Hi Vincent Delecroix,
> There is a difference at the interpreter level, look at :
> sage: timeit('len(l)')
> 625 loops, best of 3: 229 ns per loop
> sage: timeit('l.__len__()')
> 625 loops, best of 3: 442 ns per loop
>
> I don't know exactly why. Perhaps the len() do not have to parse the
> list of methods of the object ?
I'd guess : some python internal optimization for basic datatype. I.e. if l is
a list the python interpreter looks directly into to data structure without
calling .__len__() but it's special to lists.
> I really agree that the case of words is really special. A word has a
> length but no cardinality. Perhaps it's the same for other
> combinatorial object (but no combinatorial classes). And I think that
> a word is more a combinatorial object.
For combinatorial objects, in the "real life" (ie talk/course) as well as in
MuPAD, we use to call this the size of the object. Eg: the size of a
the permutations [3,1,2,5,4] is 5, the size of the partitions (3,2,1,1,1)
is 8, the size of a tree is its number of node...
> If we choose something for combinatorial classes the count is not so
> bad, because a combinatorial class is not a list (there is no
> repetition).
It is not clear for me and in some case wrong... Some combinatorial class are
multisets.
Cheers,
Florent
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