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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 = {(.017858 - .186711*ii)x1  + (- .237341 - .460806*ii)x1*x2 + (- .107538
     ------------------------------------------------------------------------
                    2                                          
     + .251043*ii)x2  + (.158043 + .04636*ii)x1*x3 + (.258023 +
     ------------------------------------------------------------------------
                                                   2              
     .221878*ii)x2*x3 + (- .233454 - .0653528*ii)x3 , (- .180383 -
     ------------------------------------------------------------------------
                 3                              2               
     .37141*ii)x1  + (- .287635 - .0792032*ii)x1 x2 + (.524437 +
     ------------------------------------------------------------------------
                     2                           3               
     .103542*ii)x1*x2  + (.108675 + .207946*ii)x2  + (- .104997 +
     ------------------------------------------------------------------------
                   2                                                  
     .0297854*ii)x1 x3 + (.808004 - .561311*ii)x1*x2*x3 + (- .129049 -
     ------------------------------------------------------------------------
                  2                                   2               
     .190702*ii)x2 x3 + (- .0926517 + .116399*ii)x1*x3  + (- .110344 -
     ------------------------------------------------------------------------
                     2                              3
     .215319*ii)x2*x3  + (- .0389145 - .252646*ii)x3 }

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

o3 = {{.504616-.085506*ii, -.047371+.407022*ii, .705759-.268411*ii}}

o3 : List

See also