#17979: Reimplementation of IntegerListsLex
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Reporter: aschilling | Owner:
Type: defect | Status: needs_work
Priority: blocker | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: days64 | Merged in:
Authors: Bryan Gillespie, | Reviewers:
Anne Schilling, Nicolas M. Thiery | Work issues: support n in an
Report Upstream: N/A | iterable
Branch: | Commit:
public/ticket/17979 | cb18ced22db714063e744bb907a035b4fe3afa24
Dependencies: | Stopgaps:
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Comment (by bgillespie):
Replying to [comment:39 jdemeyer]:
> There is still this bug:
> {{{
> sage: it = iter(IntegerListsLex(4))
> sage: for _ in range(20): print next(it)
> [4]
> [3, 1]
> [3, 0, 1]
> [3, 0, 0, 1]
> [3, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
> }}}
> It seems that `[1,3]` will never appear in the output!
Not a bug, but an issue that's worth discussing. The premise of
IntegerListsLex, as I understand it, is that it should return integer
lists satisfying certain constraints, in lexicographic ordering, starting
with the largest. The lists returned in your example are exactly what
they should be for this specification--none of them is smaller than
`[1,3]` in lex ordering, since the `4` or `3` in the first position is
larger than the corresponding `1`.
The issue is in specifying a priori a total ordering on the set that may
not be isomorphic with that on NN (in fact, may not even be well-ordered).
Does it even make sense to call an object which iterates through a proper
countable subset of a set an iterator? On the other hand, the iteration
itself might still be useful in this case.
At the very least, this behavior is shared with that of the old
implementation.
--
Ticket URL: <http://trac.sagemath.org/ticket/17979#comment:70>
Sage <http://www.sagemath.org>
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