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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 = {(- .058974 + .012227*ii)x1  + (.140303 + .175383*ii)x1*x2 + (.134127 +
     ------------------------------------------------------------------------
                  2                                           
     .240343*ii)x2  + (.110182 + .249492*ii)x1*x3 + (.126109 +
     ------------------------------------------------------------------------
                                                  2            
     .644281*ii)x2*x3 + (.196786 - .00448252*ii)x3 , (.138842 +
     ------------------------------------------------------------------------
                   3                              2               
     .0216441*ii)x1  + (- .0796308 + .162193*ii)x1 x2 + (.178582 -
     ------------------------------------------------------------------------
                     2                          3               
     .489438*ii)x1*x2  + (.151438 - .22946*ii)x2  + (- .509702 -
     ------------------------------------------------------------------------
                   2                                              
     .0730228*ii)x1 x3 + (.266971 + .72823*ii)x1*x2*x3 + (.45181 -
     ------------------------------------------------------------------------
                  2                                   2              
     .111625*ii)x2 x3 + (- .568373 - .0946065*ii)x1*x3  + (.0274127 -
     ------------------------------------------------------------------------
                     2                               3
     .257322*ii)x2*x3  + (- .0856308 + .0781243*ii)x3 }

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

o3 = {{{-.059503+.127253*ii, -.0085976+.22324*ii, .964506+.009169*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .498226}}

o3 : List

Ways to use randomSd :