A C++ Library For Computational Number Theory

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News

February 2010

End of LiDIA maintenance

The LiDIA project is now officially dormant.

The release packages and the SVN repository will stay online, if only for historical purposes. Neither are there plans to shut down the mailing lists in the near future. However, the lidiaadm mailbox won't be monitored anymore.

LiDIA 2.3 released

LiDIA 2.3 is available for download!

The most important changes in this release are:

• several resource leak fixes provided by Martin Ettl
• added a number of declarations that used to exist as friend declarations only
• properly initialize members of galois_field_rep (reported by Grant Atoyan)
• fix input of bigfloats with leading zeros

Older News

More news and facts about LiDIA can be found on LiDIA's NEWS page.

Introduction

LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and time-intensive algorithms. LiDIA is developed by the LiDIA Group at the Darmstadt University of Technology.

The current release of LiDIA contains:

• Arithmetic Interfaces to cln, gmp, libI, piologie.
• Basic arithmetic over Z, Q, R, C, interval arithmetic, GF(2^n), GF(p^n)
• Factorization: Integer Factorization (Trial Division, Elliptic Curve Method, Self-Initializing Multipolynomial Quadratic Sieve with Lanczos algorithm), Factorization of Polynomials over finite fields (V. Shoup's algorithms), Factoring ideals of algebraic number fields.
• Lattice Basis Reduction: various versions of LLL/MLLL (Schnorr-Euchner, Benne de Weger)
• Linear Algebra over Z: basic operations, normal forms of matrices (G. Havas algorithms)
• Number Fields: Quadratic Number Fields including a new implementation of Buchmann's subexponential algorithm for computing classgroups using mpqs techniques, Higher-Degree Number Fields arithmetic and maximal order.
• Polynomials: template classes for univariate polynomials with special algorithms for different domains.
• Elliptic Curves: elliptic curves over the rationals and over finite fields (includes code written by J.Cremona and N. Smart). There is also a package for counting points on elliptic curves as well as a package for generating cryptographically strong curves.
• Primality Proofing: Besides the standard probabilistic primality tests in the base package there is a new elliptic curve based primality proofer in the GEC package.
• Other Generic Data Types: vectors, matrices, power series, and hash tables implemented as templates.

LiDIA's documentation consists of a 700-page manual describing the philosophy, the usage, and the entire functionality of the system. The manual's LaTeX sources are included in the LiDIA distribution and can be used to create a PDF document besides the DVI version. You can also download the current manual from our Web server.

LiDIA source code is available under the GNU Public License v2.

Documentation

You can download a PDF version of the LiDIA manual from our Web server.

System Requirements

LiDIA is supposed to run on every POSIX machine that supports long filenames and provides an appropriate C++ compiler. We use the GNU Autotools for configuration.

We tested that LiDIA compiles and links on the following plattforms:

License

LiDIA is available under the GNU Public License v2 since 2006.

Download

LiDIA

The current release of LiDIA is 2.3 (February 2010). See COPYING for copyright terms, see RELEASE for the latest changes, and see INSTALL as well as README for installation instructions. LiDIA is split into several packages:

• the base package LiDIA-base
• the finite fields package LiDIA-FF (depends on LiDIA-base)
• the linear algebra package LiDIA-LA (depends on LiDIA-FF)
• the lattices package LiDIA-LT (depends on LiDIA-LA)
• the number fields package LiDIA-NF (depends on LiDIA-LT)
• the elliptic curves package LiDIA-EC (depends on LiDIA-LA)
• the elliptic curve order package LiDIA-ECO (depends on LiDIA-EC)
• the elliptic curve generation package LiDIA-GEC (depends on LiDIA-ECO and LiDIA-NF)

LiDIA can be obtained as complete distribution or asseparate packages. The complete distibution and all packages are provided as tar.gz archives.

The sources can be downloaded from the CDC Web server.

libI

The current release of libI is 2.1pre6. The sources can be downloaded from the Web server.

Mailing Lists

There are currently two open mailing list regarding LiDIA:

LiDIA@cdc.informatik.tu-darmstadt.de

is the mailing list for discussions on all topics related to LiDIA with a moderate volume. The preferred language for postings to this mailinglist is English. You must be subscribed to this list in order to post. To subscribe, send mail with "subscribe" in the subject or in the message body to LiDIA-request@cdc.informatik.tu-darmstadt.de or use the Web interface.

LiDIA-announce@cdc.informatik.tu-darmstadt.de

is the mailing list for announcements from the LiDIA Group related to LiDIA (such as new releases). This list is read-only. To subscribe send mail with "subscribe" in the subject or in the message body to LiDIA-announce-request@cdc.informatik.tu-darmstadt.de or use the Web interface.

There used to be a now defunct mailing list LiDIA-develop@cdc.informatik.tu-darmstadt.de. The list was used for discussions among LiDIA's core developers and postings were in part in German. Now all public discussion takes place on the general LiDIA mailing list. For reference purposes we put the LiDIA-develop list archive on the web as a single file in mbox format (212 KByte).

Support

Support was suspended in February 2010.

Other Mathematical Software

You want to try other mathematical software? Have a look at MathTools.net.

The Darmstadt University of Technology

Darmstadt University of Technology

Computer Science Department

Institute for Computer Algebra, Distributed Systems and Cryptography (CDC)

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Original WWW page design by Markus Maurer and Thomas Papanikolaou