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 = {(- .315783 + .0353822*ii)x1  + (- .358056 - .168352*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                               
     .364834 - .0797679*ii)x2  + (- .254559 + .0137965*ii)x1*x3 + (- .26965 +
     ------------------------------------------------------------------------
                                                     2               
     .0342655*ii)x2*x3 + (- .0487075 - .0912654*ii)x3 , (- .0547416 -
     ------------------------------------------------------------------------
                  3                              2               
     .183494*ii)x1  + (- .0224362 + .200427*ii)x1 x2 + (.146598 +
     ------------------------------------------------------------------------
                     2                              3             
     .352644*ii)x1*x2  + (- .165847 - .0523439*ii)x2  + (.129505 +
     ------------------------------------------------------------------------
                  2                                                  
     .346821*ii)x1 x3 + (- .925589 - .569926*ii)x1*x2*x3 + (.611819 -
     ------------------------------------------------------------------------
                   2                                2               
     .0482909*ii)x2 x3 + (.293761 - .294161*ii)x1*x3  + (- .106364 +
     ------------------------------------------------------------------------
                     2                              3
     .176702*ii)x2*x3  + (- .178874 - .0110113*ii)x3 }

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

o3 = {{{-.320965+.186184*ii, .25049-.262151*ii, .851439+.076811*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .388086}}

o3 : List

Ways to use randomSd :