The primitive partition identities up to a largest part of 27
have been computed using a specialized algorithm that is much faster
than a general-purpose Buchberger procedure. See
Haus, Köppe, Weismantel: *A Primal All-Integer
Algorithm Based on Irreducible Solutions,*
Math. Programming, Series B, 96 (2003), no. 2, pp. 205-246.

The computer program that we used is available as a single C++ source file, hilbert.cc. It is free software and distributed under the GNU General Public License.

It was written in 1998/1999, and updated in 2002, so as to work with current C++ compilers.

**It is now available as part of 4ti2**.

We provide pre-computed tables of primitive partition identities in the following binary format.

The first byte of the file is the order *n* of the table.
The rest of the file consists of the vectors representing primitive
partition identities. The order of the vectors is arbitrary.
Because for each vector, its negative is also a solution, only the
vector whose greatest nonzero component is positive is stored.
Each vector is stored as *n* signed bytes (negative numbers being
encoded in 2's complement).

For each of the provided tables, we show the number of vectors and the computation time on a Sun Fire 480 R (UltraSparc III+, 1050 MHz).

- Table of PPIs up to a largest part of 17 (181.514 vectors, 3 MB, 11 seconds).
- Compressed table of PPIs up to a largest part of 23 (3.210.736 vectors, 74 MB, compressed 17 MB, 24 minutes)
- Compressed table of PPIs up to a largest part of 27 (16.536.803 vectors, 446 MB, compressed 98 MB, 8 hours 45 minutes)