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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 a unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                               2                                            
o1 = {(- .157172 - .24721*ii)x1  + (.337188 + .148605*ii)x1*x2 + (.0518221 +
     ------------------------------------------------------------------------
                  2                                             
     .196394*ii)x2  + (.124787 - .0402177*ii)x1*x3 + (.0442711 +
     ------------------------------------------------------------------------
                                                2              
     .201355*ii)x2*x3 + (.272061 - .275246*ii)x3 , (- .115712 +
     ------------------------------------------------------------------------
                   3                           2               
     .0223602*ii)x1  + (.194194 - .122808*ii)x1 x2 + (.134761 +
     ------------------------------------------------------------------------
                      2                               3                
     .0982946*ii)x1*x2  + (.000445234 - .0222777*ii)x2  + (- .0850005 +
     ------------------------------------------------------------------------
                   2                                                
     .0299284*ii)x1 x3 + (.794362 - .315745*ii)x1*x2*x3 + (.230703 +
     ------------------------------------------------------------------------
                   2                                 2               
     .0800674*ii)x2 x3 + (- .40639 + .761539*ii)x1*x3  + (- .411365 -
     ------------------------------------------------------------------------
                    2                              3
     .47021*ii)x2*x3  + (- .234768 + .0787387*ii)x3 }

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

o3 = {{{-.609069+.084684*ii, .002512-.568415*ii, .504793+.209632*ii}, #steps
     ------------------------------------------------------------------------
     => 13, status  => REGULAR, last t => 1, cond#^{-1} => .299197}}

o3 : List

Ways to use randomSd :