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linbox

LinBox is a C++ template library, so no compiled library need be built. To use linbox code, you include <linbox/subdir/file.h>, using the appropriate subdir and file.

Todo:

discuss role of other packages such as gmp, ntl, atlas, givaro and the use of configuration info.

fix linbox.doxy to be a discussion of overall library organization. (and make sure right stuff is on mainpage too)

LinBox is a C++ template library providing for exact linear algebra over arbitrary fields. It specializes in large sparse and structured problems over finite fields, but also contains capabilities for smaller matrices, dense matrices, and matrices over the integers.

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This release 0.1.4 provides for solution of a number of linear algebra problems including system solution, rank, determinant, minimal polynomial. In some cases, characteristic polynomial, Frobenius form, and/or Smith form are available. Computation may be over any finite field and for some problems over the integers.

A good collection of finite field implementations is available as is a suite of blackbox matrix classes.

Some algorithms are probabilistic in such a way that they are not to be used over very small fields (say, less than 1000 elements). In that case some computations may be performed over a suitable extension field.

The algorithms are still under active development and are missing or known to be suboptimal in some cases, despite known good solutions in principle. The documentation is also under active development and is limited or contains errors or outright missing for some components. (Date of this paragraph is 2004June, -bds)

\URL[Project LinBox]{http://linalg.org} is a collaborative effort among researchers at a number of locations in Europe and North America. The goals are to produce algorithms and software for symbolic linear algebra, particularly using black box matrix methods, i.e. iterative methods requiring only the linear transform property of the matrix (that, given A and x, one can compute y <-- Ax ).

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