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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 = {(.0326112 - .0856505*ii)x1  + (.270081 + .0641851*ii)x1*x2 + (.184855 +
     ------------------------------------------------------------------------
                  2                                             
     .063045*ii)x2  + (- .381453 + .283463*ii)x1*x3 + (.275354 +
     ------------------------------------------------------------------------
                                                   2             
     .0916456*ii)x2*x3 + (.199112 + .00101157*ii)x3 , (- .24581 -
     ------------------------------------------------------------------------
                  3                              2                 
     .347713*ii)x1  + (- .0128096 - .125595*ii)x1 x2 + (- .161647 -
     ------------------------------------------------------------------------
                     2                            3               
     .387147*ii)x1*x2  + (.0641532 + .210837*ii)x2  + (- .295154 -
     ------------------------------------------------------------------------
                  2                                                
     .115904*ii)x1 x3 + (.484368 + .558309*ii)x1*x2*x3 + (.449719 -
     ------------------------------------------------------------------------
                   2                                2             
     .0653323*ii)x2 x3 + (.061868 + .368732*ii)x1*x3  + (.405942 +
     ------------------------------------------------------------------------
                     2                            3
     .491551*ii)x2*x3  + (.0970158 - .203646*ii)x3 }

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

o3 = {{.215279+.368746*ii, .0549194+.0960615*ii, .891407+.104073*ii}}

o3 : List

See also