .158822 + .724994*ii)x1 x2 + (.445294 +
     ------------------------------------------------------------------------
                     2                                 3              
     .457378*ii)x1*x2  + (- .000402175 + .0283134*ii)x2  + (.0901338 +
     ------------------------------------------------------------------------
                  2                                                   
     .502121*ii)x1 x3 + (- .26656 + .429012*ii)x1*x2*x3 + (- .432296 +
     ------------------------------------------------------------------------
                  2                                2             
     .368381*ii)x2 x3 + (.015025 + .170258*ii)x1*x3  + (.716774 -
     ------------------------------------------------------------------------
                     2                          3
     .340182*ii)x2*x3  + (.16251 + .248221*ii)x3 }, {{.15328+.459867*ii,
     ------------------------------------------------------------------------
     .333562-.292027*ii, .753904+.010624*ii}})

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

o3 = {{.319347+.337399*ii, -.070956-.665262*ii, .553895+.172542*ii}}

o3 : List

See also

Ways to use randomInitialPair :