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NumericalAlgebraicGeometry :: randomSd

randomSd -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials T_i such that deg T_i = d_i. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                              2                                            
o1 = {(.161277 - .031938*ii)x1  + (.164636 + .100686*ii)x1*x2 + (.0254825 +
     ------------------------------------------------------------------------
                    2                                             
     .00924784*ii)x2  + (- .0992991 + .385847*ii)x1*x3 + (.15643 -
     ------------------------------------------------------------------------
                                                  2               
     .118401*ii)x2*x3 + (- .156243 - .306161*ii)x3 , (- .0737882 +
     ------------------------------------------------------------------------
                   3                           2                
     .0531542*ii)x1  + (.668887 - .211408*ii)x1 x2 + (.0475452 -
     ------------------------------------------------------------------------
                      2                               3             
     .0442403*ii)x1*x2  + (- .0772665 - .0186963*ii)x2  + (.109937 -
     ------------------------------------------------------------------------
                  2                                                
     .197457*ii)x1 x3 + (.819345 + .435833*ii)x1*x2*x3 + (.381142 -
     ------------------------------------------------------------------------
                  2                                2             
     .278824*ii)x2 x3 + (.330539 - .402545*ii)x1*x3  + (.377959 -
     ------------------------------------------------------------------------
                     2                             3
     .334674*ii)x2*x3  + (- .164133 - .345817*ii)x3 }

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

o3 = {{.315386-.272226*ii, -.014003+.477892*ii, .773059-.015097*ii}}

o3 : List

Ways to use randomSd :