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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 = {(.0376602 - .0447396*ii)x1  + (- .519929 - .482331*ii)x1*x2 + (.0939509
     ------------------------------------------------------------------------
                    2                                                
     + .144085*ii)x2  + (- .184056 - .0250638*ii)x1*x3 + (- .333604 -
     ------------------------------------------------------------------------
                                                2              
     .119254*ii)x2*x3 + (.0860869 + .12647*ii)x3 , (- .237488 -
     ------------------------------------------------------------------------
                   3                             2                 
     .0799752*ii)x1  + (- .328086 + .225562*ii)x1 x2 + (- .425923 -
     ------------------------------------------------------------------------
                     2                             3               
     .361043*ii)x1*x2  + (- .183725 - .282828*ii)x2  + (- .443154 -
     ------------------------------------------------------------------------
                   2                                                  
     .0388674*ii)x1 x3 + (.020115 - .589232*ii)x1*x2*x3 + (- .281813 +
     ------------------------------------------------------------------------
                  2                                 2                
     .350848*ii)x2 x3 + (.330015 + .0506779*ii)x1*x3  + (- .0789336 -
     ------------------------------------------------------------------------
                      2                              3
     .0637525*ii)x2*x3  + (- .0240411 + .214985*ii)x3 }

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

o3 = {{{-.284672+.248656*ii, -.037512-.530589*ii, .756949+.035049*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .507391}}

o3 : List

Ways to use randomSd :