#16227: Product construction of Transversal Designs
-------------------------+-------------------------------------------------
Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | a512ab154b21caaf74d6ccef2cf32bf67179eee9
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16227 |
Dependencies: |
#15310 |
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Comment (by vdelecroix):
Replying to [comment:5 ncohen]:
> Yo !
>
> > 1) As I mentioned in #15310, I would prefer to have `TD_product` to be
something called with arguments `k,n1,n2` as it is for Wilson
construction. Specifications {{{def
TD_product(k,n1,n2,TD1=None,TD2=None)}}} might be better. But then, if you
provide TD1 and TD2, the arguments k,n1,n2 are redundant.
>
> What is the point of having a function `TD_product` which only takes
integer as input ? What can it do that `designs.transversal_design(...)`
does not already do ?
>
> What we could do is implement a second function
TD_product_from_parameters which calls the other ?
Sometimes you want only functions with the same prototype and sometimes
you claim it is better otherwise...
> > 3) As Brett mentioned in #15310, it would make sense to have a more
involved `find_wilson_decomposition` which also contains product. There
are tons of variants of Wilson decomposition and according to Colbourne-
Dinitz this is how most of the current records are obtained. We might
concentrate all the non-direct constructions into a global function
`build_TD_from_smaller_ones` or `generalized_Wilson_construction`.
>
> Whyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy ?
>
> Right now I am building all the constructions of OA in such a way that
they all take the same parameters :
>
> {{{function_that_builds_OA(k,n,availability)}}}
>
> and it does what you expect, i.e. try if it is able to build this OA and
answers accordingly. If we can make all functions that return OA behave
this way, and the constructor can look like this :
All right. What I meant is that it makes sense to try Wilson and product
in the same function that builds OA. But on the other hands, calling
divisors is relatively cheap on the kind of entries you will have. In a
near future (and according to the TODO) the Wilson construction might be
much more involved... will see.
There was doctest error that I solved on u/vdelecroix/16227. I also added
curiosity doctests (the current maximum k that Sage knows from n between
10 and 20).
See the changes in u/vdelecroix/16227, if you are happy with them this is
good to go.
--
Ticket URL: <http://trac.sagemath.org/ticket/16227#comment:8>
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