# Introduction to *conley*

The algebraic theory of connection and C-connection matrices is concerned with
condensing the information of a graded module octahedron in a matrix called a
connection matrix or C-connection matrix
(cf. Mis95,
Fra89).
The package *conley* is more or less a tiny application of the more
elaborate homological algebra package
*homalg*.
We are very much indebted to
Stanislaus Maier-Paape,
who initiated the joint Conley index seminar in Aachen, introduced us to the
subject and explained us the fascinating dynamical side of the theory.

The main facilities of *conley* are the following:
- compute connection matrices
- compute C-connection matrices for a given initial complex C
- compute transition matrices
- allow restrictions dictated by symmetries (of the dynamical system)

### Convention

Note that we apply morphisms from the *right* and hence we use the
*row convention* for matrices. As one consequence we talk about *lower*
triangular instead of upper triangular matrices.