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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 = {(.109585 - .0370487*ii)x1  + (.401575 + .344832*ii)x1*x2 + (.0326941 +
     ------------------------------------------------------------------------
                   2                                            
     .0435814*ii)x2  + (.118279 - .24824*ii)x1*x3 + (- .223744 +
     ------------------------------------------------------------------------
                                                     2             
     .0314925*ii)x2*x3 + (- .0854583 + .0245169*ii)x3 , (.0630998 +
     ------------------------------------------------------------------------
                  3                              2               
     .102856*ii)x1  + (- .131314 - .0270164*ii)x1 x2 + (.125109 -
     ------------------------------------------------------------------------
                     2                           3             
     .262763*ii)x1*x2  + (.31898 + .0418348*ii)x2  + (.204279 -
     ------------------------------------------------------------------------
                  2                                                    
     .515151*ii)x1 x3 + (- .564311 - .462983*ii)x1*x2*x3 + (- .354559 +
     ------------------------------------------------------------------------
                   2                               2               
     .0927713*ii)x2 x3 + (.200507 + .89504*ii)x1*x3  + (- .290885 -
     ------------------------------------------------------------------------
                     2                            3
     .325306*ii)x2*x3  + (.0765599 - .185278*ii)x3 }

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

o3 = {{.0916444+.153394*ii, -.148531+.0604988*ii, .962565-.125771*ii}}

o3 : List

See also