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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 = {(.162262 + .266635*ii)x1  + (- .149983 - .194203*ii)x1*x2 + (.27028 -
     ------------------------------------------------------------------------
                  2                                                
     .223571*ii)x2  + (- .167405 + .108798*ii)x1*x3 + (- .0911316 -
     ------------------------------------------------------------------------
                                             2                          3  
     .3831*ii)x2*x3 + (.21897 + .107727*ii)x3 , (.349247 + .148844*ii)x1  +
     ------------------------------------------------------------------------
                             2                               2             
     (.203501 + .129885*ii)x1 x2 + (.43831 - .119254*ii)x1*x2  + (.136704 -
     ------------------------------------------------------------------------
                   3                            2                
     .0879996*ii)x2  + (.0983887 + .472478*ii)x1 x3 + (.0410912 -
     ------------------------------------------------------------------------
                                                  2               
     .296796*ii)x1*x2*x3 + (.254752 - .38572*ii)x2 x3 + (.370633 +
     ------------------------------------------------------------------------
                     2                              2            
     .268141*ii)x1*x3  + (.199754 - .130233*ii)x2*x3  + (.19591 +
     ------------------------------------------------------------------------
                 3
     .20672*ii)x3 }

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

o3 = {{-.228859+.539977*ii, -.289747-.371291*ii, .655985+.062616*ii}}

o3 : List

See also