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Improve performance of __getitem__ of CFiniteSequence #36764

Merged
merged 4 commits into from
Dec 14, 2023
Merged

Improve performance of __getitem__ of CFiniteSequence #36764

merged 4 commits into from
Dec 14, 2023

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ryuhei-mori
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Efficiency of __getitem__ for CFiniteSequence is improved.

Fixes #36763

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  • The title is concise, informative, and self-explanatory.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation accordingly.

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mezzarobba
mezzarobba reviewed Nov 27, 2023
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Thank you for your contribution! The code looks good to me. In addition to the two comments I already left, I would suggest that you add a reference to your paper with Alin in the docstring, and maybe an example that shows that the code can handle recurrences of higher order.

It could be nice to also improve the case where one wants a whole slice of the sequence, but maybe not in this PR.

src/sage/rings/cfinite_sequence.py Outdated
V = Matrix(QQ, d, 1, self._a[:d][::-1])
(quo, num) = num.quo_rem(den)
P = self.parent().polynomial_ring()
x = self.parent().gen()
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I find it suspect that CFiniteSequences(ZZ).gen() returns a polynomial rather than a C-finite sequence, so I would write x = P.gen() here to be safe.

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Thank you. I think both are equivalent in the current implementation as in the definition of gen() in this file. But, 'P.gen()' is slightly more efficient.

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Yes, I agree they are equivalent, but I view the current definition of gen() as a bug.

src/sage/rings/cfinite_sequence.py Outdated
return wp + list(M ** (key - off) * V)[d - 1][0]
wp = quo[n]
while n:
num = P((num * den(-x)).list()[n % 2::2])
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den(-x) actually takes quite a bit of time to compute in practice with the current implementation, so you may want to do it only once.

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Thank you. I improved it. In my enviorment, the improvment was very small. I also tried

nden = P([v if i % 2 == 0 else -v for i, v in enumerate(den)])

But, it was slower.

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ryuhei-mori commented Nov 28, 2023 •
edited

Thank you! I found you teached this algorithm in your course :)
I will add the docstring. Yes, I plan to implement the algorithm for slices.

By the way, I hope CFiniteSequences can be defined for general commutative rings or fields.
I think only closed_form() requires that the ring is QQ (or QQbar essentially).
Probably, guess() requires that it is field since the Berlekamp--Massey is explained by the Euclidean algorithm.
Except for them, I guess that we can allow general commutative rings for CFiniteSequences.

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I added a reference and examples at the docstring of __getitem__(). I also added the information of the paper in src/doc/en/reference/references/index.rst.

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Except for them, I guess that we can allow general commutative rings for CFiniteSequences.

I haven't looked in detail at the rest of the code, but this seems likely, and yes, this would be nice to have.

Let's wait for someone with the right permissions to approve the test workflows. (@fchapoton maybe?)

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Thank you! The implementation of Berlekamp--Massey in SageMath is available for integral domains because we can construct a fraction field from an integral domain.

By the way, I notice that we need the middle product for implementing our MSB-first algorithm, which is used for the computation of slices. In general, algorithms obtained by the transposition usually requires the middle product. So, I hope the middle product will be implemented as a primitive for polynomial rings, etc.

Of course, I can implement the algorithm for slices without the middle product although it includes the overhead of the constant factor.

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Documentation preview for this PR (built with commit 486c776; changes) is ready! 🎉

mezzarobba
mezzarobba approved these changes Nov 30, 2023
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Thank you!

vbraun pushed a commit to vbraun/sage that referenced this pull request Dec 10, 2023
sagemathgh-36764: Improve performance of __getitem__ of CFiniteSequence
9f2966a 
    
Efficiency of `__getitem__` for CFiniteSequence is improved.

Fixes sagemath#36763

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URL: sagemath#36764
Reported by: Ryuhei Mori
Reviewer(s): Marc Mezzarobba, Ryuhei Mori
@vbraun vbraun merged commit 2ab6da5 into sagemath:develop Dec 14, 2023
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@mkoeppe mkoeppe added this to the sage-10.3 milestone Dec 14, 2023
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Performance of __getitem__ of CFiniteSequence
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