next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = {(- .144821 + .101495*ii)x1  + (.173221 - .288105*ii)x1*x2 + (- .150996
     ------------------------------------------------------------------------
                    2                                           
     - .123752*ii)x2  + (.407152 - .271408*ii)x1*x3 + (.283032 +
     ------------------------------------------------------------------------
                                                   2               
     .268134*ii)x2*x3 + (- .0673791 - .247094*ii)x3 , (- .0769108 -
     ------------------------------------------------------------------------
                    3                            2                   
     .00218997*ii)x1  + (.0564048 - .333056*ii)x1 x2 + (- .00895171 -
     ------------------------------------------------------------------------
                     2                             3              
     .371975*ii)x1*x2  + (- .168426 + .138858*ii)x2  + (- .20591 -
     ------------------------------------------------------------------------
                  2                                                   
     .624949*ii)x1 x3 + (.568482 + .0952043*ii)x1*x2*x3 + (- .361019 +
     ------------------------------------------------------------------------
                  2                                   2              
     .299775*ii)x2 x3 + (- .123668 - .0832102*ii)x1*x3  + (- .73145 -
     ------------------------------------------------------------------------
                      2                              3
     .0158251*ii)x2*x3  + (- .119417 - .0430852*ii)x3 }

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

o3 = {{-.037061+.500758*ii, -.0995306+.0966631*ii, .845792-.115128*ii}}

o3 : List

Ways to use randomSd :