Maple is a general-purpose computer algebra system with
very large audience among the world.
The *RegularChains* library in Maple organizes its
functionalities into a two-level user-interface.
The first level provides the basic
functionalities easy to use for the non-expert. Those functionalities
allow to compute triangular decompositions and manipulate polynomials.
The second level of the user-interface provides more technical
functionalities that are available through optional
arguments of the basic functionalities
and through two submodules, called *ChainTools*
and *MatrixTools*.
Those two sub-libraries respectively provide tools for
manipulating triangular decompositions and regular chains, and for
doing linear algebra over non-integral domains.
This makes Maple the unique computer algebra system offering
automatic case discussion and recombination.