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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 = {(.208114 + .252341*ii)x1  + (.0633197 - .183496*ii)x1*x2 + (.437024 +
     ------------------------------------------------------------------------
                 2                                              
     .35381*ii)x2  + (- .106042 - .061948*ii)x1*x3 + (.0305084 +
     ------------------------------------------------------------------------
                                                   2            
     .0822606*ii)x2*x3 + (- .138711 - .103344*ii)x3 , (.190948 -
     ------------------------------------------------------------------------
                  3                           2                 
     .341593*ii)x1  + (.0760559 + .11677*ii)x1 x2 + (- .296073 +
     ------------------------------------------------------------------------
                       2                             3             
     .00696879*ii)x1*x2  + (- .167789 - .175392*ii)x2  + (.038766 -
     ------------------------------------------------------------------------
                  2                                                  
     .109157*ii)x1 x3 + (- .235467 + .478228*ii)x1*x2*x3 + (.222345 +
     ------------------------------------------------------------------------
                  2                                 2               
     .153789*ii)x2 x3 + (.0445469 + .480439*ii)x1*x3  + (- .148536 -
     ------------------------------------------------------------------------
                     2                             3
     .539147*ii)x2*x3  + (.0617048 + .0840721*ii)x3 }

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

o3 = {{.584486-.400569*ii, -.179195-.142284*ii, .645084-.171557*ii}}

o3 : List

See also