Program Files and Packages

Ratpoints

This is a program that uses an optimized quadratic sieve algorithm in order to find rational points on hyperelliptic curves.

The program is distributed under the GNU GPL, version 2 (or later).

Read the documentation.  arXiv (the arXiv version may not be completely up to date)

The current version is ratpoints-3.1.1 from October 9, 2026. This version has been optimized with the help of Claude Code and the single-threaded version runs twice to ten times faster compared to ratpoints-2.2.4. From version 3.1.0, ratpoints can also run the sieve in multiple threads, thus speeding up the search further (in particular for large height bounds).
Caveat: this version no longer supports 32-bit architectures; the last version doing that is ratpoints-2.2.4 from September 19, 2026 (available via the v2.2.4 tag on GitHub).

Download ratpoints-3.1.1.tar.gz.

ratpoints on GitHub.

J-Points

J-points searches for rational points on the Jacobian of a genus 2 curve. This is done by searching for points on the associated Kummer surface that lift to the Jacobian. The implementation is based on a fast quadratic sieve algorithm.

The program is distributed under the GNU GPL, version 2 (or later).

For documentation, see the README. For a description of the use of the -a option, see also this paper.

The current version is j-points-3.0.2 from November 8, 2026. Version 3.0.2 fixes some bugs (not relevant for realistic runs) found during the verification of the program in Lean and makes a constant smaller (giving a speed-up in certain cases) based on the verification.
Version 3.0.1 fixes several bugs of 3.0 that could cause points to be missed in rare cases.
Version 3.0 has been optimized with the help of Claude Code and runs much faster compared to previous versions. Like ratpoints, it can use multiple threads.

Download j-points-3.0.2.tar.gz.

j-points on GitHub.

CLISP

CLISP is a Common Lisp implementation that was originally started by Bruno Haible and myself. I am no longer active as a developer. See the CLISP Website for more information.

reals.lisp

This is a Common Lisp program that implements “lazy reals”. You can construct real numbers from rational numbers, field operations, and the basic transcendental functions, and have them compute themselves to any desired precision afterwards. The code is essentially free (see the statement at the beginning of the file).
Note: This is meant as a case study, not as an efficient implementation.

The code is available under the 3-Clause BSD License.

Download reals.lisp.

See also https://github.com/stylewarning/computable-reals for a version maintained by Robert Smith (stylewarning).