#16866: Radical difference families
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.4
Component: combinatorial | Resolution:
designs | Merged in:
Keywords: | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | 721af75ec2b2c6ca904f2feaf86e75e054cb089d
u/vdelecroix/16866 | Stopgaps:
Dependencies: #16863 |
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Comment (by vdelecroix):
Replying to [comment:22 ncohen]:
> Yo!
>
> > Too bad. If you tell me where, I can be clearer in the comments.
>
> Well, for a start I had no idea at first what was this "A" that you
defined, least of all why you have this `-1`. Then you seemed to say that
all differences belonged to different cosets of `H^{mt}` (I don't
understand what this set is), but it seems to mean that you can only
consider the differences obtained with 1.
No. I want that all differences belong to different coset. This is
something that need to be checked and which are precisely the two lines
{{{
if len(set(logA)) != m:
return None
}}}
> I don't get why you have this `A.append(K.one())`, I would have expected
`-K.one()` (i.e. the difference 0-1). Then I do not understand the cut
with the `len(set(logA))`.
This comes from computing what is Delta {1, r, r^2^, ..., r^k-1^} (where r
is a k-th root of unity). If you do that you will see that it is the same
as {+1, -1} A H^mt^. In the case of k even you want to compute Delta {0,
1, r, ..., r^k-2^} (where r is a (k-1)-th root of unity).
For the cut, see above.
> > What do you mean by "the same time". There is the same number of tiles
in the packing at the end but if you ignore the symmetries there are much
more possible translations.
>
> I do not get exactly what your reduction of the ground set means with
respect to the partition instance. What I mean is that an instance with
the A0 U A0', A1 U A1', ... above is totally equivalent (in terms of
resolution, and in terms of time) to an instance with A0, A1, ...
H has cardinality q-1 while H/H^mt^ has cardinality mt = (q-1)/(k-1) or
(q-1)/k depending on the parity of k.
> I was wondering if that was the difference that there is, in this
branch, between considering the cosets that you mention and not
considering them.
>
> > That my code works and that it is good to have smaller instances of
the problem to solve.
>
> It is not necessarily an improvement to reduce the number of vertices,
e.g. the example above.
> And so far I do not understand how your code works.
Good point
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16866#comment:23>
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