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 = ({(- .0648489 - .27952*ii)x1  + (- .064707 + .104157*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                           2                                              
     .150722 - .31066*ii)x2  + (.0565735 + .294428*ii)x1*x3 + (- .314743 +
     ------------------------------------------------------------------------
                                                   2            
     .170536*ii)x2*x3 + (- .0940582 + .321923*ii)x3 , (.106706 -
     ------------------------------------------------------------------------
                  3                              2               
     .220676*ii)x1  + (- .0323274 + .294205*ii)x1 x2 + (.410217 +
     ------------------------------------------------------------------------
                     2                              3               
     .218145*ii)x1*x2  + (- .0055837 - .349787*ii)x2  + (- .135507 +
     ------------------------------------------------------------------------
                  2                                                     
     .491842*ii)x1 x3 + (- .384276 + .392605*ii)x1*x2*x3 + (- .0230877 -
     ------------------------------------------------------------------------
                   2                                2             
     .0941458*ii)x2 x3 + (.334767 + .201961*ii)x1*x3  + (.224754 +
     ------------------------------------------------------------------------
                     2                            3
     .332474*ii)x2*x3  + (.320117 - .0542332*ii)x3 }, {{.401156+.18617*ii,
     ------------------------------------------------------------------------
     .750721-.083889*ii, .274726-.397896*ii}})

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

o3 = {{.379262+.343942*ii, .586442-.1099*ii, .373641-.492204*ii}}

o3 : List

See also

Ways to use randomInitialPair :