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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 = {(- .16447 - .1608*ii)x1  + (- .467573 - .27231*ii)x1*x2 + (- .204755 -
     ------------------------------------------------------------------------
                   2                                                
     .0966254*ii)x2  + (- .0849938 - .378179*ii)x1*x3 + (- .110902 -
     ------------------------------------------------------------------------
                                                  2             
     .174149*ii)x2*x3 + (.311326 + .00165552*ii)x3 , (.0251742 +
     ------------------------------------------------------------------------
                  3                             2               
     .269867*ii)x1  + (.0788958 - .0127314*ii)x1 x2 + (.472402 -
     ------------------------------------------------------------------------
                     2                             3              
     .202373*ii)x1*x2  + (- .230362 - .132427*ii)x2  + (.0419231 -
     ------------------------------------------------------------------------
                  2                                                  
     .125841*ii)x1 x3 + (- .564448 + .473276*ii)x1*x2*x3 + (.271237 -
     ------------------------------------------------------------------------
                  2                                  2               
     .307155*ii)x2 x3 + (- .329762 + .308251*ii)x1*x3  + (- .071471 -
     ------------------------------------------------------------------------
                     2                              3
     .520761*ii)x2*x3  + (- .0440833 - .087269*ii)x3 }

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

o3 = {{-.519237+.209823*ii, -.429+.234301*ii, .557126-.370188*ii}}

o3 : List

See also