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redesign projective plane #16281
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comment:1
Here it is... New commits:
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Commit: |
Branch: u/vdelecroix/16281 |
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comment:3
Heeeeeeeeereis the review !
Nathann |
comment:4
Replying to @nathanncohen:
Thanks!
Ok.
Because of the argument "type"... funny isn't it?
All right.
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).
Nope: in a projective plane there should be a quadrilateral. Vincent |
comment:5
Yo !
Come on.... I am not even sure this thing ever appeared in a public release, and it does nothing.... I think it is safe to use a
Well. If you have a ProjectivePlane (a Projective Plane is a BIBD) named
Right. I had some (theoretical) problems with degenerate projective planes recently Nathann |
comment:6
Replying to @nathanncohen:
All right. I remove it.
Ok. I see. Perfect. Vincent |
comment:7
by the way: a BIBD is an edge-decomposition of a Complete graph on n elements with complete graphs of k elements. It is a collection of sets of size k such that any pair of elements in [n] belong to exactly one of these sets of size k. Somehow it is a projective plane with uniform lines, but two lines do not necessarily intersect. Nathann |
Branch pushed to git repo; I updated commit sha1. New commits:
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comment:9
I was not able to use the function '_relabel_bibd'. If you want to play with it... |
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comment:11
Do you think that the "pt" argument is useful ? If it is not, I can rewrite this in 4-5 lines. I do not think that it is useful, given that from the pair "PP,pt" there is not an "unique" resulting OA. So well, the function just creates a OA from a PP, and we cannot say much more. Nathann |
comment:12
I added a commit that does that in public/16281 Nathann |
comment:13
The thing is that the pair (pp,pt) gives a unique stuff up to isomorphism if and only if the automorphism group of the pp acts enough transitively... it is the case for Desarguesian planes but I do not no yet for the others. |
comment:14
Do you think we could leave this for later, until somebody actually ... cares to compute this with Sage ?... Nathann |
comment:15
new version in 10 minutes that leaves the feature. Nathann |
comment:16
Here it is, in public/16281. Nathann |
comment:17
Hi Nathann, Looks cool like that. Thanks. Is that ready to go? Vincent |
comment:18
In your construction of the projective plane I do not understand what you mean by the coordinates, especially while reading the code. A way to make it clearer would be to define the following functions. If you have another idea I really don't mind, I just want to understand the code
This way we can read the code without trying to translate the coordinates Nathann |
comment:19
Hi, The projective plane over a field is the set of equivalence classes of non-zero vectors
I am making it. Vincent |
comment:20
Well, what I find confusing is that you give all these things 3 coordinates, and I do not see the point For me there are three kinds of points, one with two coordinates one with 1, and the last one. Nathann |
comment:21
Three because of the definition I know... quotient out How about a HUGE comment as follows
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comment:22
....... Really, what force is making you define three coordinates for those points ? In which 3d space do they live ? Nathann |
comment:23
OOhhhhhhhhhh I see how you see it now... Well, I personally find the explanation clearer without any mention of the 3d coordinates... But well, it's up to you.. Tastes, I guess Nathann |
comment:24
It is the standard definition of the projective plane: it is the set of vectorial lines in |
comment:25
Defined as equivalence classes okay, but it stays abstract and you still have no coordinates. But then you say "I can either normalize the third coordinate if it is nonzero, otherwise I normalize the second coordinate,and if I can't I normalize the first". Well... I am used to defined this thing with "three kinds of points" :-P Anyway, if you can put this inside of the branch then no problem Nathann |
comment:26
here you go |
comment:28
Oups: there is a warning in docbuild
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comment:29
Oh right. The Nathann |
Reviewer: Nathann Cohen |
Branch pushed to git repo; I updated commit sha1. New commits:
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comment:31
Great. Let's go back to #16272 and manage the merge... |
comment:32
Come ooooooooon. That will be easy. Hey Vincent, I'm not sure I told you but it is great to work together on something. Stuff happens, gets merged and written. Much better than the usual "write a patch, then wait forever" Nathann |
Changed branch from u/vdelecroix/16281 to |
Projective planes are currently implemented as block designs but are very slow to construct (see timings in #16272). Moreover the specifications and the behaviour are contradictory.
In this ticket
ProjectivePlaneDesign
DesarguesianProjectivePlane
that return the corresponding projective plane or raise aValueError
projective_plane
that return a projective plane if there is an available construction, or raise aEmptySetError
if no construction is possible or raise aNotImplementedError
if no construction is currently available.We also implement two translation functions
projective_plane_to_OA
andOA_to_projective_plane
that make the translation between orthogonal arrays (with parametersk=n+1
andt=2
) and projective planes.This is an intermediate step for #16272. See also the follow up #16283 about construction of more projective planes.
CC: @nathanncohen
Component: combinatorics
Keywords: design, projective plane
Author: Vincent Delecroix
Branch/Commit:
51daa7f
Reviewer: Nathann Cohen
Issue created by migration from https://trac.sagemath.org/ticket/16281
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