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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                              2                                             
o1 = {(.414069 - .183405*ii)x1  + (- .052354 - .304648*ii)x1*x2 + (- .243649
     ------------------------------------------------------------------------
                    2                                                
     + .177889*ii)x2  + (- .0353242 - .0876507*ii)x1*x3 + (.0422158 -
     ------------------------------------------------------------------------
                                                 2                          3
     .080393*ii)x2*x3 + (.204484 - .0947491*ii)x3 , (.230504 + .139148*ii)x1 
     ------------------------------------------------------------------------
                                 2                                   2     
     + (- .454937 + .184547*ii)x1 x2 + (- .452349 - .0178865*ii)x1*x2  + (-
     ------------------------------------------------------------------------
                            3                          2                 
     .418432 + .099627*ii)x2  + (.406572 + .16812*ii)x1 x3 + (- .238157 -
     ------------------------------------------------------------------------
                                                  2                  
     .379992*ii)x1*x2*x3 + (.146073 - .16766*ii)x2 x3 + (- .0191964 -
     ------------------------------------------------------------------------
                     2                                  2                 
     .238741*ii)x1*x3  + (- .137156 + .00911327*ii)x2*x3  + (- .00179177 -
     ------------------------------------------------------------------------
                  3
     .225032*ii)x3 }

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

o3 = {{-.113631+.613264*ii, -.0375711+.362874*ii, .688653-.06053*ii}}

o3 : List

See also