id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
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",