ternary

The code is related to the article preprint Ternary quadratic forms representing arithmetic progressions by T. Hejda a V. Kala.

Description

There are two basic parts. First, universal is the script used in §3.1 of the article. Second, count is the script used in §3.3 and §3.4 of the article. The code used in §3.2 is not included.

universal

Two files are needed from the repo: universal.py and create_number_lists.sage. If you do not have SageMath installed, you also need number_lists.py. How to run:

1. Run create_number_lists.sage. This will generate the file number_lists.py.
2. Check that n_threads at the beginning of universal.py matches the number of cores of your computer.
3. Run universal.py.
4. The output shows all primes the program computed, and the candidate forms, if there are any.

count

Three files are needed from the repo: count.cpp, count.sh and create_run_count.sage. If you do not have SageMath installed, you also need run_count.sh. How to run:

1. Run create_run_count.sage. This will generate the file run_count.sh.
2. Make run_count.sh executable by chmod +x run_count.sh
3. Check that THREADS at the beginning of count.cpp matches the number of cores of your computer.
4. Run run_count.sh.
5. The output is in files c_<a>_<b>_<c>_<p>.txt. If the file contains a line with ZERO <n>, this indicates that the form <a,b,c*p> is a candidate for a (p,l)-universal for n different l's. These candidates can be identified for instance by grep ZERO c_*.txt.