Allow coercion from Frac(QQ[x]) to LaurentSeriesRing(QQ) #39365
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Maybe an option would to replace 'A.is_field() |
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What doesn't is (on the positive side once |
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You are probably right. So we have the choice either to do nothing and avoid triggering the primality check, or do what you propose. I think that we can accept the cost of primality testing. So I agree to give a positive review. By the way, thanks a lot for your many pull requests, that I find very good and that are helping us to improve sage. I am currently at a Sage Days meeting, and several of us are appreciating your contributions. |
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Thanks! |
vbraun
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sagemathgh-39365: Allow coercion from Frac(QQ[x]) to LaurentSeriesRing(QQ) If `A` is a field then `self = LaurentSeriesRing(A)` is a field, by universal property of fraction field, a coercion `P.base() → self` can be uniquely extended to `P → self`. So this makes sense. As a side effect, this coercion allows the user to write things such as ```sage sage: R.<x> = QQ[] sage: 1/(x-1)+O(x^100) -1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16 - x^17 - x^18 - x^19 + O(x^20) ``` Another side effect: If the base ring is something like `Zmod(5)` or `QQ["x"].quotient(...)` then a primality/irreducibility check will be carried out. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [ ] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#39365 Reported by: user202729 Reviewer(s):
vbraun
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Feb 21, 2025
sagemathgh-39485: Implement conversion from laurent series to rational function field As in the title. I think this behavior makes sense because `QQ(RR(…))` currently uses `.simplest_rational()` instead of like exact value (like `x / 2^53` for some integer `x`), so it makes sense for similar conversions to compute a good approximation too. I cannot prove that this round-trips, however. Note that currently conversion from power series `QQ[[x]]` to polynomial ring `QQ[x]` truncates, because of implementation detail this leads to conversion from `QQ[[x]]` to `Frac(QQ[x])` also truncates. I think this is undesirable behavior because identical-looking elements in `QQ[[x]]` versus `Frac(QQ[[x]]) = LaurentSeriesRing(QQ, "x")` has different conversion behavior. Elements which are already Laurent polynomial are preserved. Side note: `.one()` is faster because it's cached ```sage sage: R.<x> = QQ[] sage: S = Frac(R) sage: %timeit S.one() # fast because it's cached 90.6 ns ± 1.27 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each) sage: ring_one = S.ring().one() sage: %timeit S._element_class(S, ring_one, ring_one, coerce=False, reduce=False) 3.42 μs ± 75 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each) ``` Maybe this doesn't need to be explicitly written in the documentation (users trying to do the conversion will just see the result) There exists also <code>:meth:\`.PowerSeries_poly.pade\`</code> which should probably be mentioned in the documentation. Reverse direction (that one is a morphism): sagemath#39365 Possible caveat: ``` sage: S(Frac(V)(1/(x+1))/(x^10)) 1/(x^11 + x^10) sage: S(Frac(V)(1/(x+1))/(x^30)) (-x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)/x^30 ``` It could be argued the latter would be simpler as `1/(x^31+x^30)`, but then that way gives higher denominator degree. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#39485 Reported by: user202729 Reviewer(s): Travis Scrimshaw, user202729
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If
Ais a field thenself = LaurentSeriesRing(A)is a field, by universal property of fraction field, a coercionP.base() → selfcan be uniquely extended toP → self. So this makes sense.As a side effect, this coercion allows the user to write things such as
Another side effect: If the base ring is something like
Zmod(5)orQQ["x"].quotient(...)then a primality/irreducibility check will be carried out.📝 Checklist
⌛ Dependencies