#19418: skew-Hadamard matrices and related srg's
-------------------------+-------------------------------------------------
Reporter: | Owner:
dimpase | Status: needs_work
Type: | Milestone: sage-6.10
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Nathann Cohen
combinatorics | Work issues:
Keywords: | Commit:
Authors: Dima | 3503d6218c68b2d1f8e08ffe832daeb0c4b393d4
Pasechnik | Stopgaps:
Report Upstream: N/A |
Branch: |
public/19418 |
Dependencies: |
#19309 |
-------------------------+-------------------------------------------------
Comment (by dimpase):
Replying to [comment:37 ncohen]:
> - I don't think that you need to import functions at the top of every
single
> '::' block. If you imported them in a previous doctest of the same
function
> they are usually around. I say 'usually' because I don't think I read
that
> anywhere, but it just works. If the order in which doctests are run
can be
> 'random', I think that it just shuffles the functions and not the
doctests
> inside of a function.
OK. Removed some of these...
>
> - docstring of zero_position: bad alignment of 'place it first'. Misses
one
> space.
>
> - Same line: the sentence is not complete -- what about adding 'When it'
at its
> beginning?
>
> - You did not doctest your new flag. Also, the code *looks* wrong.
well, actually in this case the code is not doing what is advertised;
without my flag the matrix for n=4k-1 is not symmetric w.r.t. the anti-
diagonal; the submatrix obtained by removal of the 1st row and the 1st
column is symmetric w.r.t. the anti-diagonal.
I changed the doc accordingly.
And added a doctest.
>
> - Docstring of `williamson_goethals_seidel_skew_hadamard_matrix`. Things
seem to
> miss from the first sentence of the paragraph. Or it's me being sick
again.
> P.S.: syntactically, a ')' is missing at least.
>
fixed.
> - Same function. The following doc should be in the function that
actually
> returns those matrices:
> {{{
> + Matrices for `n=36` and `52` are given in [GS70s]_. Matrices for
`n=92` are given
> + in [Wall71]_.
> }}}
>
moved
> - `_GS_skew_hadamard` -- the name of that function is a bit too vague.
What
> about `GS_skew_hadamard_smallcases`? You don't necessarily need to
make it
> private, by the way. It lives in a module and does not appear in the
global
> namespace, so only the interested guys will find it. And it's not
technically
> complicated to use, the input/output is well defined and reliable. It
can't be
> misused.
>
renamed as you proposed.
> - private functions need doctests too. 'cdef' is the only situation in
which you
> don't need them.
OK, OK... added
>
> - `def pmtoZ(s):` could be defined in the only 'if' that requires it
(not very
> important).
well, if we added more data in +- - format, it would be at the right place
as it is.
>
> - docstring of `skew_hadamard_matrix` -- in the block of doc about
'existence',
> one reads 'but that design does not exist'. Could you replace 'design'
by
> 'matrix'?
done
>
> - I don't see why the following doctest has a 'long' flag
> {{{
> sage: skew_hadamard_matrix(784,existence=True) # long time
> }}}
> If you actually built the matrix, however, that would be correct.
>
good catch - fixed
> - I don't think that `check=False` is useful when `existence=True`
> {{{
> skew_hadamard_matrix(n//2,existence=True, check=False)
> }}}
uh oh... fixed.
>
> - `if _GS_skew_hadamard(n, existence=True)` -- it hardly matters, but it
would
> be 'cleaner' to call this (quick) function before checking the more
> complicated (recursive) constructions.
Oh, well, if you feel like changing this, go ahead...
>
> - Shouldn't you also check that the matrix is 'skew-normalized', as we
do with
> the regular normalization?
> {{{
> + if skew_normalize:
> + dd = diagonal_matrix(M[0])
> + M = dd*M*dd
> + if check:
> + assert is_hadamard_matrix(M, normalized=False, skew=True)
> }}}
added a check.
>
> - If you are too humble to do it yourself, I will change that to 'Return
the
> Pasechnik graph of order n' `:-)`
> {{{
> + Pseudo-`OA(2n-1,4n-1)`-graph from a skew Hadamard matrix of order
`4n`
> }}}
if you must...
>
> - Please add your new graphs to the `graphs.<tab>` constructor.
actually, I removed them, but I'll add them again...
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=fd7894aa1f32d08c0836d506f33e883d870a9bfc
fd7894a]||{{{check that skew_normalize worked}}}||
||[http://git.sagemath.org/sage.git/commit/?id=3503d6218c68b2d1f8e08ffe832daeb0c4b393d4
3503d62]||{{{rest of fixes for hadamard_matrix.py}}}||
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=fd7894aa1f32d08c0836d506f33e883d870a9bfc
fd7894a]||{{{check that skew_normalize worked}}}||
||[http://git.sagemath.org/sage.git/commit/?id=3503d6218c68b2d1f8e08ffe832daeb0c4b393d4
3503d62]||{{{rest of fixes for hadamard_matrix.py}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/19418#comment:40>
Sage <http://www.sagemath.org>
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