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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 = {(- .017782 - .0240561*ii)x1  + (.117392 + .0894329*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                             
     .0182664 - .213809*ii)x2  + (.146965 - .0179638*ii)x1*x3 + (.0162803 +
     ------------------------------------------------------------------------
                                                2              
     .55861*ii)x2*x3 + (.0249487 - .361574*ii)x3 , (- .318894 +
     ------------------------------------------------------------------------
                  3                              2                 
     .183534*ii)x1  + (- .0425708 - .225732*ii)x1 x2 + (- .147614 +
     ------------------------------------------------------------------------
                     2                           3              
     .319205*ii)x1*x2  + (.345294 - .187012*ii)x2  + (.0107794 -
     ------------------------------------------------------------------------
                   2                                               
     .0043345*ii)x1 x3 + (.165858 - .242316*ii)x1*x2*x3 + (.26341 +
     ------------------------------------------------------------------------
                  2                                  2             
     .491466*ii)x2 x3 + (- .174123 - .372167*ii)x1*x3  + (.299213 +
     ------------------------------------------------------------------------
                      2                           3
     .0181321*ii)x2*x3  + (.237304 + .186276*ii)x3 }

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

o3 = {{.527767+.299701*ii, .2526+.371225*ii, .637298+.154525*ii}}

o3 : List

See also