Hi Sebastien,

On 2/8/13 2:36 PM, slabbe wrote:
> Hi sage-combinat !!
> 
> 1. In the file sage/combinat/backtrack.py, it is written::
> 
>     - :class:`TransitiveIdeal`: Depth first search through a
>       graph described by a ``neighbours`` relation.
>     - :class:`TransitiveIdealGraded`: Breath first search
>       through a graph described by a ``neighbours`` relation.
> 
> But it does not look like it::
> 
>     sage: C = TransitiveIdeal(lambda x: [2*x, 2*x+1], (1,))
>     sage: it = iter(C)
>     sage: [next(it) for _ in range(10)]
>     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]      < ---------- should not it be 
> [1,2,4,8,16,....] my problem if it is infinite...?
> 
> ::
> 
>     sage: C = TransitiveIdealGraded(lambda x: [2*x, 2*x+1], (1,))
>     sage: it = iter(C)
>     sage: [next(it) for _ in range(10)]
>     [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
> 
> 2. It is written (for both classes)::
> 
>     The memory complexity is the depth, that is the maximal
>     distance between a generator and an element of `S`.
> 
> But in the code, there is a set of ``known`` elements that are kept in 
> memory, so why is the complexity said to be the depth !?
> 
> 3. I really don't like the idea of having two classes (TransitiveIdeal and 
> TransitiveIdealGraded). Their __init__ are the exact same. The only 
> difference is the way the iterator is coded (TI is depth
> first and TIG is breadth first by default). They should just be merged and 
> provide two distinct iterators method instead. See my patch at 
> http://trac.sagemath.org/sage_trac/ticket/14052 where I am
> asking Anne not to add a new argument to the __init__ of TIG because I 
> believe this class should just be deprecated. To me having two classes is 
> like if the hypothesis on the relation were different,
> but they are the same, so it should be the same class!

We need this new feature for crystals for the program at ICERM (to be able to 
draw top slices
of infinite dimensional crystals).

I agree that the backtracker code should be refactored, but as Nicolas wrote on 
the ticket
http://trac.sagemath.org/sage_trac/ticket/14052 this will most likely also 
deprecate
TransitiveIdeal, so for now hopefully my patch can go in (since it is really 
about
crystals -- using features of the backtracker).

Cheers,

Anne

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