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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 = {(- .101902 + .145867*ii)x1  + (- .0390183 - .502979*ii)x1*x2 + (.153114
     ------------------------------------------------------------------------
                    2                                             
     - .269641*ii)x2  + (- .4517 - .259726*ii)x1*x3 + (- .548201 +
     ------------------------------------------------------------------------
                                                   2               
     .160737*ii)x2*x3 + (.00908325 + .0585312*ii)x3 , (- .0220556 +
     ------------------------------------------------------------------------
                  3                             2               
     .105606*ii)x1  + (- .132716 - .267915*ii)x1 x2 + (.409834 +
     ------------------------------------------------------------------------
                     2                           3                
     .382774*ii)x1*x2  + (.286477 - .174162*ii)x2  + (- .0559152 -
     ------------------------------------------------------------------------
                  2                                                   
     .480296*ii)x1 x3 + (- .0469787 - .285441*ii)x1*x2*x3 + (.183185 +
     ------------------------------------------------------------------------
                  2                                2               
     .205112*ii)x2 x3 + (- .169568 - .1521*ii)x1*x3  + (- .217276 -
     ------------------------------------------------------------------------
                      2                           3
     .0126069*ii)x2*x3  + (.153595 + .100325*ii)x3 }

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

o3 = {{.396315-.399944*ii, -.272589+.151765*ii, .755181+.123869*ii}}

o3 : List

See also