Hughes Plane (combinatorial design)

[q.honore]

Add a function in sage.combinat.designs.block_design to build Hughes planes.

[git]

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

​0824ca6	Add is_projective_plane to incidence_structure
​9806803	Add example, considered is_t_design method, errors removed
​6e9489d	Changed the wrong reference to GroupDivisibleDesign
​41ed54d	Add functions to build Hughes planes

[vdelecroix]

Hello Quentin,

You need to start a new branch for this ticket. Here you started from the same as for #18439.

Vincent

[vdelecroix]

Some more comments:

1. you should break the lines in your comments. The line The construction of a Hughes plane is based on a nearfield ... is one kilometer long. Try to keep the width around 80.

2. you should align the comments # xyz with the code

3. It would be cool to have some code in the EXAMPLES section which proves that Hughes plane are indeed different from the standard finite projective plane. You can show that the theorem of Desargues is not satisfied.

4. For the function normalize it would be better to say that it is only intended to be used in HughesPlane. And you can even call it normalize_hughes_plane_point, in other words choose something more explicit.

5. In the function HughesPlane, it would be nice to add few words explaining the construction and also add references (for example to Hughes original article and also Dembowski 1971)

Vincent

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​e8c9895	Add is_projective_plane to designs_pyx
​4e4e4a4	Add functions to build Hughes planes
​e4b099a	Add HughesPlane in the catalog
​dce0e82	Changed normalize function name, add descriptions and examples

[ncohen]

Instead of calling 'is_projective_plane' in the constructor of desarguesian projective planes, could you make it return a BIBD instead of a Block Design? This way, the constructor would automatically check the property.

Thanks,

Nathann

[git]

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

​3ca2bb8	Changed the HughesPlane description (\leq, not \subseteq)
​5a7832b	Changed BlockDesign to BIBD for HughesPlane and DesarguesianProjectivePlaneDesign

[vdelecroix]

The modification in 5a7832b is responsible for this failure:

sage -t --long combinat/designs/incidence_structures.py
**********************************************************************
File "combinat/designs/incidence_structures.py", line 1500, in sage.combinat.designs.incidence_structures.IncidenceStructure.automorphism_group
Failed example:
    P = designs.DesarguesianProjectivePlaneDesign(2); P
Expected:
    Incidence structure with 7 points and 7 blocks
Got:
    (7,3,1)-Balanced Incomplete Block Design
**********************************************************************
1 item had failures:
   1 of  12 in sage.combinat.designs.incidence_structures.IncidenceStructure.automorphism_group
    [294 tests, 1 failure, 1.42 s]

When you are done with this correction, you can switch the status to needs review.

Vincent

[git]

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

​2182aaa

Example corrected in incidence_structure.py

[vdelecroix]

From comment:7:

When you are done with this correction, you can switch the status to needs_review.

This means: go to modify ticket in the bottom of the page. And in the Action part chose the needs_review.

[vdelecroix]

Hello Quentin,

There is a lot of work to do in the documentation. Most of it is uncomprehensible. Hopefully I know what you are trying to do but any other person will not get a word. I already modified some of it in my commit at public/18527 but there are still a lot of things to do:

• In HughesPlane the following sentence is uncomprehensible

      For p an odd prime.
      If kernel K of order `p^n` coincides with the center of a nearfield N.
      The construction of a Hughes plane is based on N of order `p^2n`.
  

  you should explain simply what is the Hughes plane. If it is complicated just make a reference to wikipedia and just explain what it is (e.g. The Hughes plane is a finite projective plane introduced by XYZ and which is not Desarguesian)

• If you want to include mathematics formula in the documentation you must use the block MATH. This is described in details in ​the developer's guide

• the example that shows that the Hughes plane is not Desarguesian is not finished... And you should explain what you are doing with sentences (not Python comments starting with #). I already modified and simplified the begining.

Vincent

---

New commits:

​47c7c21

Trac #18527 (review): improve the documentation

[vdelecroix]

And also: always put a space around equality signs a = b and not a=b. Similarly, in functions write f(a, b, c) and not f(a,b,c).

[git]

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

​799f921

Changed HughesPlane description according to the review

[vdelecroix]

Hello,

When you are done with your changes, you need to set back to needs review. That way I know that I need to have a look.

Some more comments:

• with your last commit the test do not pass
• put spaces around equality signs a = b and not a=b. Similarly, add spaces in function declaration f(a, b) and not f(a,b).
• When you define the Hughes plane you start with p being an odd prime but it is never used
• for coherence of notations, instead of using n2 and n it would be better to use q2 and q (and do not forget to modify the INPUT section)

I did a bit of profiling and it appears that most of the time is spent in doing matrix by vector multiplication! I will try to see whether it is possible to improve that part (in another ticket).

Vincent

[git]

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

​62ff365

Corrected HughesPlane description

[git]

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

​2605694

Trac #18527: (review) remove trailing whitespaces

[git]

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

​8cd2b5b	Trac #18527: (review) rename random_q3_xxx -> q3_xxx
​a07874f	Trac #18257: (review) better q3_minus_one_matrix
​bd692ea	Trac #18527: (review) fix the case of non prime q
​7e2070f	Trac #18527: (review) small cleanup

[vdelecroix]

In my review commits I changed few things (removed random from random_q3_minus_one_matrix, make HughesPlane works for non prime q and improve a bit the code).

There are still some issues with the documentation. Please pay more attention to what you write.

You wrote

Return the Hughes projective plane of order `n2`.

But the name of the parameter is now q2. Moreover you must use double quotes for the parameters ``q2```. Simple ones are for latex code.

This is not a sentence

For q an odd prime.

When you test the fact that it is not Desarguesian, it is weird to do it in two ways. Here you print the name of the points

        sage: set(b_0_1).intersection(b_57_70)
        {2}
        sage: set(b_1_10).intersection(b_70_59)
        {73}
        sage: set(b_10_0).intersection(b_59_57)
        {60}

But then you just test equality

        sage: p = set(b_0_57).intersection(b_1_70)
        sage: q = set(b_1_70).intersection(b_10_59)
        sage: p == q
        False

You should do it coherently.

You can also add a section AUTHORS with your name in the function HughesPlane (see the developer guide).

Vincent

[vdelecroix]

Replying to vdelecroix:

When you test the fact that it is not Desarguesian, it is weird to do it in two ways. Here you print the name of the points <SNIP> But then you just test equality <SNIP>

Oups. I understood... you are not testing the same thing! Sorry. Forget about this specific comment.

[git]

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

​037017c

Add authors, cleaned description

[q.honore]

New commits:

​037017c

Add authors, cleaned description

---

New commits:

​037017c

Add authors, cleaned description

[git]

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

​e1c88ae	Trac #18257: (review) remove trailing whitespaces
​c398bbb	Trac #18527: (review) cleaning

[vdelecroix]

When you add some stuff pay attention to the fact that you do not add trailing whitespaces (i.e. spaces at the end of the lines).

I added a small commit which move around some stuff and simplify the documentation.

There is one more thing to do: the new function HughesPlane does not appear in the list of the functions available in the top of the file design_catalog.py. You can put the reference just after DesarguesianProjectivePlaneDesign.

Vincent

[git]

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

​1043640

Add HughesPlane to the catalog