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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 = {(.344536 + .11799*ii)x1  + (.0247027 - .201776*ii)x1*x2 + (.115067 -
     ------------------------------------------------------------------------
                  2                                              
     .207174*ii)x2  + (.129621 + .0811806*ii)x1*x3 + (- .112345 -
     ------------------------------------------------------------------------
                                                 2              
     .193688*ii)x2*x3 + (.220648 + .0107197*ii)x3 , (- .043329 +
     ------------------------------------------------------------------------
                    3                            2                 
     .00229527*ii)x1  + (.156519 - .0336866*ii)x1 x2 + (- .306888 +
     ------------------------------------------------------------------------
                     2                              3             
     .561072*ii)x1*x2  + (- .0359064 + .169236*ii)x2  + (.472587 +
     ------------------------------------------------------------------------
                   2                                               
     .0171967*ii)x1 x3 + (.309198 + .160914*ii)x1*x2*x3 + (.24116 +
     ------------------------------------------------------------------------
                  2                                2             
     .180827*ii)x2 x3 + (.324945 - .178286*ii)x1*x3  + (.799149 +
     ------------------------------------------------------------------------
                      2                             3
     .0756829*ii)x2*x3  + (- .115182 + .359686*ii)x3 }

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

o3 = {{-.18793+.244693*ii, .150504-.475583*ii, .805969-.079941*ii}}

o3 : List

See also