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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 = {(- .255718 + .126748*ii)x1  + (- .167043 - .0819776*ii)x1*x2 +
     ------------------------------------------------------------------------
                               2                                             
     (.00756094 + .132962*ii)x2  + (.0377973 - .317373*ii)x1*x3 + (- .26086 -
     ------------------------------------------------------------------------
                                                   2               
     .0119424*ii)x2*x3 + (- .219162 + .048867*ii)x3 , (- .0373878 +
     ------------------------------------------------------------------------
                   3                             2               
     .0903117*ii)x1  + (- .387351 + .648452*ii)x1 x2 + (.285631 +
     ------------------------------------------------------------------------
                     2                              3             
     .437252*ii)x1*x2  + (- .0861342 - .128566*ii)x2  + (.493493 -
     ------------------------------------------------------------------------
                  2                                                    
     .344726*ii)x1 x3 + (- .490981 + .430717*ii)x1*x2*x3 + (- .187219 +
     ------------------------------------------------------------------------
                  2                                   2               
     .304361*ii)x2 x3 + (- .369926 + .0873684*ii)x1*x3  + (- .365494 -
     ------------------------------------------------------------------------
                      2                             3
     .0287009*ii)x2*x3  + (- .286244 + .154762*ii)x3 }

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

o3 = {{-.0404814-.338115*ii, .177112-.83436*ii, .394751+.0262055*ii}}

o3 : List

See also