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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- 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 the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                              2                                                             2                                  
o1 = {(.125583 - .231255*ii)x1  + (- .0106283 + .495511*ii)x1*x2 + (.140689 - .0470904*ii)x2  + (- .395888 - .177428*ii)x1*x3 +
     ----------------------------------------------------------------------------------------------------------------------------
                                                             2                            3                            2       
     (- .3032 - .259731*ii)x2*x3 + (.00470858 - .244829*ii)x3 , (- .130206 - .186531*ii)x1  + (- .17129 + .368432*ii)x1 x2 + (-
     ----------------------------------------------------------------------------------------------------------------------------
                               2                             3                           2                                      
     .246583 + .719498*ii)x1*x2  + (- .143827 + .153796*ii)x2  + (- .157571 - .1962*ii)x1 x3 + (- .0910157 + .825927*ii)x1*x2*x3
     ----------------------------------------------------------------------------------------------------------------------------
                                2                                   2                                 2             
     + (.0624194 - .242607*ii)x2 x3 + (- .234055 - .0910887*ii)x1*x3  + (- .0833408 + .155138*ii)x2*x3  + (.134672 +
     ----------------------------------------------------------------------------------------------------------------------------
                   3
     .0401753*ii)x3 }

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

o3 = {{.751732+.463283*ii, .284351-.0717164*ii, .348144-.114302*ii}}

o3 : List

See also