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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 = {(.38762 - .0956219*ii)x1  + (.247067 + .0564447*ii)x1*x2 + (- .0734224
     ------------------------------------------------------------------------
                     2                                              
     + .0333153*ii)x2  + (.0447986 + .0670576*ii)x1*x3 + (.0655858 +
     ------------------------------------------------------------------------
                                                   2              
     .53977*ii)x2*x3 + (- .165094 + .00130839*ii)x3 , (- .127756 -
     ------------------------------------------------------------------------
                  3                              2               
     .066913*ii)x1  + (- .0271788 - .451665*ii)x1 x2 + (.276079 +
     ------------------------------------------------------------------------
                    2                             3             
     .14208*ii)x1*x2  + (- .174016 + .268866*ii)x2  + (.309569 -
     ------------------------------------------------------------------------
                  2                                                     
     .126443*ii)x1 x3 + (- .0823286 - .820137*ii)x1*x2*x3 + (- .711248 +
     ------------------------------------------------------------------------
                  2                                   2               
     .375648*ii)x2 x3 + (- .218294 + .0748599*ii)x1*x3  + (- .100224 +
     ------------------------------------------------------------------------
                     2                             3
     .132504*ii)x2*x3  + (.000893238 - .08235*ii)x3 }

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

o3 = {{.169576-.118056*ii, .0695523-.240463*ii, .945795-.010908*ii}}

o3 : List

See also