Projective Plane designs #15107

nathanncohen · 2013-08-27T09:45:48Z

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

Nathann

CC: @dimpase

Component: combinatorics

Author: Nathann Cohen

Branch/Commit: u/ncohen/15107 @ 6f247f6

Reviewer: Stefan van Zwam

Issue created by migration from https://trac.sagemath.org/ticket/15107

The text was updated successfully, but these errors were encountered:

nathanncohen · 2013-08-27T09:46:33Z

Branch: u/ncohen/15107

dimpase · 2013-08-29T05:27:16Z

comment:2

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.

nathanncohen · 2013-08-29T08:05:12Z

comment:3

OKayyyyyyy. Branch updated :-)

fchapoton · 2013-08-29T19:12:35Z

comment:4

in ProjectiveGeometryDesign :

one does not know what is the input F
there is a missing :: in the modified example block

nathanncohen · 2013-08-30T08:36:38Z

comment:5

Fixed ! Sorry 'bout that :-)

Nathann

dimpase · 2013-08-31T15:23:26Z

comment:6

Replying to @nathanncohen:

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.

nathanncohen · 2013-09-01T09:36:23Z

comment:7

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 · 2013-09-01T14:38:50Z

comment:8

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...

sagetrac-git · 2013-09-01T15:30:35Z

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`

sagetrac-git · 2013-09-01T15:30:35Z

Commit: 9fcfb13

nathanncohen · 2013-09-01T15:44:55Z

comment:10

Cool automatic message O_o

Nathann

dimpase · 2013-09-01T16:17:06Z

comment:11

Replying to @nathanncohen:

Cool automatic message O_o

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

sagetrac-git · 2013-10-16T13:46:51Z

Changed commit from 9fcfb13 to cf71d58

sagetrac-git · 2013-10-16T13:46:51Z

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

`[changeset:cf71d58]`	`Rebase on 5.13.beta0`

fchapoton · 2014-01-04T11:27:20Z

comment:13

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.

nathanncohen · 2014-01-04T11:58:40Z

comment:14

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

sagetrac-git · 2014-01-04T14:45:07Z

Changed commit from cf71d58 to b6aa35a

sagetrac-git · 2014-01-04T14:45:07Z

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`

nathanncohen · 2014-01-04T14:49:25Z

comment:16

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

fchapoton · 2014-01-04T18:58:06Z

comment:17

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."

sagetrac-git · 2014-01-04T19:34:33Z

Changed commit from b6aa35a to 6f247f6

sagetrac-git · 2014-01-04T19:34:33Z

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`

nathanncohen · 2014-01-04T19:38:11Z

comment:19

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

Nathann

sagetrac-Stefan · 2014-01-06T14:55:18Z

Reviewer: Stefan van Zwam

sagetrac-Stefan · 2014-01-06T14:55:18Z

comment:20

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

nathanncohen mannequin added this to the sage-6.1 milestone Aug 27, 2013

nathanncohen mannequin added c: combinatorics labels Aug 27, 2013

nathanncohen mannequin added the s: needs review label Aug 27, 2013

dimpase added s: needs work and removed s: needs review labels Aug 29, 2013

nathanncohen mannequin added s: needs review and removed s: needs work labels Aug 29, 2013

sagetrac-Stefan mannequin added s: positive review and removed s: needs review labels Jan 6, 2014

vbraun removed the s: positive review label Jan 17, 2014

vbraun closed this as completed in d1aba9a Jan 17, 2014

This was referenced Oct 30, 2013

(v,4,1)-BIBD, Latin Squares and Orthogonal arrays #15259

Closed

Bug in AffineGeometryDesign #15285

Closed

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Projective Plane designs #15107

Projective Plane designs #15107

nathanncohen mannequin commented Aug 27, 2013

nathanncohen mannequin commented Aug 27, 2013

dimpase commented Aug 29, 2013

nathanncohen mannequin commented Aug 29, 2013

fchapoton commented Aug 29, 2013

nathanncohen mannequin commented Aug 30, 2013

dimpase commented Aug 31, 2013

nathanncohen mannequin commented Sep 1, 2013

dimpase commented Sep 1, 2013

sagetrac-git mannequin commented Sep 1, 2013

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nathanncohen mannequin commented Sep 1, 2013

dimpase commented Sep 1, 2013

sagetrac-git mannequin commented Oct 16, 2013

sagetrac-git mannequin commented Oct 16, 2013

fchapoton commented Jan 4, 2014

nathanncohen mannequin commented Jan 4, 2014

sagetrac-git mannequin commented Jan 4, 2014

sagetrac-git mannequin commented Jan 4, 2014

nathanncohen mannequin commented Jan 4, 2014

fchapoton commented Jan 4, 2014

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nathanncohen mannequin commented Jan 4, 2014

sagetrac-Stefan mannequin commented Jan 6, 2014

sagetrac-Stefan mannequin commented Jan 6, 2014

Projective Plane designs #15107

Projective Plane designs #15107

Comments

nathanncohen mannequin commented Aug 27, 2013

nathanncohen mannequin commented Aug 27, 2013

dimpase commented Aug 29, 2013

nathanncohen mannequin commented Aug 29, 2013

fchapoton commented Aug 29, 2013

nathanncohen mannequin commented Aug 30, 2013

dimpase commented Aug 31, 2013

nathanncohen mannequin commented Sep 1, 2013

dimpase commented Sep 1, 2013

sagetrac-git mannequin commented Sep 1, 2013

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nathanncohen mannequin commented Sep 1, 2013

dimpase commented Sep 1, 2013

sagetrac-git mannequin commented Oct 16, 2013

sagetrac-git mannequin commented Oct 16, 2013

fchapoton commented Jan 4, 2014

nathanncohen mannequin commented Jan 4, 2014

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nathanncohen mannequin commented Jan 4, 2014

fchapoton commented Jan 4, 2014

sagetrac-git mannequin commented Jan 4, 2014

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