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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 = {(- .150092 - .314681*ii)x1  + (.147172 + .121044*ii)x1*x2 + (- .164131
     ------------------------------------------------------------------------
                    2                                              
     - .217838*ii)x2  + (.0901776 + .403387*ii)x1*x3 + (- .249449 +
     ------------------------------------------------------------------------
                                                     2            
     .0771729*ii)x2*x3 + (- .0363424 - .0662384*ii)x3 , (.124878 -
     ------------------------------------------------------------------------
                  3                             2                  
     .440897*ii)x1  + (- .224038 + .585917*ii)x1 x2 + (- .0344326 +
     ------------------------------------------------------------------------
                     2                               3             
     .238032*ii)x1*x2  + (- .137077 - .00121028*ii)x2  + (.307773 +
     ------------------------------------------------------------------------
                   2                                                   
     .0839665*ii)x1 x3 + (- .424856 + .225032*ii)x1*x2*x3 + (.0259524 +
     ------------------------------------------------------------------------
                  2                               2               
     .200334*ii)x2 x3 + (.548911 + .32237*ii)x1*x3  + (- .285722 +
     ------------------------------------------------------------------------
                     2                             3
     .257345*ii)x2*x3  + (.0908661 - .0527598*ii)x3 }

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

o3 = {{.349362-.186723*ii, .281208+.338479*ii, .797196+.117957*ii}}

o3 : List

See also