HOW TO USE THE DATA BELOW 
 
   The file eutax8.gp is in PARI-GP format, and is to be down-loaded 
in a directory in which one can open PARI-GP. 

   For each of the four series of 8-dimensional, perfect lattices, 
we give four gp-vectors, denoted by 
   lh_e, lh_s, lh_w, and lh_ges for the Laihem lattices, 
and there are similar vectors bari_*, nap_*, and batu_*. 

WARNING. To use the 16 vectors described below, one should have first 
down-loaded the files listed in 2. and 3., below. 

* lh_e[i] contains the indices such that lh(i) is eutactic, 
* lh_s[i] contains the indices such that lh(i) is semi-eutactic, 
                                               non-eutactic, 
* lh_w[i] contains the indices such that lh(i) is weakly-eutactic,
                                               non-semi-eutactic.  
* lh_ges[i] is equal to 2, 1, or 0 according to whether 
  lh(i) is eutactic, semi-eutactic but not eutactic, 
  or weakly-eutactic but not semi-eutactic. 

The meaning of the vectors bari_*, nap_*, and batu_* is similar.