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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 = {(.235764 + .32883*ii)x1  + (.092707 + .349435*ii)x1*x2 + (- .206794 +
     ------------------------------------------------------------------------
                  2                                           
     .197023*ii)x2  + (.109301 + .120644*ii)x1*x3 + (.113048 +
     ------------------------------------------------------------------------
                                                2                          3
     .123325*ii)x2*x3 + (- .110499 + .2001*ii)x3 , (.31556 - .0626803*ii)x1 
     ------------------------------------------------------------------------
                                 2                                  2  
     + (- .298852 + .128314*ii)x1 x2 + (- .441506 + .202166*ii)x1*x2  +
     ------------------------------------------------------------------------
                             3                           2                  
     (.281333 + .139862*ii)x2  + (.369275 - .187552*ii)x1 x3 + (- .0465339 -
     ------------------------------------------------------------------------
                                                     2                 
     .223841*ii)x1*x2*x3 + (- .171604 - .126652*ii)x2 x3 + (- .160717 -
     ------------------------------------------------------------------------
                     2                                2               
     .313766*ii)x1*x3  + (- .305953 - .516603*ii)x2*x3  + (- .139419 +
     ------------------------------------------------------------------------
                  3
     .178056*ii)x3 }

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

o3 = {{.481012+.0323015*ii, -.375154-.389911*ii, .677128+.127712*ii}}

o3 : List

See also