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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 = {(- .023559 - .181693*ii)x1  + (- .29438 - .0905261*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                          
     .0300061 + .350794*ii)x2  + (.151783 - .52091*ii)x1*x3 + (.325278 +
     ------------------------------------------------------------------------
                                                   2              
     .386178*ii)x2*x3 + (- .0490107 + .327389*ii)x3 , (- .131563 +
     ------------------------------------------------------------------------
                  3                           2                  
     .233143*ii)x1  + (.203963 + .256523*ii)x1 x2 + (- .0338655 -
     ------------------------------------------------------------------------
                      2                              3               
     .0486704*ii)x1*x2  + (- .223756 - .0994743*ii)x2  + (- .151039 -
     ------------------------------------------------------------------------
                  2                                                 
     .259663*ii)x1 x3 + (- .346578 + .132912*ii)x1*x2*x3 + (.38663 -
     ------------------------------------------------------------------------
                   2                                2                
     .0318245*ii)x2 x3 + (.287999 + .398673*ii)x1*x3  + (- .0859605 -
     ------------------------------------------------------------------------
                      2                            3
     .0892757*ii)x2*x3  + (.224556 - .0530986*ii)x3 }

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

o3 = {{.403044+.0150157*ii, .192698+.51817*ii, .675592-.274358*ii}}

o3 : List

See also