Hello,
I'm working on refactorization of sage.combinat.words (#12224) and I
have two general questions of design.
1) The class Alphabet (in sage.combinat.words.alphabet) does nothing
more or less than EnumeratedSets (in
sage.sets.finite_enumerated_sets). It is considered as a basis for the
free monoid named "Words" in sage.combinat.words.words. I suggest to
remove it and that Words will be built on an EnumeratedSet. Does
anyone see an obstruction to that ?
2) There is a speed question about whether or not expanding an inverse
dictionnary for FiniteEnumeratedSet. I mean a dictionnary {elt nb i ->
i}. It is critical for words (and I hope for other purposes) to test
quickly whether an element is contained in a FiniteEnumeratedSet. For
a set of size 100 there is a factor 10 of efficiency:
{{{
sage: l = range(100)
sage: s = set(l)
sage: timeit('0 in l')
625 loops, best of 3: 333 ns per loop
sage: timeit('123 in l')
625 loops, best of 3: 5.8 µs per loop
sage: timeit('0 in s')
625 loops, best of 3: 360 ns per loop
sage: timeit('123 in s')
625 loops, best of 3: 338 ns per loop
}}}
Storing the inverse dictionnary will speed up the rank function as well.
Cheers,
Vincent
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