On Oct 3, 11:16 am, Vincent Delecroix <[email protected]>
wrote:
> As far as I understand, your index.html should be built from the
> source. But I read the source and I find it not well documented from
> the point of vue of programmer. I'm really interested in your code as
> I implement similar stuff and it would be "time saving" to merge our
> classes. Moreover, I could help to submit your code to Sage.
At the moment I don't know what you have done or what you are trying
to do.
>
> 1) You wrote : "A Ribbon graph is a finite set with an involution and
> a bijection". You did not precise that the involution is without fixed
> point ? Is that volunteer ? In the book I mentionned, the author even
> authorize any permutations. This is useful from the point of vue of
> Grothendieck's "dessin d'enfants" as a Ribbon graph also encode a
> ramified covering of the sphere over three points.
>
Yes, the involution has no fixed points and it would have been helpful
if I had said this. The book you mentioned has been taken out of
the library. I have recalled it but for now I have to wait.
> 2) The advantage I get from the representation with three permutations
> (s,a,f) (s for vertices, a for edges and f for faces) is that it is
> immediate to get the inverse. Moreover, it emphasize a duality (s,a,f)
> -> (f^-1, a^-1, s^-1) which corresponds to the standard duality of
> embedded graphs. But perhaps, it is out of your interest (but your
> function anti (which is NOT documented) seems to do that operation).
>
I am not familiar with your notation. In the notation I adopted you
move
around an vertex clockwise. The function anti just moves
anticlockwise.
The dual graph is constructed by replacing the clockwise map c by
either
ce (or ec) where e is the involution.
> 3) As I mentionned, I only deal with subsets of {0,1,...,n-1} where
> you seem to be interested in more general subsets. The way
> permutations are actually implemented with Sage suggest that the base
> class deal with subsets of {0,1, ..., n-1} and a derived class could
> use a permutation with domain (which is just a mapping from {0,1, ...,
> n-1} to a subset of size n). But on the other hand, there are very
> standard operations which consists to remove edges and it is very
> natural in that context tu use "partial permutation".
I don't follow you.
>
> 4) Your main class halfedge contains two mysterious arguments "IsI"
> and "decorations". What are they ?
The IsI is for technical reasons. The decorations is to allow edges to
be drawn differently.
>
> 5) If you intend to put your code inside Sage, I find the way
> classes/functions are implemented is not clear. Why join is a function
> and not a method (as union for Python set) ? Moreover, in Sage, there
> is a convention that any class should be denoted in Wiki syntax as
> MyFavoriteClass and functions should use lower case with underscore as
> my_favorite_function (There are counterexample inside Sage). In your
> case, you should be much more precise in the choosen names : Embedding
> should become for example RibbonGraphEmbedding or similar.
I think it is clear. I accept I may not have followed conventions.
I have no problem with editing names.
>
> I have many more comments, but I would like to have more
> specifications in each of the methods (and not more example). I want
> to understand what is implemented (and how) and not what the code can
> do.
Maybe we should discuss this further off-line. Please feel free to e-
mail me.
>
> Cheers,
> Vincent
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