#9504: Add support for toric sublattices
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.5.3
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by novoselt):
I think for equality testing of quotient lattices the choice of generators
is irrelevant, especially since we have emphasis on representation by
lifts, rather than in terms of generators. I am concerned about generators
change for the same object, since the choice of generators may have been
used somewhere already and cached. In fact I have just tried the
following, which does not seem right to me:
{{{
sage: N = ToricLattice(3)
sage: Ns = N.submodule([N(1,1,1), N(1,2,3)])
sage: Q = N/Ns
sage: Q
1-d lattice, quotient of 3-d lattice N by Sublattice <N(1, 0, -1), N(0, 1,
2)>
sage: q1 = Q(1,0,0)
sage: q1
N[1, 0, 0]
sage: q1.vector()
(1)
sage: Q.gen(0)
N[0, 0, 1]
sage: Q._make_generator_positive_on(N(0,0,-1))
sage: Q.gen(0)
N[0, 0, -1]
sage: q2 = Q(1,0,0)
sage: q2
N[1, 0, 0]
sage: q2.vector()
(1)
}}}
So perhaps this change should be done on a deeper level. Note that it is
also possible to compare these elements from different lattices
{{{
sage: q1.parent() is q2.parent()
False
sage: q1 == q2
True
}}}
and in fact I would expect it to fail here since comparison of elements is
done using their coordinate representation in terms of generators, which
should be different.
As far as the computation of the "positive direction" goes, I am fine with
leaving it as is, but perhaps inserting into the docstring your
explanation above.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9504#comment:17>
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