#19332: Add discrete_complementarity_set() method for cones
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Reporter: mjo | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: geometry | Resolution:
Keywords: | Merged in:
Authors: Michael Orlitzky | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/mjo/ticket/19332 | 88b74bba339c1ff53063ebe43819b222fd478f1b
Dependencies: | Stopgaps:
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Changes (by novoselt):
* status: needs_review => needs_work
Comment:
I do not like the implementation at all, why do we need to do
{{{
sage: self = Cone([(1,0),(0,1)])
sage: V = self.lattice().vector_space()
sage: G1 = [ V(x) for x in self.rays() ]
sage: G2 = [ V(s) for s in self.dual().rays() ]
sage: [ (x,s) for x in G1 for s in G2 if x.inner_product(s) == 0 ]
[((1, 0), (0, 1)), ((0, 1), (1, 0))]
}}}
when exactly the same is achieved with
{{{
sage: [(x, s) for x in self for s in self.dual() if x * s == 0]
[(N(1, 0), M(0, 1)), (N(0, 1), M(1, 0))]
}}}
which uses only memory for tuples (but not their elements) and can be
cached???
Products work just fine between rays of dual cones and to big extent the
whole point of introducing toric lattices was to allow only "correct" ways
of mixing them, i.e. you cannot multiply rays that live in the same
lattice. If the user is not happy with the type of the above output and
wants to do illegal products, that user is welcome to do explicit
conversion.
Note also that the result can be achieved using
{{{
sage: [[(r, n) for r in f] for f, n in zip(self.facets(),
self.facet_normals())]
[[(N(1, 0), M(0, 1))], [(N(0, 1), M(1, 0))]]
sage: self.orthogonal_sublattice()
Sublattice <>
}}}
which will not be as short of a code and above, but may be faster if face
lattice is used (and thus computed/cached) for something else. Not sure if
there is any point in using it for the implementation, but perhaps the
relation can be mentioned in the documentation (and I definitely like your
detailed docstrings!).
A bipartite graph also seems to be a natural structure for the output ;-)
--
Ticket URL: <http://trac.sagemath.org/ticket/19332#comment:2>
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