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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 = {(.0836054 + .0759014*ii)x1  + (.177827 + .529376*ii)x1*x2 + (- .124045
     ------------------------------------------------------------------------
                    2                                               
     + .109362*ii)x2  + (- .0551656 + .15308*ii)x1*x3 + (- .233404 -
     ------------------------------------------------------------------------
                                                   2             
     .207119*ii)x2*x3 + (- .0677413 - .134836*ii)x3 , (.0980919 +
     ------------------------------------------------------------------------
                  3                            2               
     .138556*ii)x1  + (- .14917 - .237854*ii)x1 x2 + (.403046 -
     ------------------------------------------------------------------------
                     2                               3               
     .179997*ii)x1*x2  + (- .00181835 - .301291*ii)x2  + (- .600088 +
     ------------------------------------------------------------------------
                   2                                                   
     .0782572*ii)x1 x3 + (.590958 - .0499578*ii)x1*x2*x3 + (- .117121 +
     ------------------------------------------------------------------------
                  2                              2             
     .301235*ii)x2 x3 + (.2794 - .119579*ii)x1*x3  + (.113822 -
     ------------------------------------------------------------------------
                     2                             3
     .377036*ii)x2*x3  + (- .426025 - .170133*ii)x3 }

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

o3 = {{.440224-.380865*ii, .244823+.290175*ii, .70479-.142389*ii}}

o3 : List

Ways to use randomSd :