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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 = {(.402542 - .217866*ii)x1  + (- .146927 + .0552896*ii)x1*x2 + (.0483764
     ------------------------------------------------------------------------
                     2                                                
     - .0129752*ii)x2  + (- .170611 - .0945563*ii)x1*x3 + (- .121574 -
     ------------------------------------------------------------------------
                                                  2             
     .0445272*ii)x2*x3 + (.210485 + .0297207*ii)x3 , (.0686128 +
     ------------------------------------------------------------------------
                  3                              2                 
     .227743*ii)x1  + (- .162727 + .0731736*ii)x1 x2 + (- .419327 +
     ------------------------------------------------------------------------
                     2                            3             
     .396791*ii)x1*x2  + (.281835 - .0251299*ii)x2  + (.359266 +
     ------------------------------------------------------------------------
                   2                                                   
     .0908317*ii)x1 x3 + (- .106877 - .199015*ii)x1*x2*x3 + (- .28798 +
     ------------------------------------------------------------------------
                  2                                  2               
     .357342*ii)x2 x3 + (- .565878 + .612157*ii)x1*x3  + (- .207867 -
     ------------------------------------------------------------------------
                     2                              3
     .467973*ii)x2*x3  + (.0338367 + .00651343*ii)x3 }

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

o3 = {{.13227-.0607619*ii, .817586-.055883*ii, .511566+.213406*ii}}

o3 : List

Ways to use randomSd :