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 = ({(.177431 + .330963*ii)x1  + (- .254141 - .323144*ii)x1*x2 + (.149908 -
     ------------------------------------------------------------------------
                  2                                              
     .145469*ii)x2  + (- .105133 - .0238472*ii)x1*x3 + (.337023 +
     ------------------------------------------------------------------------
                                                 2              
     .134684*ii)x2*x3 + (.326373 - .0995538*ii)x3 , (- .190253 -
     ------------------------------------------------------------------------
                   3                             2                  
     .0608103*ii)x1  + (- .461726 + .153574*ii)x1 x2 + (- .0289844 +
     ------------------------------------------------------------------------
                      2                             3              
     .0507504*ii)x1*x2  + (- .228078 - .213209*ii)x2  + (.0820772 +
     ------------------------------------------------------------------------
                  2                                                  
     .604852*ii)x1 x3 + (.400062 + .165751*ii)x1*x2*x3 + (- .161619 +
     ------------------------------------------------------------------------
                  2                                 2               
     .130362*ii)x2 x3 + (- .21011 - .399319*ii)x1*x3  + (- .410132 -
     ------------------------------------------------------------------------
                     2                           3
     .219312*ii)x2*x3  + (.101921 - .219303*ii)x3 }, {{.544974+.096386*ii,
     ------------------------------------------------------------------------
     .075641-.521454*ii, .643719-.041269*ii}})

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

o3 = {{.532676+.128455*ii, .423807-.324748*ii, .521482-.377809*ii}}

o3 : List

See also

Ways to use randomInitialPair :