#8588: list(SL(2,2)) is inconsistent with SL(2,2).list()
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Reporter: nthiery | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone:
Component: algebra | Resolution:
Keywords: Special linear group, TestSuite | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Are you sure this is a wise fix? This way, even starting to iterate on the
elements of a matrix group involves constructing all its elements. The
iterator method on matrix groups previously was the one inherited from
`sage.combinat.backtrack.TransitiveIdeal.__iter__`, which seems a little
more conservative.
In principle, people can write `iter(SL(next_prime(10^5),2)).next()` to
get an example of a determinant 1 matrix. This doesn't need to be
expensive (with the current code it is, though. It seems the
`semigroup_generators` method is horribly inefficient). With the present
patch it's guaranteed to be very expensive.
Iterators and lists have different use cases, so why should G.list() and
list(G) give the same result? I think structures should be allowed to
choose different enumeration methods depending on the application.
G.list() knows it returns a list of all elements, so it can concentrate on
speed and not worry about storage. list(G), which is just [g for g in G]
asks G to produce an iterator over its elements, which can choose an
enumeration method that saves memory and/or ensures that it's fast even
when only a couple of elements are consumed.
It seems to me the correct fix is to amend `TestSuite` to not enforce that
iter(G.list()) and iter(G) produce the elements in the same order.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8588#comment:3>
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