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23634 A base class for integral quadratic forms seen as modules with a bilinear form. sbrandhorst "An integral lattice is a free abelian group L together with a non-degenerate integer valued bilinear form L x L --> ZZ.
In sage a lattice should consist of:
- an ambient QQ vector space with an inner product matrix
- a distinguished ZZ-basis (with possibly rational entries)
Integral lattices and quadratic forms are mathematically basically the same.
For me the difference in thinking is that lattices live in an ambient space.
Thus, one can have several lattices in an ambient space and compare their mutual relations (containment, embedding etc.)
Probably it should be derived from
sage.modules.free_quadratic_module.FreeQuadraticModule_submodule_with_basis_pi
New methods should include
- discriminant groups and forms
- over and sublattices
- Orthogonal groups
- direct sums
- is_even
- is_primitive sublattice
- orthogonal complements
- the dual ""lattice""" enhancement closed major sage-8.1 linear algebra fixed sd91 Simon Brandhorst David Roe N/A 707a74e27dd6fea52d3785fe4dbe1f46b61d3a84 707a74e27dd6fea52d3785fe4dbe1f46b61d3a84 #22720,#23703