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 = ({(.168933 + .190836*ii)x1  + (.339446 - .236677*ii)x1*x2 + (.0701958 +
     ------------------------------------------------------------------------
                  2                                              
     .435431*ii)x2  + (.247746 - .209968*ii)x1*x3 + (- .0353201 -
     ------------------------------------------------------------------------
                                                     2               
     .0223828*ii)x2*x3 + (- .0344402 - .0778689*ii)x3 , (- .0469274 -
     ------------------------------------------------------------------------
                   3                           2                 
     .0338739*ii)x1  + (.390769 + .449881*ii)x1 x2 + (- .195668 +
     ------------------------------------------------------------------------
                      2                              3               
     .0933642*ii)x1*x2  + (- .258097 + .0320503*ii)x2  + (- .130072 -
     ------------------------------------------------------------------------
                  2                                                  
     .012494*ii)x1 x3 + (- .214111 + .906179*ii)x1*x2*x3 + (.596733 +
     ------------------------------------------------------------------------
                2                                 2                
     .1916*ii)x2 x3 + (.0553923 - .257816*ii)x1*x3  + (- .0762633 +
     ------------------------------------------------------------------------
                     2                             3
     .208615*ii)x2*x3  + (- .175908 + .229552*ii)x3 }, {{-.189472+.79956*ii,
     ------------------------------------------------------------------------
     .142087+.0596468*ii, .54842+.017118*ii}})

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

o3 = {{-.175417+.359593*ii, .64135+.500567*ii, .411523-.0931314*ii}}

o3 : List

See also

Ways to use randomInitialPair :