Hi,
> I know nothing of combinatorics, but shouldn't accessing a set's n-th
> element be more understandable using S[n] ?
I agree.
I would think S.index(x) would be more intuitive to a non-
combinatorist
like me. Do I understand correctly that these are sets enumerated by
an indexing set (e.g. of natural numbers)? I vote for EnumeratedSets,
or IndexedSets.
(Countable|Enumerable)Sets would be descriptive for a datastructure
without indexing function.
IterableSets does not capture the fact that there is a indexing
structure,
and CombinatorialSets doesn't convey anything to me, except that I
probably should never use it (not belonging to the club of
combinatorists
who immediately understand what auxilliary properties of a class
[class
in the Python/object-oriented sense] of sets are defined and used by
combinatorists).
For comparison, in Magma one has enumerated sets:
SetEnum:
finite sets with hashing in which the elements are expanded
or "enumerated" in memory (as opposed to defined by some
membership test function)
and indexed sets (SetIndx):
SetIndx:
a SetEnum X with an indexing function {1,...,n} -> X.
I don't like the former name (for the Magma structure), since the
sets are in fact only finite, and the sense in which they are
enumerated is vague. I would be happy if an EnumeratedSets
class in Sage reclaimed the term "enumerated" to mean that
the sets are actually enumerated by an indexing function, and
which are enumerable but not necessarily finite.
I would also like to see a class which is generally useful
throughout Sage, as the default return type for many different
finite or enumerable structures.
--David
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