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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 = {(.0515352 + .0455098*ii)x1  + (- .223919 - .0862576*ii)x1*x2 + (.260249
     ------------------------------------------------------------------------
                    2                                              
     + .327871*ii)x2  + (- .169075 - .280138*ii)x1*x3 + (.0981705 +
     ------------------------------------------------------------------------
                                                 2               
     .014396*ii)x2*x3 + (.0165813 - .333416*ii)x3 , (- .0830746 -
     ------------------------------------------------------------------------
                  3                           2                
     .180341*ii)x1  + (.371444 + .120373*ii)x1 x2 + (- .40643 -
     ------------------------------------------------------------------------
                      2                           3             
     .0144586*ii)x1*x2  + (.257838 + .103371*ii)x2  + (.197976 -
     ------------------------------------------------------------------------
                  2                                                 
     .185626*ii)x1 x3 + (.336728 + .0441006*ii)x1*x2*x3 + (.409298 +
     ------------------------------------------------------------------------
                  2                                2               
     .244263*ii)x2 x3 + (.646119 + .378719*ii)x1*x3  + (- .366742 +
     ------------------------------------------------------------------------
                     2                             3
     .278873*ii)x2*x3  + (- .11715 - .0887056*ii)x3 }

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

o3 = {{-.146239+.556222*ii, -.541691+.106783*ii, .483687-.361174*ii}}

o3 : List

See also