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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                               2                                      
o1 = {(.0596587 + .078481*ii)x1  + (- .0126856 + .281152*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .192984 - .0949595*ii)x2  + (.0916879 + .00703713*ii)x1*x3 + (- .210789
     ------------------------------------------------------------------------
                                                   2               
     + .700643*ii)x2*x3 + (.154287 - .0815679*ii)x3 , (- .0266688 -
     ------------------------------------------------------------------------
                   3                           2               
     .0108926*ii)x1  + (.245792 - .458543*ii)x1 x2 + (.223996 -
     ------------------------------------------------------------------------
                    2                               3               
     .47547*ii)x1*x2  + (- .0889729 - .0411003*ii)x2  + (- .495616 -
     ------------------------------------------------------------------------
                 2                                                     
     .18245*ii)x1 x3 + (- .229507 - .375065*ii)x1*x2*x3 + (- .0852194 -
     ------------------------------------------------------------------------
                  2                                  2               
     .513254*ii)x2 x3 + (- .176655 - .166463*ii)x1*x3  + (- .551592 +
     ------------------------------------------------------------------------
                       2                             3
     .00577294*ii)x2*x3  + (- .244497 - .114223*ii)x3 }

o1 : List
i2 : (S,solsS) = goodInitialPair T;
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.242168+.537945*ii, .130163+.0828197*ii, .784489+.1129*ii}}

o3 : List

See also