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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 = {(- .282622 + .126008*ii)x1  + (.213364 - .265677*ii)x1*x2 + (.0468515 +
     ------------------------------------------------------------------------
                   2                                                
     .0957627*ii)x2  + (- .437192 - .320942*ii)x1*x3 + (- .0335191 -
     ------------------------------------------------------------------------
                                                  2              
     .0539048*ii)x2*x3 + (.153673 - .0296877*ii)x3 , (- .191082 -
     ------------------------------------------------------------------------
                  3                              2               
     .154785*ii)x1  + (- .646238 - .0438996*ii)x1 x2 + (.136138 -
     ------------------------------------------------------------------------
                     2                              3            
     .103057*ii)x1*x2  + (- .0674173 + .120365*ii)x2  + (.16545 +
     ------------------------------------------------------------------------
                  2                                                    
     .101831*ii)x1 x3 + (- .420857 + .700695*ii)x1*x2*x3 + (- .514237 -
     ------------------------------------------------------------------------
                  2                                  2                 
     .508321*ii)x2 x3 + (- .023499 + .163422*ii)x1*x3  + (- .00914905 -
     ------------------------------------------------------------------------
                     2                            3
     .385911*ii)x2*x3  + (.272593 - .0300473*ii)x3 }

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

o3 = {{{.305521+.104669*ii, -.593534+.122679*ii, .695642+.210833*ii}, #steps
     ------------------------------------------------------------------------
     => 18, status  => REGULAR, last t => 1, cond#^{-1} => .276218}}

o3 : List

Ways to use randomSd :