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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 = {(.16495 + .18253*ii)x1  + (.0767737 - .370207*ii)x1*x2 + (.223771 -
     ------------------------------------------------------------------------
                   2                                          
     .0871662*ii)x2  + (.392215 + .34105*ii)x1*x3 + (.394425 -
     ------------------------------------------------------------------------
                                                 2             
     .445463*ii)x2*x3 + (.0997896 - .157346*ii)x3 , (.0494964 +
     ------------------------------------------------------------------------
                  3                              2                 
     .161291*ii)x1  + (- .266111 + .0283146*ii)x1 x2 + (- .136301 -
     ------------------------------------------------------------------------
                      2                             3                
     .0562399*ii)x1*x2  + (.0425935 - .0884583*ii)x2  + (- .0507735 -
     ------------------------------------------------------------------------
                  2                                                  
     .391625*ii)x1 x3 + (.120015 - .136122*ii)x1*x2*x3 + (- .624159 +
     ------------------------------------------------------------------------
                 2                                    2             
     .69263*ii)x2 x3 + (- .0478869 - .0298888*ii)x1*x3  + (.133899 +
     ------------------------------------------------------------------------
                     2                              3
     .110228*ii)x2*x3  + (- .163534 + .0961173*ii)x3 }

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

o3 = {{{.343179+.332821*ii, .0899309-.177783*ii, .855424-.00359*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .35585}}

o3 : List

Ways to use randomSd :