Libalgebra

Libalgebra is a header only template library for performing high level computations in abstract mathematical structures, such as the tensor algebra and free Lie algebras. The core components in the library are the vector classes. In the current version of libalgebra, there are three vector templates: dense_vector, sparse_vector, and hybrid_vector. These underlying vector types are unified in a single vector interface class vector, upon which the rest of the class hierarchy is based.

A object of the vector template class describes a generic element in the linear span of a basis, provided by a template argument, with coefficients from a field, also provided by a template argument. For example, an element of the tensor algebra with 4 letters with real coefficients (described by double precision floating point numbers), would be represented by objects of the class

alg::vector<alg::tensor_basis<4, 2>, alg::double_field>

The second template argument to tensor_basis describes the maximum degree of tensor words to consider in the basis.

Built on top of the vector interface is the general algebra template class. The algebra class takes an additional template argument in addition to those required by vector that describes the multiplication operation. This is further specialised to give top level template classes for the free tensor algebras, shuffle tensor algebras, free Lie algebras, polynomial algebras, and poly-Lie algebras. Also included is a class that provides an interface for using the Campbell-Baker-Hausdorff formula for computing the solution to an equation of the form exp(x) = exp(a)exp(b) in the free Lie algebras, and a class for converting between various algebra types.

Installation

This library uses CMake to manage builds. There are several ways to include Libalgebra into your projects. The simplest method is to include libalgebra as a git submodule, or even just clone into a subdirectory of your main project folder. A better way is to use the CMake FetchContent module to obtain and make available the libalgebra target to your own CMake project file. To do this, you can use the commands

include(FetchContent)

FetchContent_Declare(libalgebra
        GIT_REPOSITORY https://github.com/terrylyons/libalgebra.git
        GIT_TAG master
        )
FetchContent_MakeAvailable(libalgebra)

Once this is done, you can link the Libalgebra::Libalgebra target in your own targets.

Libalgebra has dependencies on Boost and GMP (or MPIR on Windows), so these will need to be installed and available for CMake to find; we use the FindBoost and FindBigNum CMake modules to locate and link the required components.