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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 = {(.047742 + .0406588*ii)x1  + (.0331893 + .113279*ii)x1*x2 + (- .168005
     ------------------------------------------------------------------------
                    2                                            
     - .198678*ii)x2  + (.587557 - .148815*ii)x1*x3 + (.0520006 +
     ------------------------------------------------------------------------
                                                   2              
     .00503063*ii)x2*x3 + (.0406142 + .250998*ii)x3 , (- .144541 +
     ------------------------------------------------------------------------
                  3                           2                 
     .141597*ii)x1  + (.185182 - .250232*ii)x1 x2 + (- .137333 +
     ------------------------------------------------------------------------
                     2                           3              
     .232589*ii)x1*x2  + (.225888 - .242373*ii)x2  + (- .17796 -
     ------------------------------------------------------------------------
                  2                                                    
     .631105*ii)x1 x3 + (- .407456 - .395712*ii)x1*x2*x3 + (- .353912 +
     ------------------------------------------------------------------------
                  2                                2               
     .127198*ii)x2 x3 + (.339835 - .170919*ii)x1*x3  + (- .180221 -
     ------------------------------------------------------------------------
                     2                              3
     .578931*ii)x2*x3  + (- .0499237 + .216479*ii)x3 }

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

o3 = {{-.163428-.248799*ii, -.296217-.592207*ii, .687102+.028769*ii}}

o3 : List

See also