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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 = {(- .0412119 + .267276*ii)x1  + (.144813 - .311035*ii)x1*x2 + (.20491 -
     ------------------------------------------------------------------------
                   2                                            
     .0377017*ii)x2  + (.276597 - .0545837*ii)x1*x3 + (.245051 -
     ------------------------------------------------------------------------
                                               2                          3  
     .147889*ii)x2*x3 + (.168697 - .18572*ii)x3 , (- .2204 - .180312*ii)x1  +
     ------------------------------------------------------------------------
                             2                                   2           
     (.503037 - .534593*ii)x1 x2 + (- .0105158 - .280127*ii)x1*x2  + (.136594
     ------------------------------------------------------------------------
                     3                              2                 
     + .0467294*ii)x2  + (- .114111 + .0566707*ii)x1 x3 + (- .165079 +
     ------------------------------------------------------------------------
                                                     2               
     .587947*ii)x1*x2*x3 + (- .221306 + .218074*ii)x2 x3 + (.159371 -
     ------------------------------------------------------------------------
                     2                                 2             
     .842473*ii)x1*x3  + (- .0203897 + .166009*ii)x2*x3  + (.100755 -
     ------------------------------------------------------------------------
                   3
     .0945243*ii)x3 }

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

o3 = {{-.224538-.147297*ii, .021786+.611818*ii, .733874+.120495*ii}}

o3 : List

Ways to use randomSd :