Add skew Hadamard matrices up to order 1000 #35211

MatteoCati · 2023-02-27T09:24:14Z

📚 Description

This PR adds constructions for all known skew Hadamard matrices of order up to 1000. The following changes have been made:

more skew Supplementary difference sets have been added
The functions for supplementary difference sets in difference_family.py have been changed so that now they also return the group to which the sets belong. This makes the functions consistent with the others contained in this file, and makes them more efficient.
Added construction of skew Hadamard matrices from complementary difference sets (and construction for complementary difference sets).
Added construction of skew Hadamard matrices from amicable Hadamard matrices and Orthogonal Designs (and construction for some amicable Hadamard matrices).

Note that only commits from c0eb0c1 are new, the older ones where created in #35059.

📝 Checklist

I have made sure that the title is self-explanatory and the description concisely explains the PR.
I have linked an issue or discussion.
I have created tests covering the changes.
I have updated the documentation accordingly.

⌛ Dependencies

#35059: this PR adds (non skew) Hadamard matrices of order <= 1000

…m polynomial ring

… SDS function)

dimpase · 2023-03-23T12:02:31Z

can we get a test function, with _ prefix, to check consistency: for each $0< k < 251$, check that a matrix of order $4k$ can be built (unless it it is one of the few exceptions we know). It can be doctested with # long time tag (unless it's too long to run)

And something similar for the skew case.

MatteoCati · 2023-03-23T16:27:42Z

I've added the function, but I didn't write the tests because they would take too long (around 10 min each).

github-actions · 2023-03-23T23:04:49Z

Documentation preview for this PR is ready! 🎉
Built with commit: c4abaaf

tscrim · 2023-03-25T05:35:42Z

It still needs a doctest that is run. I would extend the functionality slightly by adding an extra k parameter for the upper bound to check (specifying that it must be less than some fixed number where we know where Sage should not be successful. It should also raise an error when it cannot construct something Sage thinks it can and print a warning when it can construct something we didn't think it could.

dimpase · 2023-03-25T07:31:29Z

a function with prefixed by _ name does not require documentation, leave alone a doctest.

tscrim · 2023-03-25T09:20:20Z

@dimpase That is completely wrong. That only applies to cdef functions for the technical reason they cannot be directly called by Python, but it is good for even those to have an indirect test. Every function and method is required to have some form of a doctest (see the doctest coverage part of the reviewer's checklist; plus it is just good programming practice.

dimpase · 2023-03-25T09:23:48Z

No, this is too restrictive. If true, this'd have effectively prevented Sage to have functions which are too long to run in doctests. And the function we are talking about is one of these.

dimpase · 2023-03-25T09:28:35Z

It is effectively a test itself, to be triggered by hand. There are other such functions, e.g. in graphs/

tscrim · 2023-03-25T09:38:51Z

It is the rule, one I fully support. To me, this is suggesting that the function design is wrong. Again, see my suggestion about adding another parameter to set the upper bound. Or this should just become a doctest, with perhaps a smaller bound that is tested. Right now, this function is useless because it is not tested (so if something breaks, nobody will know) and not publicly shown (so nobody will even know to do this test).

dimpase · 2023-03-25T09:42:10Z

It is in the source, thus it is known.
Look, we can just remove it, and then you have no reasons to complain - but then doing what it does has to be done by hand. This is ludicrous, isn't it?

dimpase · 2023-03-25T09:43:35Z

It is an important function, just too slow, for a good reason, to be tested in a doctest. That's all.

tscrim · 2023-03-25T10:06:19Z

Being in the source code (but not in the public documentation) does not make it discoverable. Who is going to even know about this, much less test it (which you are saying needs to be done by hand)? It is not even clear what that correct output should be. If it was just a doctest itself (marked with # not tested), then it would just need to be copy/pasted by an interested party (and made available to the public).

From another perspective, all of these constructions are actually tested at some place in the code. The point is to have a way for the user to iterate over the list of constructions to see which actually work in some range. Right now, it is basically just a doctest since the bounds are fixed, but it is put as a function. It seems like you want something more like primes(a, b) that returns all prime numbers in the range [a, b]. This could then have a shorter test and would make sense to make public.

In short, if it is important, then why isn't it public (and part of the standard doctests with some cutoff)?

dimpase · 2023-03-25T11:38:38Z

would it be OK to remove _ from the name and add a doctest tagged # not tested - too long ?

Also, make the name more descriptive, i.e. not _get_all_hadamard_matrices()
but check_hadamard_matrices_up_to_order_1000(), but

tscrim · 2023-03-25T13:45:34Z

Strictly speaking, that is not sufficient, but I can compromise on it. However, it still is speaking to me and saying that it should just be a doctest rather than a function. It feels like a magic number is being used.

dimpase · 2023-03-25T13:58:37Z

OK, @MatteoCati - how about indeed converting it into doctests, (tagged # not tested) to be put into the header
of the file (like, for instance, is done in src/sage/numerical/mip.pyx).

tscrim

Thank you. One last little thing (mostly formatting), but you are free to choose which option (some variation of it is also okay).

src/sage/combinat/matrices/hadamard_matrix.py

tscrim

Thank you.

dimpase

Great!

sagemathgh-39262: Add script for checking for old deprecations       To find deprecations that can now safely removed. Example: ``` python tools/check_deprecations.py src/sage/combinat Found 9 deprecations. 100%| Deprecations over one year ago: File: src\sage\combinat\permutation.py, PR: sagemath#26810, Closed Date: 2019-01-23 File: src\sage\combinat\permutation.py, PR: sagemath#27467, Closed Date: 2019-06-12 File: src\sage\combinat\words\finite_word.py, PR: sagemath#30187, Closed Date: 2020-09-15 File: src\sage\combinat\designs\difference_family.py, PR: sagemath#35211, Closed Date: 2023-04-01 ``` ### 📝 Checklist  - [ ] The title is concise and informative. - [ ] The description explains in detail what this PR is about. - [ ] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies    URL: sagemath#39262 Reported by: Tobias Diez Reviewer(s): Frédéric Chapoton, Tobias Diez

MatteoCati added 30 commits February 26, 2023 16:29

SDS functions return also the group from which sets are generated

c0eb0c1

Improve is_supplementary_difference_set, fix bug when lambda=0

7f30eef

Add is_complementary_difference_set function

5c45baf

Add first construction for complementary difference sets

f777090

Rename is_complementary_difference_set to plural

f68b661

Add second construction for complementary difference sets

270396c

change return type of complementary_difference_setI

6b3a5a9

Add third construction of complementary difference sets

876236f

Add general construction of complementary difference sets

a53394c

Add SEEALSO blocks

5186102

Add Spence construction for skew Hadamard matrix

622c3fe

Add spence construction to skew_hadamard_matrix

e96b9d6

Add construction of skew SDS over polynomial ring

3dd63fc

skew_supplementary_difference_set function uses also construction fro…

b0f4599

…m polynomial ring

GS_skew_hadamard_smallcases work even if SDS are from polynomial ring

a7b8665

Remove skew_hadamard_matrix_324 (it is now implemented using the skew…

6d558bd

… SDS function)

Add SDS of order 213, 251, 631

c4e749e

Add construction of skew SDS of order 239 with Paley-Todd difference set

6506ce0

Add skew SDS of order 331

f852f0f

Add link to new skew SDS function

f505f51

Fix complementary difference sets existence conditions

effeb87

Fix spence skew_hadamard_matrix_spence_1975 existence conditions

6e502a2

use plural name for complementary_difference_sets functions

e1bf711

Add complementary difference sets to difference_family function

225d6ea

Add function for checking amicable Hadamard matrices

36d348a

Add construction for amicable Hadamard matrices of order q+1

661bdb2

Add general construction for amicable Hadamard matrices

d5d1a37

Add construction for skew Hadamard matrices from OD

60c1f0f

Change Spe1975 reference to avoid clash

bebeec2

Move Spe1975 to correct alphabetical position in reference file

b7f29ec

Add function for checking all Hadamard matrices

7ac2641

Fix docstring of _get_all_hadamard_matrices

c4abaaf

MatteoCati and others added 2 commits March 27, 2023 09:25

Move tests to file header

0bacdb2

Merge branch 'develop' into add_skew_hadamard_matrices_up_to_1000

1c45544

tscrim requested changes Mar 27, 2023

View reviewed changes

src/sage/combinat/matrices/hadamard_matrix.py Outdated Show resolved Hide resolved

Add explanation for test

f1e5033

tscrim approved these changes Mar 28, 2023

View reviewed changes

tscrim added s: positive review t: enhancement and removed s: needs review labels Mar 28, 2023

dimpase approved these changes Mar 29, 2023

View reviewed changes

vbraun merged commit ac79f65 into sagemath:develop Apr 1, 2023

mkoeppe added this to the sage-10.0 milestone Apr 1, 2023

mkoeppe removed the s: positive review label Apr 1, 2023

Uh oh!

Add skew Hadamard matrices up to order 1000 #35211

Add skew Hadamard matrices up to order 1000 #35211

Uh oh!

Conversation

MatteoCati commented Feb 27, 2023

📚 Description

📝 Checklist

⌛ Dependencies

Uh oh!

dimpase commented Mar 23, 2023 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

MatteoCati commented Mar 23, 2023

Uh oh!

github-actions bot commented Mar 23, 2023

Uh oh!

tscrim commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

tscrim commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

tscrim commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

tscrim commented Mar 25, 2023 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

dimpase commented Mar 25, 2023 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

tscrim commented Mar 25, 2023

Uh oh!

dimpase commented Mar 25, 2023

Uh oh!

tscrim left a comment

Choose a reason for hiding this comment

Uh oh!

Uh oh!

tscrim left a comment

Choose a reason for hiding this comment

Uh oh!

dimpase left a comment

Choose a reason for hiding this comment

Uh oh!

Uh oh!

dimpase commented Mar 23, 2023 •

edited

Loading

tscrim commented Mar 25, 2023 •

edited

Loading

dimpase commented Mar 25, 2023 •

edited

Loading