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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 = {(.352297 - .248404*ii)x1  + (.196975 + .366526*ii)x1*x2 + (.0624408 +
     ------------------------------------------------------------------------
                   2                                             
     .0988645*ii)x2  + (- .113253 + .373123*ii)x1*x3 + (.088393 -
     ------------------------------------------------------------------------
                                                   2              
     .0541475*ii)x2*x3 + (- .137054 + .190779*ii)x3 , (- .431038 -
     ------------------------------------------------------------------------
                     3                           2               
     .000260566*ii)x1  + (.61778 + .0718135*ii)x1 x2 + (.136195 -
     ------------------------------------------------------------------------
                      2                               3               
     .0328833*ii)x1*x2  + (- .0857858 - .0388616*ii)x2  + (- .399253 -
     ------------------------------------------------------------------------
                   2                                                 
     .0256324*ii)x1 x3 + (.755451 + .629229*ii)x1*x2*x3 + (.0403537 +
     ------------------------------------------------------------------------
                  2                                    2               
     .079638*ii)x2 x3 + (- .00373321 - .129686*ii)x1*x3  + (- .185684 +
     ------------------------------------------------------------------------
                      2                             3
     .0884216*ii)x2*x3  + (.0984491 + .0264902*ii)x3 }

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

o3 = {{{-.31936-.126444*ii, .15506+.142676*ii, .881355+.246648*ii}, #steps =>
     ------------------------------------------------------------------------
     15, status  => REGULAR, last t => 1, cond#^{-1} => .304578}}

o3 : List

Ways to use randomSd :