#27347 closed enhancement (fixed)
Lazy Laurent series
Reported by:  klee  Owned by:  

Priority:  minor  Milestone:  sage8.8 
Component:  algebra  Keywords:  
Cc:  Merged in:  
Authors:  Kwankyu Lee  Reviewers:  Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  989f009 (Commits, GitHub, GitLab)  Commit:  
Dependencies:  Stopgaps: 
Description (last modified by )
Introduce lazy Laurent series to Sage.
A lazy Laurent series computes coefficients only when demanded or needed. In a sense, lazy Laurent series are Laurent series of infinite precision.
A generating function example from the code:
Generating functions are laurent series over the integer ring:: sage: from sage.rings.lazy_laurent_series_ring import LazyLaurentSeriesRing sage: L = LazyLaurentSeriesRing(ZZ, 'z') This defines the generating function of Fibonacci sequence:: sage: def coeff(s, i): ....: if i in [0, 1]: ....: return 1 ....: else: ....: return s.coefficient(i  1) + s.coefficient(i  2) ....: sage: f = L.series(coeff, valuation=0); f 1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + ... The 100th element of Fibonacci sequence can be obtained from the generating function:: sage: f.coefficient(100) 573147844013817084101
Lazy Laurent series is of course useful for other things. This will be used to implement infinite precision Laurent series expansion of algebraic functions in function fields, as a sequel to #27418.
Change History (58)
comment:1 Changed 2 years ago by
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comment:3 Changed 2 years ago by
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ace4282  pyflakes fixes

comment:5 Changed 2 years ago by
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389798e  Add series method

comment:6 Changed 2 years ago by
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Branch pushed to git repo; I updated commit sha1. New commits:
43ba785  Small fixes on docstrings

comment:7 Changed 2 years ago by
 Description modified (diff)
comment:8 Changed 2 years ago by
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comment:9 Changed 2 years ago by
 Commit changed from 43ba7859f92d707e2f6f3cf93aafbc4f7f4b453a to e7ff9993551778c67c6a6168f0e26c5943f14925
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
e7ff999  Add lazy laurent series

comment:10 Changed 2 years ago by
 Commit changed from e7ff9993551778c67c6a6168f0e26c5943f14925 to 15e1b1c671d61ef279f1c32a715ddd56a2fa7997
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
15e1b1c  Add lazy laurent series

comment:11 Changed 2 years ago by
 Commit changed from 15e1b1c671d61ef279f1c32a715ddd56a2fa7997 to f70fca8e3303c51b98c3f9311da277fd954b1ebe
Branch pushed to git repo; I updated commit sha1. New commits:
f70fca8  Add __bool__

comment:12 followups: ↓ 13 ↓ 17 ↓ 18 Changed 2 years ago by
Some comments:
Is there a reason why you do not use the LazyPowerSeriesRing
for the main element (with a nonzero constant term until the whole series is zero) and then just store the valuation? This is how things are done for the Laurent polynomials. That way there is less duplication of code and improvements to one improve both.
Why do you override __eq__
and not use the one provided by Element
and the coercion framework? It is more flexible and allows you do implement comparisons (if you want) all in one function of _richcmp_
.
Do not have bare except:
statements (see coefficient
).
Does the elements pickle? I am a little worried that the addition of two power series will not pickling because of the little helper add
function. You should add a loads(dumps(foo))
test if it does work.
Typo laurent
> Laurent
(it is proper noun).
if len(s) == 0:
> if not s:
comment:13 in reply to: ↑ 12 Changed 2 years ago by
 Status changed from needs_review to needs_work
Replying to tscrim:
Is there a reason why you do not use the
LazyPowerSeriesRing
for the main element (with a nonzero constant term until the whole series is zero) and then just store the valuation? This is how things are done for the Laurent polynomials. That way there is less duplication of code and improvements to one improve both.
I looked into the LazyPowerSeriesRing
many years ago:
I think I didn't like it in several ways :) Still I don't understand this behavior:
sage: L.<t>=LazyPowerSeriesRing(QQ) sage: s=L([0,0,1,2]) sage: s.coefficient(0) 0 sage: s.coefficient(1) 0 sage: s.coefficient(2) 1 sage: s.coefficient(3) 2 sage: s t^2 + 2*t^3 + O(x^4) sage: s.get_order() 1 sage: s.get_aorder() 1
The reason was that it was easy to implement lazy laurent series with an interface and behaviors that I prefer, while I could not understand well enough LazyPowerSeriesRing
...
I would reconsider basing lazy laurent series on LazyPowerSeriesRing
, if you help me understand the strange behaviour above.
comment:14 Changed 2 years ago by
So here is what refine_aorder
does. It first checks if self.order
has been set, if it has, do not do anything. Then it goes through all of the n
computed entries if self.aorder
is 0 and we have already computed at least one entry. Then find the first nonzero entry. If we have found one, set the order.
The problem is the bold part. After the first iteration when n = 1
, the self.aorder
gets set to 1
, then on the second run through, that block does not get run, which then means self.aorder < n
and we set the order to be 1
.
sage: s.coefficient(1) 0 sage: s.aorder 1 sage: s.order Unknown series order sage: s.coefficient(2) 1 sage: s.aorder 1 sage: s.order 1
IMO, this is a bug.
comment:15 Changed 2 years ago by
 Commit changed from f70fca8e3303c51b98c3f9311da277fd954b1ebe to fb4d65d9dfdb53a735ca33e7800ef79e4ea8ece4
comment:16 Changed 2 years ago by
 Commit changed from fb4d65d9dfdb53a735ca33e7800ef79e4ea8ece4 to 41f3a4237cc0f574334a6e26e00f16d73d23972a
Branch pushed to git repo; I updated commit sha1. New commits:
41f3a42  Lazy Laurent series is not picklable

comment:17 in reply to: ↑ 12 Changed 2 years ago by
Why do you override
__eq__
and not use the one provided byElement
and the coercion framework? It is more flexible and allows you do implement comparisons (if you want) all in one function of_richcmp_
.
Ok. Fixed.
Do not have bare
except:
statements (seecoefficient
).
Fixed.
Does the elements pickle? I am a little worried that the addition of two power series will not pickling because of the little helper
add
function. You should add aloads(dumps(foo))
test if it does work.
No. Your worry is real; lazy Laurent series is not picklable in general. This seems an inherent nature of my implementation...
I added a test to show this.
Typo
laurent
>Laurent
(it is proper noun).
Right. Fixed.
if len(s) == 0:
>if not s:
Done.
New commits:
41f3a42  Lazy Laurent series is not picklable

comment:18 in reply to: ↑ 12 ; followup: ↓ 20 Changed 2 years ago by
Replying to tscrim:
Some comments:
Is there a reason why you do not use the
LazyPowerSeriesRing
for the main element (with a nonzero constant term until the whole series is zero) and then just store the valuation? This is how things are done for the Laurent polynomials. That way there is less duplication of code and improvements to one improve both.
I thought about this. Now I think:
Lazy Laurent series is not just about Laurent series but also about how coefficients are computed lazily. A LazyPowerSeriesRing
element gets its coefficients from a stream object, which essentially yields coefficients as required. On the other hand, lazy Laurent series s
gets its coefficients from a python function that outputs nth coefficient for input s
and n
. This allows coefficients to be computed recursively. For example, it is very easy to define the Fibonacci series.
So it is impossible to base my lazy Laurent series code on LazyPowerSeriesRing
without abandoning the essential feature of the implementation.
Frankly, I would rather provide new lazy power series as a subclass of my lazy Laurent series. But this is of course highly biased opinion :)
You may be reluctant to accept my implementation of lazy Laurent series into sage.rings
as it then gets kind of standard status among different possible implementations of lazy Laurent series in Sage. Then I am willing to relocate it into sage.rings.function_field
.
comment:19 Changed 2 years ago by
 Commit changed from 41f3a4237cc0f574334a6e26e00f16d73d23972a to b09cd84220dc5878d03db5d1ee1d721388457b4e
Branch pushed to git repo; I updated commit sha1. New commits:
b09cd84  Fix pickling doctest

comment:20 in reply to: ↑ 18 ; followup: ↓ 22 Changed 2 years ago by
Replying to klee:
Replying to tscrim:
Some comments:
Is there a reason why you do not use the
LazyPowerSeriesRing
for the main element (with a nonzero constant term until the whole series is zero) and then just store the valuation? This is how things are done for the Laurent polynomials. That way there is less duplication of code and improvements to one improve both.I thought about this. Now I think:
Lazy Laurent series is not just about Laurent series but also about how coefficients are computed lazily. A
LazyPowerSeriesRing
element gets its coefficients from a stream object, which essentially yields coefficients as required. On the other hand, lazy Laurent seriess
gets its coefficients from a python function that outputs nth coefficient for inputs
andn
. This allows coefficients to be computed recursively. For example, it is very easy to define the Fibonacci series.
Well, I am fairly certain you could do this with an RecursivelyEnumeratedSet
and a bit of knowhow, but I agree that it is more complicated and less intuitive. I also agree that having general functions as input would probably be a good thing for LazyPowerSeriesRing
to have, but I believe that was designed for more specific use for the combinat/species
code.
One benefit I do see is that you do not need to explicitly know the valuation at creationtime. With my suggested implementation, it does need to be computed at element creation.
Frankly, I would rather provide new lazy power series as a subclass of my lazy Laurent series. But this is of course highly biased opinion :)
I don't have an opinion on this matter, but there are likely some considerations required to replace or extend the current implementation.
You may be reluctant to accept my implementation of lazy Laurent series into
sage.rings
as it then gets kind of standard status among different possible implementations of lazy Laurent series in Sage. Then I am willing to relocate it intosage.rings.function_field
.
This I don't really care about. I just am a little unhappy with the large difference between the semantics (and syntax) between the two implementations. I guess that is a bit unavoidable here because this definitely is serving a purpose.
However, I do think we should at least try to address the pickling issues. I believe this means you cannot use this in parallel implementations (IIRC this uses pickling to communicate between the processes). It also means you cannot (easily) store the data you compute. I think it is sufficient to separate out the add
and similar operations into functions, but maybe they need to be small little helper class, such as
class LaurentSeriesOperator(object): def __init__(self, lps, op): self.lps = lps self.op = op def __call__(self, s, n): return self.op(self.lps[n], s[n]) def __reduce__(self): return (type(self), (self.lps, self.op), {}) def __eq__(self, other): return (isinstance(other, LaurentSeriesOperator) and self.lps == other.lps and self.op == other.op)
where op
is, e.g., operator.add
. This way you might be able to do something with comparisons in some semireasonable capacity too.
comment:21 Changed 2 years ago by
 Commit changed from b09cd84220dc5878d03db5d1ee1d721388457b4e to 89992b806e2d534343bb57c2a6cec1d0fecd9394
Branch pushed to git repo; I updated commit sha1. New commits:
89992b8  Reimplement arithmetic operations for series to be picklable

comment:22 in reply to: ↑ 20 Changed 2 years ago by
Replying to tscrim:
However, I do think we should at least try to address the pickling issues. I believe this means you cannot use this in parallel implementations (IIRC this uses pickling to communicate between the processes). It also means you cannot (easily) store the data you compute. I think it is sufficient to separate out the
add
and similar operations into functions, but maybe they need to be small little helper class, such asclass LaurentSeriesOperator(object): def __init__(self, lps, op): self.lps = lps self.op = op def __call__(self, s, n): return self.op(self.lps[n], s[n]) def __reduce__(self): return (type(self), (self.lps, self.op), {}) def __eq__(self, other): return (isinstance(other, LaurentSeriesOperator) and self.lps == other.lps and self.op == other.op)where
op
is, e.g.,operator.add
. This way you might be able to do something with comparisons in some semireasonable capacity too.
Using modulelevel classes to define operators is a good idea. Hinted by your template class, I could reimplement lazy Laurent series to be picklable. Great!
comment:23 Changed 2 years ago by
 Commit changed from 89992b806e2d534343bb57c2a6cec1d0fecd9394 to 989a3ac561bed35c9466a848e2a9ef441f94f560
Branch pushed to git repo; I updated commit sha1. New commits:
989a3ac  Comparison now works in semireasonable capacity

comment:24 Changed 2 years ago by
 Commit changed from 989a3ac561bed35c9466a848e2a9ef441f94f560 to e12fd5b6511f90ccb9b5b7bc59cb61e30d75cc93
comment:25 Changed 2 years ago by
 Description modified (diff)
comment:26 Changed 2 years ago by
 Summary changed from Lazy laurent series to Lazy Laurent series
comment:27 Changed 2 years ago by
 Commit changed from e12fd5b6511f90ccb9b5b7bc59cb61e30d75cc93 to 5214a3a020c8e268c62957990f3ef5351641bd3f
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
afeae09  Merge branch 'functionfieldsinfinityprecision' into functionfields

bf81509  Merge branch 'lazypowerseriestrac27347' into functionfields

e552770  fix

6c5fc73  Merge branch 'functionfieldsinfinityprecision' into functionfields

f616d20  Merge branch 'lazypowerseriestrac27347' into functionfieldsinfinityprecision

8d77ecc  Merge branch 'functionfieldsinfinityprecision' into functionfields

bbeebef  Merge branch 'functionfields' into curvesirreducible

64c9c6b  Add deltainvariant

6142750  Add ag codes

5214a3a  Add list operator and allow list input

comment:28 Changed 2 years ago by
 Commit changed from 5214a3a020c8e268c62957990f3ef5351641bd3f to eac7047c33c8fd1201e86493df34ef9cb805e893
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
eac7047  Add list operator and allow list input

comment:29 Changed 2 years ago by
Oops. Pushed a wrong branch!
comment:30 Changed 2 years ago by
 Status changed from needs_work to needs_review
comment:31 followup: ↓ 33 Changed 2 years ago by
This is looking good.
Past experience tells me you should also implement a __ne__
at the base class. I also think you should include more ABCs to avoid the extra duplication with the __eq__
methods. Similarly, why not use the op
version for +*/
to avoid class duplication? You may also want a __hash__
and incorporate that into the hash of the lazy Laurent series. With how many operator classes you have, it may also be worthwhile pulling that out to a separate file for better separationsofconcerns between files.
comment:32 Changed 2 years ago by
 Commit changed from eac7047c33c8fd1201e86493df34ef9cb805e893 to f5b579285b0daf9bab2955dbb397174467fd3e47
Branch pushed to git repo; I updated commit sha1. New commits:
f5b5792  Add hash and fix other issues from reviewer comments

comment:33 in reply to: ↑ 31 ; followup: ↓ 34 Changed 2 years ago by
Replying to tscrim:
This is looking good.
Past experience tells me you should also implement a
__ne__
at the base class.
Done.
I also think you should include more ABCs to avoid the extra duplication with the
__eq__
methods.
Ok.
Similarly, why not use the
op
version for+*/
to avoid class duplication?
I don't get it. They cannot be treated uniformly. Look at the __call__
method.
You may also want a
__hash__
and incorporate that into the hash of the lazy Laurent series.
Done.
With how many operator classes you have, it may also be worthwhile pulling that out to a separate file for better separationsofconcerns between files.
Done.
comment:34 in reply to: ↑ 33 ; followup: ↓ 36 Changed 2 years ago by
Replying to klee:
Replying to tscrim:
Similarly, why not use the
op
version for+*/
to avoid class duplication?I don't get it. They cannot be treated uniformly. Look at the
__call__
method.
You can do what I suggested in comment:20 for these classes:
LazyLaurentSeriesOperator_add
(by passingoperator.add
)LazyLaurentSeriesOperator_sub
(by passingoperator.sub
)
You're right that multiplication must be treated separately. Although you could also do this for a scalar multiplication version of this (which will be faster than coercion and multiplication). For 2 cases, there is a less compelling reason to factor the common code out like this.
There is not really a benefit for doing this for unitary operations (as there is only 1 that could work this way).
In some ways it feels like we are reinventing the wheel here because we are effectively building an evaluation tree, and we already have something like this within SR
(or sympy/pynac/etc.). However, I don't see a way around this by using SR
(and we might have to work a little bit to avoid doing computations unnecessarily inside of there). So I think we have to keep doing things this way. Just an observation.
comment:35 Changed 2 years ago by
 Commit changed from f5b579285b0daf9bab2955dbb397174467fd3e47 to 3bf2101b59d3d13aca9815fbe907ff7ad6c33cdb
Branch pushed to git repo; I updated commit sha1. New commits:
3bf2101  Add scalar multiplication operator

comment:36 in reply to: ↑ 34 Changed 2 years ago by
Replying to tscrim:
Although you could also do this for a scalar multiplication version of this (which will be faster than coercion and multiplication).
Added scalar multiplication.
In some ways it feels like we are reinventing the wheel here because we are effectively building an evaluation tree, and we already have something like this within
SR
(or sympy/pynac/etc.). However, I don't see a way around this by usingSR
(and we might have to work a little bit to avoid doing computations unnecessarily inside of there). So I think we have to keep doing things this way. Just an observation.
True. It is just inevitable that sometimes we make wheels for different needs :)
comment:37 followup: ↓ 44 Changed 2 years ago by
I find this quite wonderful! It would be great if we could replace LazyPowerSeries
with this. One feature of LazyPowerSeries
was that it allows recursive definitions "guessing" the correct initialisations, as for example in
sage: L = LazyPowerSeriesRing(QQ) sage: one = L(1) sage: monom = L.gen() sage: s = L() sage: s._name = 's' sage: s.define(one+monom*s*s) sage: [s.coefficient(i) for i in range(6)] [1, 1, 2, 5, 14, 42]
Although this is based on the original code by Ralf Hemmecke and myself, which in turn is based on code of Nicolas Thiery (I think), I am not sure anymore whether it is so important. Of course, if we could have something similar, even better.
comment:38 followup: ↓ 43 Changed 2 years ago by
One question with respect to equality. It seems to me that your implementation of __eq__
is quite brittle. It is clear that one cannot have proper equality, so it should be clearly stated what it can do and what it can't.
Apart from that, in the case of truncation, one could make it exact easily.
comment:39 followup: ↓ 42 Changed 2 years ago by
Some other comments on the code:
For __bool__
, I think erroring out immediately when self._constant is None
is not the way to go. I think you should check the computed coefficients in that case to see if any of them are nonzero. If they are all 0
, then you should error out. Also, a fast first check when self._constant
is not None
is to see if that constant is nonzero 0
.
In _repr_
, I do not see how self.valuation()
would normally raise a ValueError
. That method does not raise one, nor does self.coefficient()
(the only other method it calls).
Instead of self.parent()(1)
, which calls the coercion framework, you should use self.parent().one()
.
Are you sure you want _div_
to be two separate operations and not one combined one? I feel like the latter would be faster (at least since it is implemented at the Python level).
Actually, you may want to make the operator file into a Cython file (since is forms the key computational part and it is in a separate file).
I think the truncate should return an honest Laurent polynomial. Furthermore, I don't think there are coercions (or at least conversions) from the corresponding Laurent polynomial ring. This feels like a very natural to have. I don't want to go too far with ticket expansion, but this feels like something people will try soon after having this.
comment:40 Changed 2 years ago by
 Commit changed from 3bf2101b59d3d13aca9815fbe907ff7ad6c33cdb to 86ccdc42aab475d7ffb04e02eb210f58b79f04b6
comment:41 Changed 2 years ago by
 Commit changed from 86ccdc42aab475d7ffb04e02eb210f58b79f04b6 to e028ed60fbfb7457a1302bc8ecef69300311a2da
Branch pushed to git repo; I updated commit sha1. New commits:
e028ed6  A little change in truncate method

comment:42 in reply to: ↑ 39 ; followup: ↓ 48 Changed 2 years ago by
Replying to tscrim:
For
__bool__
, I think erroring out immediately whenself._constant is None
is not the way to go. I think you should check the computed coefficients in that case to see if any of them are nonzero. If they are all0
, then you should error out.
Good idea. Done.
Also, a fast first check when
self._constant
is notNone
is to see if that constant is nonzero0
.
This check is already there.
In
_repr_
, I do not see howself.valuation()
would normally raise aValueError
. That method does not raise one, nor doesself.coefficient()
(the only other method it calls).
Right. Fixed.
Instead of
self.parent()(1)
, which calls the coercion framework, you should useself.parent().one()
.
Ok. Fixed.
Are you sure you want
_div_
to be two separate operations and not one combined one? I feel like the latter would be faster (at least since it is implemented at the Python level).
I don't feel so. I don't see a way to implement series division such that 1 + 1 < 2 with a significant margin.
I think the truncate should return an honest Laurent polynomial.
I don't agree. One might still want a truncated series with laziness. For your cases, I added polynomial
method to convert to an honest polynomial.
Furthermore, I don't think there are coercions (or at least conversions) from the corresponding Laurent polynomial ring. This feels like a very natural to have. I don't want to go too far with ticket expansion, but this feels like something people will try soon after having this.
Right. I added coercions from (Laurent) polynomial rings.
Actually, you may want to make the operator file into a Cython file (since is forms the key computational part and it is in a separate file).
Hmm. I doubt if there would be significant speed boost, compensating increased build time (that I hate). Moreover I am not versed with Cython. So I don't want to do that, at least for this ticket. But if you do it, I would not object.
comment:43 in reply to: ↑ 38 ; followup: ↓ 46 Changed 2 years ago by
Replying to mantepse:
One question with respect to equality. It seems to me that your implementation of
__eq__
is quite brittle. It is clear that one cannot have proper equality, so it should be clearly stated what it can do and what it can't.
The implementation gives an answer if possible without computing coefficients indefinitely. Otherwise raise an exception.
I added a short explanation to the method.
Apart from that, in the case of truncation, one could make it exact easily.
Truncation still gives a lazy series. I added polynomial
method to convert to an exact polynomial.
comment:44 in reply to: ↑ 37 Changed 2 years ago by
Replying to mantepse:
I find this quite wonderful! It would be great if we could replace
LazyPowerSeries
with this. One feature ofLazyPowerSeries
was that it allows recursive definitions "guessing" the correct initialisations, as for example insage: L = LazyPowerSeriesRing(QQ) sage: one = L(1) sage: monom = L.gen() sage: s = L() sage: s._name = 's' sage: s.define(one+monom*s*s) sage: [s.coefficient(i) for i in range(6)] [1, 1, 2, 5, 14, 42]Although this is based on the original code by Ralf Hemmecke and myself, which in turn is based on code of Nicolas Thiery (I think), I am not sure anymore whether it is so important. Of course, if we could have something similar, even better.
Recursive definition is possible as a result of being lazy and being power series. Now you can do the same in the following way:
sage: from sage.rings.lazy_laurent_series_ring import LazyLaurentSeriesRing sage: L = LazyLaurentSeriesRing(ZZ, 'z') sage: sage: z = L.gen() sage: def f(s,n): ....: return (1 + z*s^2).coefficient(n) ....: sage: L.series(f, valuation=0) 1 + z + 2*z^2 + 5*z^3 + 14*z^4 + 42*z^5 + 132*z^6 + ...
comment:45 Changed 2 years ago by
 Commit changed from e028ed60fbfb7457a1302bc8ecef69300311a2da to 8f8adf2ef2c0d209a63111e46354d8ead0e29cb0
Branch pushed to git repo; I updated commit sha1. New commits:
8f8adf2  Add __getitem__ special method to series

comment:46 in reply to: ↑ 43 Changed 2 years ago by
Apart from that, in the case of truncation, one could make it exact easily.
Truncation still gives a lazy series. I added
polynomial
method to convert to an exact polynomial.
excellent point! I missed that!
comment:47 Changed 2 years ago by
 Commit changed from 8f8adf2ef2c0d209a63111e46354d8ead0e29cb0 to b3a679216402c0db7d046c771012500ce1fd7595
Branch pushed to git repo; I updated commit sha1. New commits:
b3a6792  Add division operator

comment:48 in reply to: ↑ 42 Changed 2 years ago by
Are you sure you want
_div_
to be two separate operations and not one combined one? I feel like the latter would be faster (at least since it is implemented at the Python level).I don't feel so. I don't see a way to implement series division such that 1 + 1 < 2 with a significant margin.
You are right. I was wrong!
comment:49 Changed 2 years ago by
 Commit changed from b3a679216402c0db7d046c771012500ce1fd7595 to 575022ce0595e70d4c285651061b2286c9e3cbf7
Branch pushed to git repo; I updated commit sha1. New commits:
575022c  Typos

comment:50 Changed 2 years ago by
 Commit changed from 575022ce0595e70d4c285651061b2286c9e3cbf7 to c55925faeae43fc25fb76542b13e59233f4403af
Branch pushed to git repo; I updated commit sha1. New commits:
c55925f  Added a recursive definition example

comment:51 followup: ↓ 52 Changed 2 years ago by
Are composition and reversion planned in a later ticket?
I am really looking forward to this! I hope very much we can rebase the species code on it. Should LazyPowerSeriesRing
be a subclass?
comment:52 in reply to: ↑ 51 Changed 2 years ago by
Replying to mantepse:
Are composition and reversion planned in a later ticket?
Not by me. Anyone is invited to add them in a later ticket.
I hope very much we can rebase the species code on it. Should
LazyPowerSeriesRing
be a subclass?
Yes, in a separate file alongside with lazy Laurent series. It would be great. I don't have a plan to do it in any short time, simply because I don't need it now.
comment:53 Changed 2 years ago by
 Commit changed from c55925faeae43fc25fb76542b13e59233f4403af to 410ca3806500b2518485b74d0daaab1931e49ec8
Branch pushed to git repo; I updated commit sha1. New commits:
410ca38  Add prec and approximate_series method

comment:54 Changed 2 years ago by
 Reviewers set to Travis Scrimshaw
Last little thing:
R(0)
> R.zero()
(as it is cached and R
is always a LazyLaurentSeriesRing
).
Once done you can set a positive review on my behalf.
comment:55 Changed 2 years ago by
 Commit changed from 410ca3806500b2518485b74d0daaab1931e49ec8 to 989f009a851c9dc91c8650d7e554138886951a3a
Branch pushed to git repo; I updated commit sha1. New commits:
989f009  Fix R(0)

comment:56 Changed 2 years ago by
 Status changed from needs_review to positive_review
Thank you, Travis!
comment:57 Changed 2 years ago by
 Branch changed from u/klee/27347 to 989f009a851c9dc91c8650d7e554138886951a3a
 Resolution set to fixed
 Status changed from positive_review to closed
comment:58 Changed 2 years ago by
 Commit 989f009a851c9dc91c8650d7e554138886951a3a deleted
Nice work! Followup ticket at #27694 for allowing syntactic sugar
sage: L.<x> = LazyLaurentSeriesRing(ZZ)
Branch pushed to git repo; I updated commit sha1. New commits:
Introduce lazy laurent series