  Topological insulators have been of considerable interest in the last
decades. These materials show new states of matter that are insulating in the
bulk but have conducting states on their surfaces. The conducting states on the
surface are protected by the topology of the bulk band structure, and
topological numbers, such as first Chern number, second Chern number,
$\mathbb{Z}_2$ number, etc., are used to characterize them. As a typical
example, the quantum Hall effect has the quantized Hall conductivity, which can
be calculated by the first Chern number. Other topological numbers similarly
become important physical quantities that characterize the system, depending on
the system dimension and symmetry classes. To obtain the topological numbers,
we often need numerical calculations, and it may require an enormous amount of
computation before convergence is achieved. Therefore, creating tools to easily
compute these numbers will lead to advances in research for the topological
phase of matters. So far, several methods have been reported that suggest that
some topological numbers can be computed efficiently. However, since each
method is specialized for a specific dimension or symmetry class, it is
necessary to implement the algorithm for each problem, respectively. Our
project, TopologicalNumbers.jl, aims to provide a package that can easily and
efficiently compute topological numbers comprehensively in various dimensions
and symmetry classes.
