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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 = {(- .130724 + .128626*ii)x1  + (.144889 + .295537*ii)x1*x2 + (.144866 -
     ------------------------------------------------------------------------
                  2                                            
     .161495*ii)x2  + (.068983 - .201197*ii)x1*x3 + (.0939778 +
     ------------------------------------------------------------------------
                                                   2               
     .393344*ii)x2*x3 + (- .223487 - .0866493*ii)x3 , (- .0957875 -
     ------------------------------------------------------------------------
                  3                              2                 
     .127368*ii)x1  + (- .246892 + .0851533*ii)x1 x2 + (- .438789 +
     ------------------------------------------------------------------------
                     2                            3              
     .541356*ii)x1*x2  + (.0862797 + .182366*ii)x2  + (- .34328 +
     ------------------------------------------------------------------------
                   2                                                   
     .0176942*ii)x1 x3 + (.0991212 - .327725*ii)x1*x2*x3 + (- .214173 -
     ------------------------------------------------------------------------
                  2                                   2               
     .214488*ii)x2 x3 + (- .353308 + .0614377*ii)x1*x3  + (- .412307 +
     ------------------------------------------------------------------------
                     2                           3
     .684407*ii)x2*x3  + (.263121 + .195267*ii)x3 }

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

o3 = {{.613497+.244602*ii, .233672-.295396*ii, .538156-.363755*ii}}

o3 : List

See also