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 = ({(- .226735 - .0837537*ii)x1  + (.125834 + .0118603*ii)x1*x2 + (.162544
     ------------------------------------------------------------------------
                    2                                             
     - .247639*ii)x2  + (.479955 + .176141*ii)x1*x3 + (.00161033 +
     ------------------------------------------------------------------------
                                                   2              
     .0234142*ii)x2*x3 + (.00880559 + .173057*ii)x3 , (- .270446 +
     ------------------------------------------------------------------------
                  3                              2               
     .158728*ii)x1  + (.0504427 + .00710192*ii)x1 x2 + (.623549 -
     ------------------------------------------------------------------------
                     2                            3               
     .314363*ii)x1*x2  + (.318477 + .0769223*ii)x2  + (- .407148 +
     ------------------------------------------------------------------------
                  2                                                  
     .461006*ii)x1 x3 + (.332386 + .450126*ii)x1*x2*x3 + (- .223685 +
     ------------------------------------------------------------------------
                  2                                  2             
     .154988*ii)x2 x3 + (- .131354 + .477778*ii)x1*x3  + (.262992 +
     ------------------------------------------------------------------------
                     2                            3
     .208783*ii)x2*x3  + (.167336 - .0869966*ii)x3 }, {{.30649-.394435*ii,
     ------------------------------------------------------------------------
     -.085662-.655374*ii, .369679-.420677*ii}})

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

o3 = {{.0886486+.0346629*ii, .162286-.918576*ii, -.259257-.231532*ii}}

o3 : List

See also

Ways to use randomInitialPair :