next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 a unit sphere in the Bombieri-Weyl norm.
i1 : T = randomSd {2,3}

                              2                                             
o1 = {(.10473 - .0575884*ii)x1  + (- .029774 + .0271015*ii)x1*x2 + (.0502097
     ------------------------------------------------------------------------
                    2                                            
     - .051335*ii)x2  + (.0794858 + .268616*ii)x1*x3 + (.038631 -
     ------------------------------------------------------------------------
                                                 2                          3
     .60407*ii)x2*x3 + (- .181431 - .153574*ii)x3 , (- .144086 - .2793*ii)x1 
     ------------------------------------------------------------------------
                                 2                                 2  
     + (- .284174 + .778583*ii)x1 x2 + (.591934 + .0399738*ii)x1*x2  +
     ------------------------------------------------------------------------
                              3                          2                 
     (.343601 - .0600675*ii)x2  + (.111811 + .13057*ii)x1 x3 + (- .455239 -
     ------------------------------------------------------------------------
                                                       2               
     .246386*ii)x1*x2*x3 + (- .117235 - .00506995*ii)x2 x3 + (.185738 +
     ------------------------------------------------------------------------
                     2                                 2               
     .128729*ii)x1*x3  + (- .162792 + .0583883*ii)x2*x3  + (- .109523 +
     ------------------------------------------------------------------------
                  3
     .189678*ii)x3 }

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

o3 = {{{.120954-.418885*ii, -.265437+.0827293*ii, .843671+.144303*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .315073}}

o3 : List

Ways to use randomSd :