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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 = {(- .0424842 + .125116*ii)x1  + (- .143478 + .399338*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .0759677 - .354495*ii)x2  + (- .380065 + .116974*ii)x1*x3 + (- .0265356
     ------------------------------------------------------------------------
                                                    2             
     + .06108*ii)x2*x3 + (- .0239851 - .137974*ii)x3 , (.0837725 +
     ------------------------------------------------------------------------
                  3                          2               
     .104262*ii)x1  + (.471481 - .17841*ii)x1 x2 + (.189328 +
     ------------------------------------------------------------------------
                    2                           3               
     .22251*ii)x1*x2  + (.355815 + .130096*ii)x2  + (- .122197 +
     ------------------------------------------------------------------------
                  2                                                  
     .260442*ii)x1 x3 + (.520343 - .292133*ii)x1*x2*x3 + (- .108087 +
     ------------------------------------------------------------------------
                  2                                2             
     .151791*ii)x2 x3 + (.197802 + .498408*ii)x1*x3  + (.717209 -
     ------------------------------------------------------------------------
                    2                           3
     .12153*ii)x2*x3  + (.111664 - .048884*ii)x3 }

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

o3 = {{.408882-.201694*ii, -.170234-.287259*ii, .824908+.012798*ii}}

o3 : List

See also