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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 = {(- .206686 - .173167*ii)x1  + (- .264071 + .0889282*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                             
     .0341644 + .114318*ii)x2  + (.230214 - .169248*ii)x1*x3 + (- .307948 +
     ------------------------------------------------------------------------
                                                     2              
     .00956547*ii)x2*x3 + (.0750718 + .00307867*ii)x3 , (- .181587 -
     ------------------------------------------------------------------------
                   3                              2                  
     .0906451*ii)x1  + (.000954343 + .105633*ii)x1 x2 + (- .0192594 -
     ------------------------------------------------------------------------
                     2                              3             
     .308961*ii)x1*x2  + (- .141563 - .0371894*ii)x2  + (.658087 -
     ------------------------------------------------------------------------
                   2                                                   
     .0393968*ii)x1 x3 + (- 1.02719 + .718638*ii)x1*x2*x3 + (.0605897 +
     ------------------------------------------------------------------------
                   2                                 2               
     .0384354*ii)x2 x3 + (.211691 + .0283359*ii)x1*x3  + (- .741165 +
     ------------------------------------------------------------------------
                     2                              3
     .259619*ii)x2*x3  + (- .0744603 - .217227*ii)x3 }

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

o3 = {{-.26072-.346776*ii, .190643-.307935*ii, .822106+.068877*ii}}

o3 : List

See also