Projective Plane designs

[ncohen]

Shortcut to another function. In order to save a stranger the time it took me to understand it :-P

Nathann

[dimpase]

Your code returns a very particular projective plane, the one obtained from the finite field of order n, whereas there could be many nonisomorphic ones (the first such case being n=9). This should be reflected in the docs, IMHO.

[ncohen]

OKayyyyyyy. Branch updated :-)

[chapoton]

in ProjectiveGeometryDesign :

• one does not know what is the input F

• there is a missing :: in the modified example block

[ncohen]

Fixed ! Sorry 'bout that :-)

Nathann

[dimpase]

Replying to ncohen:

OKayyyyyyy. Branch updated :-)

the function name is unfortunate; it should reflect the fact that there could be several examples, or, rather, make it unique, like ClassicalProjectivePlane or DesarguesianProjectivePlane or something like this. Otherwise it would preclude adding code for non-classical examples.

[ncohen]

Well, I see a ProjectivePlane method as one that will give me "some projective plane", and I can't make more assumptions on what it is. I would also like someone who just wants "a projective plane" to be able to find the method, for I need projective planes and I have no idea what a Desarguesian projective plane is, nor if the one I implemented is classical.

Plus I implemented a steiner_triple_system method which returns only one kind of steiner triple systems, I did the same for steiner_quadruple_systems, ... :-P

What would you think of this : we keep ProjectivePlaneDesign as the method name for the moment, and if we end up with more data we will just make it accessible visible in the doc ?

Combinat-style, this thing should be a new ProjectivePlanes class with an an_element method to return some projective plane, and none other. But we can't even write a .cardinality() method, nor enumerate them... :-P

And if you insist I will rename this to ClassicalProjectivePlaneDesign.

Have fuuuuuuuuuuuuuuuuuuuuuuuun ! ;-)

Nathann

[dimpase]

​http://en.wikipedia.org/wiki/Desargues%27_theorem is a geometric criterion satisfied by projective planes obtained from the 3-dimensional vector spaces over division rings; every finite division ring is a field, so in the finite case every such plane is Pappian, see ​http://en.wikipedia.org/wiki/Pappus%27s_hexagon_theorem.

Keeping the current name sucks, as adding more examples would force you to rename stuff. So, please, call it, as you prefer: Classical, or Pappian, or Desarguesian...

As far as ProjectivePlanes class would go, you can do cardinality() up to n=10...

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

[changeset:9fcfb13]	Rename the method from ProjectivePlaneDesign? to DesarguesianProjectivePlaneDesign?
[changeset:363badb]	trac 15107 -- reviewer's comments
[changeset:ee6d412]	Projective Plane designs constructor

[ncohen]

Cool automatic message O_o

Nathann

[dimpase]

Replying to ncohen:

Cool automatic message O_o

By git... Perhaps the sage git dev scripts should get a better, more descriptive, name... Shlimazl, maybe :-)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

[changeset:cf71d58]

Rebase on 5.13.beta0

[chapoton]

Sorry Nathann, but what is exactly the purpose of the newfunction DesarguesianProjectivePlaneDesign ?

In my opinion, with this name, it does no longer make sense to answer 'No projective plane design of order 10 exists' or 'If such a projective plane exists, we do not know how to build it.' One should rather check if the input is a prime power and that's it.

Then it would be just a restriction of ProjectiveGeometryDesign? to the dimension 2, i.e. some kind of alias. Either this is considered not useful, and this ticket can be forgotten, or you want to keep it as an useful alias, and it will be ok.

[ncohen]

Helloooooo !

Well, the purpose of this function is to return a projective plane design, i.e. a d^2+d+1, d+1 BIBD.

I agree with what you said. Actually, thinking about it again, I don't agree with what Dima said above. I don't see the problem with calling this ProjectivePlaneDesign, as I need a function which returns a projective plane design. Changing the name just makes it harder to find when one looks for it >_<

What do you think ?

I think that this alias is useful, but I personally spent quite some time trying to figure out of to obtain a projective plane design with Sage.

Nathann

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b6aa35a	trac #15107: back to the first name with a new argument
​e2935fe	Trac #15107: Rebase on 6.1.beta3

[ncohen]

I just updated this ticket after the englightening discussion held on sage-devel : ​https://groups.google.com/d/topic/sage-devel/a6I0SUZVgNM/discussion

We now have an additional argument to ProjectivePlaneDesign? which does nothing. That's for the sake of art.

Nathann

[chapoton]

There is a typo "afinite projective plane"

I propose to replace "No other value is available for this parameter." by

"For the moment, no other value is available for this parameter."

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6f247f6	trac #15107: back to the first name with a new argument
​e2935fe	Trac #15107: Rebase on 6.1.beta3
​cf71d58	Rebase on 5.13.beta0
​9fcfb13	Rename the method from ProjectivePlaneDesign to DesarguesianProjectivePlaneDesign
​363badb	trac 15107 -- reviewer's comments
​ee6d412	Projective Plane designs constructor

[ncohen]

Here it is ! I updated the last commit :-)

Nathann

[Stefan]

I think this looks fine and is ready to go in.

Just for fun, I did the following additional consistency check:

sage: S = designs.ProjectiveGeometryDesign(2,1,GF(3))
sage: M = Matroid(circuit_closures={2:S.blocks(),3:[range(13)]})
sage: M.is_isomorphic(matroids.PG(2,3))
True