#15976: IntegerLattice class
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Reporter: malb | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: linear algebra | Resolution:
Keywords: | Merged in:
Authors: Martin Albrecht | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/malb/15976_integer_lattice | a13b4aad3e9578866922d01932e6abac02687718
Dependencies: | Stopgaps:
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Comment (by malb):
Replying to [comment:6 SimonKing]:
Hi Simon,
thanks a lot for your comments!
> If your lattices are supposed to be groups (in particular, sets), then
the lattice should inherit from `Parent`, and you should implement
elements as well, inheriting from `Element` (or rather `ModuleElement`,
since you want to add elements). I guess it would be fine to import some
implementation of integer vectors (I am sure those things exist somewhere
in Sage), and assign it as a class attribute `IntegerLattice.Element`.
>
> Next, ''if'' you decide to inherit from `Parent` and assign `.Element`,
you should do `self._init_category_(Groups())` (or a better category, if
there is any) during initialisation of your lattice. This should be enough
to enable element creation and let the test suites
(`TestSuite(YourLattice).run()`) pass. If it isn't---well, then we'll take
care of it later.
I tried to go down this route: I inherited from `Parent` and set
`self._init_category_(CommutativeAdditiveGroups())`. The
`TestSuite(L).run()` now first complaints that there is no
`_an_element_()` which is easily fixable. However, the next complaint is
that elements created by `some_element()` do not live in the lattice but
in '''Z'''^n^. I am not sure I want my lattice vectors to live in the
lattice, but if I wanted to do that, I'd have to define my lattice as a
proper submodule of '''Z'''^n^? I'd view the lattice somewhat analogously
to an ideal in a multivariate ring, would we want our ideal elements to
live anywhere but the ring?
> On a different note: Would it make sense to use `UniqueRepresentation`
or at least `CachedRepresentation` for lattices? It seems strange to me to
have a function `Lattice` that does nothing more than hand the arguments
to the `IntegerLattice` constructor and return the result.
I don't want to cache my representations or make lattices unique. It is
useful to have two objects representing the same lattice: one with a good
basis and one with a bad basis (that's the secret and public key
respectively in many crypto systems). I'd expect `Lattice` to grow when
the need arises: lattices over '''Q''', over '''R''', over polynomial
rings and stuff.
--
Ticket URL: <http://trac.sagemath.org/ticket/15976#comment:7>
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