#8227: Improving iterated palindromic closure computation
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Reporter: abmasse | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.3
Component: algebra | Keywords: iterated palindromic closure
Author: abmasse | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by abmasse):
* status: new => needs_review
Old description:
> There is a faster way to compute the iterated paindromic closure of a
> word than using the definition. The problem with the latter is that it
> needs to compute the longest f-palindromic suffix of the current word at
> each step, while it is possible to easily deduce this length only by
> looking at the directive word.
New description:
There is a faster way to compute the iterated paindromic closure of a word
than using the definition. The problem with the latter is that it needs to
compute the longest f-palindromic suffix of the current word at each step,
while it is possible to easily deduce this length only by looking at the
directive word.[[BR]]
Here is an example:
{{{
sage: w = words.RandomWord(10)
sage: w.iterated_right_palindromic_closure(algorithm='definition')
word: 0010010001001000100100010010001001001000...
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='definition').length()")
5 loops, best of 3: 211 ms per loop
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='recursive').length()")
25 loops, best of 3: 9.46 ms per loop
}}}
The difference is particularly notable for longer words:
{{{
sage: w = words.RandomWord(15)
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='definition').length()")
5 loops, best of 3: 3.73 s per loop
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='recursive').length()")
25 loops, best of 3: 37.4 ms per loop
}}}
--
Comment:
I had to implement two other functions: find() and rfind() that were only
available for Word_str words. It is not the more efficient implementation
yet, but that was not the goal of this ticket...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8227#comment:1>
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