#16281: redesign projective plane
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: design, | Merged in:
projective plane | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | 429d815568a0e4a90e4968e55d45548f2e0c7262
u/vdelecroix/16281 | Stopgaps:
Dependencies: |
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Comment (by vdelecroix):
Replying to [comment:3 ncohen]:
> Heeeeeeeeereis the review !
Thanks!
> - Designs end with "Design", i.e. !DesarguesianProjectivePlaneDesign. I
don't say that it is a good idea, but that we should change it for all of
them or not at all. Plus Dima will complain.
Ok.
> - Why not use deprecated_function_alias for
designs.!ProjectivePlaneDesign ?
Because of the argument "type"... funny isn't it?
> - You can do this instead
> {{{
> relabel = {x:i for i,x in enumerate(K)}
> Klist = relabel # Klist represent the set of elements of K
> }}}
All right.
> - `projective_plane_to_OA`: there is a function in bibd.py called
`_relabel_BIBD` that takes a BIBD on n points as input (here it would be a
projective plane) and relabels its elements in such a way that
[[0,..,k-2,n],[k-1,...,2*k-2,n],...,[n-k-1,n-1]] are sets of the BIBD. So
well. It actually does what you are doing : it relabels the BIBD such that
when you remove all blocks containing n-1 you get a well-labelled TD.
> - `OA_to_projective_plane` I implemented something VERY SIMILAR in
#16279 but not equivalent :-)
>
> - `OA_to_projective_plane` : Why do you need to relabel anything ?
> {{{
> + # add the n^2 lines that correspond to transversals
> + for l in OA:
> + blcks.append([i+(n+1)*j for i,j in enumerate(l)])
> }}}
> The OA is already well labelled. The BIBD is exactly the blocks from
the OA plus the k groups union the new element, isn't it ? This should
just be a deepcopy.
>
I do not know what is a bibd and I did not have a look at it (except
changing the call to !ProjectivePlaneDesign). If you feel like removing
more code I am happy with that but I will not do it (if you do, wait until
the other remarks are implemented).
> - Isn't the triangle a Projective Plane of order 1 ?
Nope: in a projective plane there should be a quadrilateral.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16281#comment:4>
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