#7301: Gale Ryser theorem
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Reporter: ncohen | Owner: mhansen
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: combinatorics | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by wdj):
In reply to an email Nathann Cohen sent me:
> Several questions about your patch :
> * Do you think function slider01 is useful by itself in the
> integer_vector class ( and if so, under, should'nt it be renamed to be
> more "explicit", if possible ? ) ? My advice is that it may be better
> to move it *inside* of function fale_ryser_theorem
Python has a mechanism for "private" functions like slider01, so
I renamed it _slider01. I think that is better than hiding it inside
gale_ryser_theorem. Is that okay?
> * There is one commented line in is_gale_ryser
> * Why don't you want to use the method Partition.dominates for
> your test in is_gale_ryser ?
I think this will not work, if you want to allow trailing 0's.
Maybe I am missing something?
> * Why do you say that the LP formulation is Gale's construction ?
> You mean that Gale proved this result using LinearProgramming ? If so,
> do you have access to an electronic version of the text you are citing
> ? I'd be extremely interested in giving it a look... Very few
> theretical results are proved using LP :-)
I was told that by my colleague which is much much more of an expert on
this stuff. I have not read Gale's paper and don't know of an electronic
version.
> * In you docstrings you frequently use $$ for LaTeX expressions.
> As I never saw it anywhere in Sphinx, I do not know whether it works :
> I always use ` instead of $. Is the documentation built correctly this
> way ? I prefer your $ to my usual `, so I'm interested in the
> answer....
I changed all $ to '. Thanks!
> * I will be running tests to compare the speed of your
> construction of the matrices... I expect your method to be much faster
> than mine, perhaps something about it should be said in the docstrings
> * I do not know if it is a requirement of Sphinx, but Minh ( who I
> claim is perfection made flesh ) gave me several "needs work" because
> of the way I formatted docstrings for References. What I take for
> model now is the functions citing Cliquer in the graph.py file. The
> document's keys are not integers but "the usual" concatenations of the
> authors'initials and the year, for example [Ryser63] and [Gale57].
> Besides, they appear with a trailing _ when used to cite the paper.
> You are bound to find one if you look for the string "]_" in Sage's
> files ( but you will definitely find them if you look for "Cliquer" in
> sage/graphs/graph.py"
Thank you for the reference! I think the docstrings are okay now.
> * In gale_ryser_theorem the two :: after EXAMPLES should be
> removed for the generated documentation to be correct. Same thing
> after References, and in slider01. The sign :: is saying to Sphinx
> that what is following is a piece of Sage code. So you should only
> write them when it is the case, for example after EXAMPLES in
> is_gale_ryser. It may be better to generate the documentation to check
> that it is visually correct :-)
Done. Thanks.
>
> I will be keeping an eye on Sage-devel to be kept aware of the next
> alpha release... I tried alpha0 which failed to compile on my computer
> and I am at the moment without any Sage install available ( I have
> sage.math in case of need, though ). I hope it will be available soon
> :-))))))
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7301#comment:29>
Sage <http://www.sagemath.org>
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