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!
And if one really want __iter__ to behave depth first and /or breadth
first, then we can make add changeable argument for type of enumeration
used by __iter__.
Cheers,
Sébastien
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