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NumericalAlgebraicGeometry :: randomSd

randomSd -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials T_i such that deg T_i = d_i. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                                 2                                           
o1 = {(- .0321357 - .050706*ii)x1  + (.111059 + .190465*ii)x1*x2 + (- .081921
     ------------------------------------------------------------------------
                     2                                            
     + .0142529*ii)x2  + (.350808 - .472175*ii)x1*x3 + (.0936245 -
     ------------------------------------------------------------------------
                                                   2              
     .173159*ii)x2*x3 + (- .267855 - .0653372*ii)x3 , (- .301788 -
     ------------------------------------------------------------------------
                   3                             2             
     .0110515*ii)x1  + (- .393046 + .185407*ii)x1 x2 + (.4875 +
     ------------------------------------------------------------------------
                    2                             3             
     .39881*ii)x1*x2  + (- .135906 + .097305*ii)x2  + (.173562 +
     ------------------------------------------------------------------------
                  2                                                    
     .343833*ii)x1 x3 + (.748625 + .0982731*ii)x1*x2*x3 + (- .0403672 +
     ------------------------------------------------------------------------
                 2                                  2             
     .11481*ii)x2 x3 + (- .241151 + .421828*ii)x1*x3  + (.118155 -
     ------------------------------------------------------------------------
                   2                           3
     .3758*ii)x2*x3  + (.295539 + .123619*ii)x3 }

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

o3 = {{.28401+.309796*ii, -.0554997-.192805*ii, .828813-.310129*ii}}

o3 : List

Ways to use randomSd :