#16231: Equivalence between OA/TD/MOLS
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Reporter: ncohen | Owner:
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-6.2
Component: PLEASE CHANGE | Keywords:
Merged in: | Authors: Nathann Cohen
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: #15310, #16227
Stopgaps: |
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This branch implements the following equivalence result : there exists a
TD(k,n) iif there exists a OA(k,n) iif there exists k+2 MOLS.
With this branch, the three constructors communicate with each other, and
a construction of any of these objects can be used to create objects of
the other kinds.
Because the constructor of OA calls the constructor of TD,and because the
constructor of TD calls the constructor of OA, there is a new `who_asked`
parameters in these constructors which can be used to remember who asked
the question first.
On the down side : the constructor of MOLS used to be able to return "the
maximum number of MOLS of size nxn that Sage can build". With this patch,
the feature is removed.
Explanation: I created this feature because we only had two simple
constructions of MOLS, and because it was easy to guess this number k from
those constructions. With the new equivalences, this is not as easy
anymore, thus I removed it for the moment.
I think that it is not that bad, considering that it appeared very
recently, and that not many people may even know that Sage can build MOLS
yet.
This feature, however, can be interesting, and *can* be reimplemented.
While with the two former constructions it was easy to guess in one line,
we now have to try all possible parameters to find the largest integer k
we are looking for. This is not necessarily very time-consuming given that
all these objects now have an "availability" flag.
Hence it will be implemented again, this time for all constructions at the
same time.
Two important points:
1) The fact that the constructions communicate with each other means that
Sage returns better results than before (and in particular the "maximum"
number formerly returned by the constructor of MOLS is in many cases
smaller than what Sage can now do
2) The McNeish theorem from the constructors of MOLS has now been removed,
as the same constructions has been implemented for TD since (#16227), and
better (i.e. the best decomposition is found, not necessarily a
decomposition into prime powers)
HEeeeeeeeeeeeeeeeeere it is ! `:-)`
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/16231>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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