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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 = {(- .237754 - .20489*ii)x1  + (- .206379 + .40749*ii)x1*x2 + (- .0184192
     ------------------------------------------------------------------------
                     2                                             
     + .0331919*ii)x2  + (- .170931 + .29985*ii)x1*x3 + (.0584023 -
     ------------------------------------------------------------------------
                                                    2              
     .199762*ii)x2*x3 + (- .00923785 + .461798*ii)x3 , (- .101074 -
     ------------------------------------------------------------------------
                   3                             2                 
     .0976469*ii)x1  + (- .172439 + .119645*ii)x1 x2 + (- .405315 -
     ------------------------------------------------------------------------
                      2                             3              
     .0425881*ii)x1*x2  + (- .185364 - .105279*ii)x2  + (.0914069 -
     ------------------------------------------------------------------------
                   2                                             
     .0614924*ii)x1 x3 + (1.09703 - .268*ii)x1*x2*x3 + (.111618 +
     ------------------------------------------------------------------------
                  2                                2             
     .237476*ii)x2 x3 + (.0169107 - .42188*ii)x1*x3  + (.207325 -
     ------------------------------------------------------------------------
                     2                           3
     .152403*ii)x2*x3  + (.149645 - .149971*ii)x3 }

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

o3 = {{-.692766+.018217*ii, .0484931+.267582*ii, .643233+.179006*ii}}

o3 : List

See also