conley: Computing connection matrices in Maple. We announce the Maple package conley to compute connection and $C$-connection matrices. conley is based on our abstract homological algebra package homalg. We emphasize that the notion of braids is irrelevant for the definition and for the computation of such matrices. We introduce the notion of triangles that suffices to state the definition of ($C$-) connection matrices. The notion of octahedra, which is equivalent to that of braids is also introduced.