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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 = {(- .140881 + .0362927*ii)x1  + (- .345233 - .113454*ii)x1*x2 +
     ------------------------------------------------------------------------
                              2                                              
     (.0696385 - .099468*ii)x2  + (.165113 - .301216*ii)x1*x3 + (- .0444784 -
     ------------------------------------------------------------------------
                                               2              
     .42838*ii)x2*x3 + (.126305 - .130924*ii)x3 , (- .202793 -
     ------------------------------------------------------------------------
                   3                            2               
     .0486973*ii)x1  + (.475435 + .0535318*ii)x1 x2 + (.144154 +
     ------------------------------------------------------------------------
                     2                          3               
     .227836*ii)x1*x2  + (.18094 + .149373*ii)x2  + (- .304144 -
     ------------------------------------------------------------------------
                  2                                                  
     .529278*ii)x1 x3 + (- .315167 - .435886*ii)x1*x2*x3 + (.158091 +
     ------------------------------------------------------------------------
                  2                               2               
     .380722*ii)x2 x3 + (.360205 - .44627*ii)x1*x3  + (- .538465 -
     ------------------------------------------------------------------------
                      2                              3
     .0932127*ii)x2*x3  + (- .0571094 + .269494*ii)x3 }

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

o3 = {{{-.224943-.319742*ii, -.396944+.122555*ii, .79769+.195632*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .382495}}

o3 : List

Ways to use randomSd :