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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 = {(.285655 + .0588587*ii)x1  + (- .291469 + .370907*ii)x1*x2 + (.00149172
     ------------------------------------------------------------------------
                     2                                           
     + .0809735*ii)x2  + (.102297 - .180721*ii)x1*x3 + (.294951 +
     ------------------------------------------------------------------------
                                                  2              
     .100816*ii)x2*x3 + (.0210445 - .0281454*ii)x3 , (- .135082 -
     ------------------------------------------------------------------------
                   3                             2                 
     .0672128*ii)x1  + (- .532235 + .082288*ii)x1 x2 + (- .275871 +
     ------------------------------------------------------------------------
                      2                               3               
     .0639438*ii)x1*x2  + (- .0434444 + .0244243*ii)x2  + (.00312553 -
     ------------------------------------------------------------------------
                  2                                                  
     .215157*ii)x1 x3 + (- .390945 - .295655*ii)x1*x2*x3 + (.433089 +
     ------------------------------------------------------------------------
                  2                                  2               
     .473287*ii)x2 x3 + (- .133874 + .123848*ii)x1*x3  + (- .362745 -
     ------------------------------------------------------------------------
                     2                           3
     .492583*ii)x2*x3  + (.308982 + .391298*ii)x3 }

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

o3 = {{.43346+.105837*ii, -.0149195+.422029*ii, .64645+.452418*ii}}

o3 : List

See also