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 = ({(.0121183 + .00403574*ii)x1  + (- .0699539 - .00744897*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                            
     .140055 + .177496*ii)x2  + (.154098 - .330639*ii)x1*x3 + (- .43471 +
     ------------------------------------------------------------------------
                                                    2             
     .276453*ii)x2*x3 + (- .0980161 - .0296001*ii)x3 , (.0876352 -
     ------------------------------------------------------------------------
                   3                          2                
     .0567945*ii)x1  + (.44894 - .268355*ii)x1 x2 + (.0783242 -
     ------------------------------------------------------------------------
                     2                           3             
     .302015*ii)x1*x2  + (.0726538 + .18046*ii)x2  + (.177548 -
     ------------------------------------------------------------------------
                  2                                                 
     .295968*ii)x1 x3 + (- .678456 - .45945*ii)x1*x2*x3 + (.143747 -
     ------------------------------------------------------------------------
                  2                                  2               
     .863014*ii)x2 x3 + (- .442461 - .302043*ii)x1*x3  + (- .390659 +
     ------------------------------------------------------------------------
                  2                             3
     .289*ii)x2*x3  + (.0532469 - .0973335*ii)x3 }, {{-.344443-.494822*ii,
     ------------------------------------------------------------------------
     .376036-.616301*ii, .107442+.32208*ii}})

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

o3 = {{-.335804-.310227*ii, .171598-.418529*ii, -.696203-.31888*ii}}

o3 : List

See also

Ways to use randomInitialPair :