Lattices: G-Lattices

• Creation of G-lattices with associated operations
• Invariant lattice of a rational matrix group and the associated action (thus yielding an integral representation of the group)
• Bravais group of a finite rational matrix group
• Invariant sublattices of finite index
• Space of invariant bilinear forms
• Positive definite invariant form of a rational matrix group
• Endomorphism ring
• Centre of the endomorphism ring
• Dimension of the space of invariant bilinear forms, the endomorphism algebra or its centre using a modular algorithm

The lattice machinery has been developed by Bernd Souvignier and Allan Steel.