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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 = {(.0762036 - .122853*ii)x1  + (.196931 + .0616396*ii)x1*x2 + (- .284379
     ------------------------------------------------------------------------
                    2                                             
     + .164731*ii)x2  + (.276807 + .340855*ii)x1*x3 + (- .259539 +
     ------------------------------------------------------------------------
                                                   2           
     .0502126*ii)x2*x3 + (.234339 - .00298373*ii)x3 , (.31418 -
     ------------------------------------------------------------------------
                   3                            2               
     .0590934*ii)x1  + (.0236197 - .496751*ii)x1 x2 + (.185378 +
     ------------------------------------------------------------------------
                     2                           3               
     .360664*ii)x1*x2  + (.0677576 - .30953*ii)x2  + (- .361409 +
     ------------------------------------------------------------------------
                 2                                                    
     .44784*ii)x1 x3 + (.00876257 - .571217*ii)x1*x2*x3 + (- .325959 -
     ------------------------------------------------------------------------
                  2                                 2               
     .289165*ii)x2 x3 + (.0679853 + .234354*ii)x1*x3  + (- .353592 -
     ------------------------------------------------------------------------
                    2                             3
     .27927*ii)x2*x3  + (.0843584 + .0311062*ii)x3 }

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

o3 = {{-.204045+.386604*ii, -.576032+.059934*ii, .680462-.102317*ii}}

o3 : List

See also