Hi Volker,
On Thu, Nov 08, 2012 at 08:02:49AM -0800, Volker Braun wrote:
> This occurred to me before, its nice to have iterators/generators but
> there should be a mechanism to say that the iterator is over a finite or
> infinite set.
> Just to avoid doing exhaustive searches over infinite sets.
> Similar to C++ iterator traits, I guess. Of course if you were to manually
> implement a generator as a Python class (implementing __next__) you could
> attach other methods like is_finite(). But then you'd always have to write
> a lot of boilerplate to return an iterator. Its much easier to use yield,
> but then you can't return any additional information about finiteness.
> The alternative is to assume that the user knows what he is doing when he
> passes an iterator / generator object. V.sum(W) can and should still check
> that W is finite before starting to iterate over W.
There is already a bit of infrastructure for this; namely an parent
modeling an enumerated set which is infinite should declare itself in
the category InfiniteEnumeratedSets (soon to come: Sets().Infinite()).
Then, methods could do some checks on this; that's already the case
for e.g. ``list``::
sage: ZZ.list()
Traceback (most recent call last):
...
ValueError: since it is infinite, cannot list Integer Ring
Of course a preliminary step would be to make sure that parents are
put in this category when relevant. Here QQ^3 should not only be an
iterable but actually an infinite enumerated set:
sage: (QQ^3) in InfiniteEnumeratedSets() # todo: not implemented
True
More precisely: QQ^3 should be in the category of finite dimensional
modules with basis, and a finite dimensional module with basis over an
infinite field should be in the category of infinite enumerated sets.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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