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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 = {(.0492103 - .0802084*ii)x1  + (- .108454 + .130677*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                           
     .522839 + .120241*ii)x2  + (.236177 + .382917*ii)x1*x3 + (.117961 +
     ------------------------------------------------------------------------
                                                    2            
     .0705468*ii)x2*x3 + (- .123104 + .0842406*ii)x3 , (.194825 -
     ------------------------------------------------------------------------
                   3                              2               
     .0686422*ii)x1  + (- .191152 + .0931743*ii)x1 x2 + (.624647 +
     ------------------------------------------------------------------------
                      2                                3             
     .0539442*ii)x1*x2  + (- .221951 + .000618211*ii)x2  + (.148816 +
     ------------------------------------------------------------------------
                  2                                                
     .323185*ii)x1 x3 + (.253951 + .895269*ii)x1*x2*x3 + (.163114 +
     ------------------------------------------------------------------------
                  2                                    2             
     .258779*ii)x2 x3 + (- .0846395 + .0603538*ii)x1*x3  + (.450264 +
     ------------------------------------------------------------------------
                     2                             3
     .211623*ii)x2*x3  + (.0965886 + .0693653*ii)x3 }

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

o3 = {{.0638394-.350756*ii, -.133977-.0458508*ii, .923429-.011068*ii}}

o3 : List

See also