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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 = {(- .0835157 - .150736*ii)x1  + (.0284931 - .12705*ii)x1*x2 + (- .101021
     ------------------------------------------------------------------------
                     2                                           
     - .0401791*ii)x2  + (.355638 + .238431*ii)x1*x3 + (.333825 -
     ------------------------------------------------------------------------
                                                  2              
     .120244*ii)x2*x3 + (- .19412 - .0494887*ii)x3 , (- .188943 -
     ------------------------------------------------------------------------
                    3                              2               
     .00141839*ii)x1  + (- .201453 + .0453501*ii)x1 x2 + (.686609 -
     ------------------------------------------------------------------------
                     2                         3                
     .202343*ii)x1*x2  + (.29338 + .36044*ii)x2  + (- .0203524 +
     ------------------------------------------------------------------------
                  2                                                   
     .154338*ii)x1 x3 + (- .12617 - .00289364*ii)x1*x2*x3 + (.127546 +
     ------------------------------------------------------------------------
                  2                               2             
     .044874*ii)x2 x3 + (.389612 - .33231*ii)x1*x3  + (.406696 +
     ------------------------------------------------------------------------
                     2                             3
     .220322*ii)x2*x3  + (- .273659 - .261015*ii)x3 }

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

o3 = {{.133924+.120464*ii, .417201+.107046*ii, .883222-.044225*ii}}

o3 : List

See also