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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 = {(- .295524 - .121959*ii)x1  + (.298314 + .282403*ii)x1*x2 + (.142016 +
     ------------------------------------------------------------------------
                  2                                            
     .112737*ii)x2  + (.0401477 - .119024*ii)x1*x3 + (.204543 -
     ------------------------------------------------------------------------
                                                   2              
     .289822*ii)x2*x3 + (- .0676343 + .158865*ii)x3 , (- .314566 +
     ------------------------------------------------------------------------
                  3                           2               
     .050121*ii)x1  + (.134045 + .169503*ii)x1 x2 + (.526922 -
     ------------------------------------------------------------------------
                     2                            3              
     .126857*ii)x1*x2  + (- .19257 - .288527*ii)x2  + (- .17532 +
     ------------------------------------------------------------------------
                  2                                                
     .221419*ii)x1 x3 + (.402608 + .378466*ii)x1*x2*x3 + (.131549 -
     ------------------------------------------------------------------------
                 2                                  2               
     .21531*ii)x2 x3 + (- .193206 + .187163*ii)x1*x3  + (- .403444 -
     ------------------------------------------------------------------------
                     2                             3
     .400421*ii)x2*x3  + (- .310221 + .133764*ii)x3 }

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

o3 = {{{.315357-.595094*ii, .23152-.237903*ii, .659876-.02789*ii}, #steps =>
     ------------------------------------------------------------------------
     19, status  => REGULAR, last t => 1, cond#^{-1} => .258845}}

o3 : List

Ways to use randomSd :