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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 = {(- .0994992 + .0819237*ii)x1  + (.318869 + .56349*ii)x1*x2 + (.147352 +
     ------------------------------------------------------------------------
                   2                                                
     .0462634*ii)x2  + (- .026577 + .0554189*ii)x1*x3 + (- .415307 -
     ------------------------------------------------------------------------
                                                2                         3  
     .188226*ii)x2*x3 + (.194654 - .162584*ii)x3 , (.294595 - .23308*ii)x1  +
     ------------------------------------------------------------------------
                               2                                 2           
     (- .201424 - .183953*ii)x1 x2 + (.577853 - .0550972*ii)x1*x2  + (.161216
     ------------------------------------------------------------------------
                      3                             2               
     + .00428685*ii)x2  + (- .520967 + .223787*ii)x1 x3 + (.103095 +
     ------------------------------------------------------------------------
                                                    2               
     .352855*ii)x1*x2*x3 + (.130583 - .0116742*ii)x2 x3 + (.180911 +
     ------------------------------------------------------------------------
                      2                                 2                
     .0738268*ii)x1*x3  + (- .615713 - .0417558*ii)x2*x3  + (- .0168706 -
     ------------------------------------------------------------------------
                   3
     .0124187*ii)x3 }

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

o3 = {{{.074554+.615303*ii, .200952-.20838*ii, .728926-.026598*ii}, #steps =>
     ------------------------------------------------------------------------
     11, status  => REGULAR, last t => 1, cond#^{-1} => .503657}}

o3 : List

Ways to use randomSd :