id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
16231 Equivalence between OA/TD/MOLS ncohen "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" enhancement closed major sage-6.3 combinatorics fixed vdelecroix knsam dimpase Nathann Cohen Vincent Delecroix N/A 9e5e94f648113d6b824039651bcb8d98144e01b2 9e5e94f648113d6b824039651bcb8d98144e01b2 #15310, #16227