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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 = {(.310965 + .0740141*ii)x1  + (.100839 + .415463*ii)x1*x2 + (.0657976 -
     ------------------------------------------------------------------------
                  2                                             
     .338929*ii)x2  + (- .263414 + .187384*ii)x1*x3 + (.575574 -
     ------------------------------------------------------------------------
                                                 2              
     .123174*ii)x2*x3 + (.044981 - .0106487*ii)x3 , (- .216295 +
     ------------------------------------------------------------------------
                 3                           2                 
     .12107*ii)x1  + (.609143 - .245816*ii)x1 x2 + (- .169338 -
     ------------------------------------------------------------------------
                      2                             3                
     .0849978*ii)x1*x2  + (.00131994 - .125474*ii)x2  + (- .0791151 -
     ------------------------------------------------------------------------
                   2                                                
     .0901758*ii)x1 x3 + (.528001 - .267566*ii)x1*x2*x3 + (.313324 -
     ------------------------------------------------------------------------
                 2                                  2             
     .17788*ii)x2 x3 + (.0745387 - .0926866*ii)x1*x3  + (.381682 +
     ------------------------------------------------------------------------
                     2                           3
     .191797*ii)x2*x3  + (.168379 - .162117*ii)x3 }

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

o3 = {{-.135343+.315241*ii, -.0493921+.283293*ii, .893666+.031169*ii}}

o3 : List

See also