search

archmageirvine / joeis

Java implementations of sequences in the OEIS
49 stars 6 forks source link

readme

jOEIS

A collection of pure Java programs implementing sequences from The On-Line Encyclopedia of Integer Sequences (OEIS).

This is likely the largest coherent collection of programs for OEIS sequences beyond the Maple, Mathematica, and Pari programs directly associated with many entries. Currently over 150,000 sequences are implemented.

If you plan to simply run some existing sequences, then the best option is to download the latest release.

Installation

Instructions for installation: INSTALLATION

Notes on development: DEVELOPMENT

Background

The following plot shows how the number of implemented sequences has changed over the years.

history-plot

The following plot shows the number of sequences implemented (in bins of 1000):

done-plot

A similar plot with one pixel for each sequence. Green indicates an implemented sequence. Black indicates to be done, feel free to help.

implemented-plot

Implementations are not necessarily the best known algorithm for particular sequences. For many important sequences you are not going to be able to compute new terms using the implementations provided. However, included here are implementations that have been used to compute new previously unknown terms, including some for sequences considered hard.

Related Software

Because Java does not come with libraries supporting all the things we need to do to construct integer sequences, a lot of functionality has been built from the ground up. While a lot of this is implemented specifically for this project, there are important pieces of code which have been re-implemented or ported from other projects.

Although Java has its own BigInteger class for large integers, this project uses a big integer type, Z.java based originally on Lenstra's lip C package.

Most sequences requiring real number arithmetic are handled using classes based on Hans-J. Boehm's constructible real arithmetic. A smaller number of real number based sequences make use of Mikko Tommila's apfloat library.

A large number of linear recurrences, generating functions, and tiling sequences are based on code developed by Georg Fischer.

Certain parts of the nauty package for computing automorphism groups of graphs and digraphs were ported to Java. Included here by permission (see associated copyright). For serious work needing this functionality, I would recommend using the C implementations available from nauty.

Similarly, parts of the plantri package for generating planar graphs were ported to Java. Included here by permission (see associated copyright). Again a canonical implementation is available from plantri.

Certain sequences requiring factorization of make use of Tilman Neumann's Java Math Library, larger factorizations are backed by queries to factordb.com.

Certain sequences involving counting positions in chess make use of the Chesspresso library by Bernhard Seybold.

We also recommend having a look at the LODA project.

Testing

The tests can be run using ant and the all-tests target of build.xml. The individual sequence implementations are tested again the data lines of the corresponding OEIS entries. In order to run the tests, the stripped.gz is retrieved from the OEIS server and layed out in a way the tests expect. In addition to testing individual sequences, the test suite also covers functionality of shared library code. Running all the tests can take more than an hour.

Other Acknowledgements

This project has benefited immensely and on numerous occasions by other contributors to the OEIS and members of the seqfan mailing list. This ranges from explanations of sequences, detective work, finding papers, vetting edits resulting from this project.

References