Hello,
it would be nice to get some feedback.
This bug has consequences on other functions in the combinatorics on
words package: for instance, you get
sage: Word('abaa').is_conjugate_with(Word('aaba'))
True
sage: Word('aaba').is_conjugate_with(Word('abaa'))
False
even though conjugacy is an equivalence relation. Again, the problem
here is that "-1" mistake in the conjugate_position method. It is just
a small change, and this group is the only place I know for proposing
it.
Thanks
Alessandro
On 21 Mar, 16:11, Alessandro De Luca <alessandro.del...@utu.fi> wrote:
> I have taken a look at the code, and I think I have identified the
> bug. I'm not sure this is the most appropriate place to suggest a
> modification; if not, I hope someone can forward this to the right
> address, or at least tell me where to post it.
>
> Here are some tests showing the issue:
>
> sage: w=Word([0,0,1,0,2,1]); w
> word: 001021
>
> sage: w.conjugate(-1) #a conjugate is just a cyclic shift
> word: 100102
>
> sage: w.conjugate(5) #cyclic shifts are defined modulo the length
> word: 100102
>
> #conjugate_position correctly shows here how much you need to shift w
> to get its 0th conjugate (itself)
> sage: w.conjugate(0).conjugate_position(w)
> 0
>
> sage: w.conjugate(1).conjugate_position(w)
> 1
>
> # in general, for primitive words (i.e., non-powers) such as w, the
> result of
> # w.conjugate(n).conjugate_position(w)
> # should always equal n % w.length():
> sage: w.conjugate(-2).conjugate_position(w)
> 4
>
> sage: w.conjugate(-1).conjugate_position(w) #so here the output
> should be 5, but...
>
> sage: w.conjugate(-1).conjugate_position(w) is None #oops!
> True
>
> sage: v=Word('abacabac'); v #the square of 'abac', a non-primitive
> word
> word: abacabac
>
> #the following computation is right; the bug only appears when the
> expected answer is length-1
> #so non-primitive words always work fine.
> sage: v.conjugate(-1).conjugate_position(v)
> 3
> ________
>
> Here is the current version of the code:
>
> def conjugate_position(self, other):
> r"""
> Returns the position where self is conjugate with other.
> Returns None if there is no such position.
>
> EXAMPLES::
>
> sage: Word('12113').conjugate_position(Word('31211'))
> 1
> sage: Word('12131').conjugate_position(Word('12113')) is None
> True
> sage: Word().conjugate_position(Word('123')) is None
> True
> """
> if self.length() != other.length():
> return None
> if self == other:
> return 0
> for l in xrange(1, other.length() - 1):
> other = other.conjugate(1)
> if self == other:
> return l
> return None
>
> I believe that in order to fix this bug, it is sufficient to
> substitute line -5, i.e.,
> for l in xrange(1, other.length() - 1):
>
> with the following
> for l in xrange(1, other.length()):
>
> I hope I have made myself clear.
> Thanks again, bye
>
> Alessandro
>
> On 21 Mar, 09:35, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr>
> wrote:
>
>
>
>
>
>
>
> > Hi Alessandro,
>
> > On Sun, Mar 20, 2011 at 05:48:22PM -0700, Alessandro De Luca wrote:
> > > I am writing because the conjugate_position method (for finite words)
> > > is not working the way I expected. I believe that the output for
>
> > > w.conjugate(-1).conjugate_position(w)
>
> > > should equal w.length()-1 for all words w on at least two letters.
> > > However, I seem to get no answer, all the time (just as if the two
> > > words were not conjugate). All other positions, apart from -1, seem to
> > > work just fine.
> > > I'm running the latest Sage version, 4.6.2.
>
> > I don't know what the right thing should be here. But please include
> > examples with the obtained output and the output you'd expect:
>
> > sage: w = ...
> > sage.conjugate(-1).conjugate_position(w)
> > ...
>
> > Whatever is the conclusion of the discussion, those should be added to
> > the documentation with an explanation; so this is not wasted time, and
> > it makes things concrete.
>
> > Thanks!
> > Nicolas
> > --
> > Nicolas M. Thi�ry "Isil" <nthi...@users.sf.net>http://Nicolas.Thiery.name/
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