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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 = {(- .159064 + .0634344*ii)x1  + (.0168798 + .208318*ii)x1*x2 + (.19209 -
     ------------------------------------------------------------------------
                  2                                                
     .109992*ii)x2  + (- .0973948 + .357449*ii)x1*x3 + (- .515831 +
     ------------------------------------------------------------------------
                                                   2                
     .0684021*ii)x2*x3 + (- .324655 + .031123*ii)x3 , (- .00730937 -
     ------------------------------------------------------------------------
                  3                              2                  
     .162405*ii)x1  + (- .253175 - .0632567*ii)x1 x2 + (- .0253416 -
     ------------------------------------------------------------------------
                     2                              3               
     .013859*ii)x1*x2  + (- .238085 + .0843932*ii)x2  + (- .311749 +
     ------------------------------------------------------------------------
                  2                                                 
     .143598*ii)x1 x3 + (.754097 - .0751348*ii)x1*x2*x3 + (.379456 +
     ------------------------------------------------------------------------
                  2                                   2               
     .251901*ii)x2 x3 + (- .233178 + .0801558*ii)x1*x3  + (- .346163 -
     ------------------------------------------------------------------------
                     2                            3
     .670456*ii)x2*x3  + (.0505818 - .243941*ii)x3 }

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

o3 = {{.495219+.116778*ii, -.442561+.239546*ii, .533349-.451018*ii}}

o3 : List

See also