Opened 5 years ago
Last modified 3 years ago
#17601 new enhancement
Meta ticket: Asymptotic Expansions in SageMath — at Version 89
Reported by: | behackl | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-7.4 |
Component: | asymptotic expansions | Keywords: | asymptotics, gsoc15 |
Cc: | dkrenn, cheuberg, ncohen, vdelecroix, malb, mmezzarobba, rws, kalvotom | Merged in: | |
Authors: | Benjamin Hackl, Daniel Krenn | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | u/dkrenn/asy/prototype (Commits) | Commit: | a848139a35e95bfd67d9964fa7412743942de4a4 |
Dependencies: | #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521, #19532 | Stopgaps: |
Description (last modified by )
We intend to implement asymptotic expansions in SageMath. We would like to do computations with simple expansions such as
n2 + n3/2 + O(n1/2),
but also with expansions such as
2n * n + O(n*log(n))
or even multivariate expansions such as
3*k/n + O(k2 / n2) with |k| <= n(1/2).
Of course, O(n) - O(n) = O(n) must hold and we want to perform various arithmetic operations with these asymptotic expansions. Eventually, specified O-constants shall also be supported.
See #17716 and #19083 for more examples and the documentation files there for a more detailed description. A working prototype can be found in branch u/dkrenn/asy/prototype
.
Roadmap:
- Implementing a minimal working example
- #17600 (AsymptoticGrowthElement): elements which handle the asymptotic growth. Such an element holds, e.g. n2 or k/n or n*log(n). This can compare, multiply etc., but has no coefficient; the order of magnitude is managed here. Concretely for this ticket: MonomialGrowthElement, implementation for powers.
- #18930: Factory for user-friendly generation of growth groups
- #17715 (AsymptoticTerm): a summand for asymptotic expansions. They contain the growth and additional information on the type of the summand. For starters, there will be big-Oh terms (e.g.
O(n)
and exact terms (e.g.3*n^2
). - #17693 (MutablePoset): data structure for storing asymptotic terms within an asymptotic expansions.
- #17716 (AsymptoticRing and AsymptoticExpansion): sum of asymptotic terms.
- Extending the functionality of growth groups
- Extending the functionality of the AsymptoticRing and AsymptoticExpansion
- #19048:
AsymptoticRing.an_element()
- #19068: Implement Division for asymptotic expansions.
- #19073: categorial constructions, pushout and coercions (extended) for asymptotic ring and growth groups
- #19083: AsymptoticRing:
exp
,log
, cleanup, some improvements, documentation.- contains #19094: Implement higher-order operations like
exp
andlog
for asymptotic expansions
- contains #19094: Implement higher-order operations like
- #19400: move documentation to sage.asymptotic
- #19048:
- Bugs and minor improvements
- #19399: let category of growth group be determined by input
- #19411: hidden but caught infinite loop in action of cartesian products of growth groups
- #19412: log of an asymptotic expansion ignores coefficient ring
- #19420: make log of growth elements to the base of some powers of elements possible
- #19421: let asymptotic terms accept multivariate polynomials
- #19423: AsymptoticExpansion: combine shared code of invert, log, exp
- #19424: enable TestSuite for AsymptoticRing
- #19426: AsymptoticRing: convert Orders of symbolic ring
- #19425: Order in symbolic ring: error calling operator
- #19429: extend conversion from SR to growth groups: allow inverses
- #19431: convert asymptotic expansion to the symbolic ring
- #19504: better implementation of
AsymptoticExpansion.__hash__
- Generators for asymptotic expansions
- Further plans
- for growth groups
- implement dependencies like |k| <= n1/2 for different growth group variables.
- growth groups with asymptotic at a non-infinity point
- other
- Deal with comparison for asymptotic expansions.
- Check and improve the performance of computations in the AsymptoticRing.
- Implementation of more types of asymptotic terms (little-oh terms, omega-terms, variations of big-Oh terms ...)
- #19300: Run benchmarks on
MutablePoset.remove
to decide between two algorithms. - #19305: substitution of asymptotic expansions
- #19316 compute asymptotic expansion to some rational directly
- for growth groups
- Additional dependencies
Change History (89)
comment:1 Changed 5 years ago by
- Dependencies set to 17600
comment:2 Changed 5 years ago by
- Dependencies changed from 17600 to #17600
comment:3 follow-up: ↓ 4 Changed 5 years ago by
comment:4 in reply to: ↑ 3 Changed 5 years ago by
comment:5 Changed 5 years ago by
- Cc ncohen added
comment:6 Changed 5 years ago by
- Dependencies changed from #17600 to #17600, #17693
- Description modified (diff)
comment:7 Changed 5 years ago by
- Cc vdelecroix added
comment:8 Changed 5 years ago by
- Dependencies changed from #17600, #17693 to #17600, #17693, #17715, #17716
- Description modified (diff)
comment:9 Changed 5 years ago by
- Cc malb added
comment:10 Changed 5 years ago by
- Cc mmezzarobba added
comment:11 Changed 5 years ago by
Are "asymptotic expressions" equivalent to "transseries" (http://arxiv.org/abs/0801.4877, http://www.texmacs.org/joris/ln/ln-abs.html)? Or are they more general, less general, or partially overlapping in scope?
comment:12 Changed 5 years ago by
- Cc rws added
- Milestone changed from sage-6.5 to sage-6.6
comment:13 follow-up: ↓ 14 Changed 5 years ago by
Hi,
Whatever you propose, I would say that the most important thing to do is to consider the integration into Sage. In other words:
- how it will be used from Sage
- how it does interact with the Symbolic ring, polynomials, fraction fields, power series and any objects where asymptotic makes sens
I do not see any of this in the ticket description. And it is definitely important to think of it before starting the implementation.
I only see a list of classes, parents and elements whose goal is basically to mimic the symbolic ring by adding some big Oh. I do not see the point of creating so much classes to handle asymptotic terms. Please, motivate and explain your choices.
Vincent
comment:14 in reply to: ↑ 13 ; follow-up: ↓ 83 Changed 5 years ago by
Replying to vdelecroix:
I only see a list of classes, parents and elements whose goal is basically to mimic the symbolic ring by adding some big Oh.
I rather think of it as a version of the PowerSeriesRing
with additional features (non-integer exponents, several (not completely independent) variables).
comment:15 Changed 5 years ago by
- Cc kalvotom added
comment:16 Changed 5 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716 to #17600, #17693, #17715, #17716, #18182, #18222, #18223
- Description modified (diff)
comment:17 Changed 5 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587
- Description modified (diff)
comment:18 Changed 4 years ago by
- Description modified (diff)
- Keywords gsoc15 added
comment:19 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930
- Description modified (diff)
comment:20 Changed 4 years ago by
- Description modified (diff)
comment:21 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028
- Description modified (diff)
comment:22 Changed 4 years ago by
- Description modified (diff)
comment:23 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048
- Description modified (diff)
comment:24 Changed 4 years ago by
- Description modified (diff)
comment:25 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068
- Description modified (diff)
comment:26 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073
- Description modified (diff)
comment:27 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079
- Description modified (diff)
comment:28 Changed 4 years ago by
- Description modified (diff)
comment:29 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083
- Description modified (diff)
comment:30 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094
- Description modified (diff)
comment:31 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110
- Description modified (diff)
comment:32 Changed 4 years ago by
- Summary changed from Meta-Ticket: Asymptotic Expressions in Sage to Meta-Ticket: Asymptotic Expansions in SageMath
comment:33 Changed 4 years ago by
- Description modified (diff)
comment:34 Changed 4 years ago by
- Description modified (diff)
comment:35 Changed 4 years ago by
- Branch set to u/dkrenn/asy/prototype
- Commit set to 70abf65739587016ed71a953585ff56af33e325b
- Description modified (diff)
Last 10 new commits:
47894c8 | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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8894fce | Merge branch 't/17716/asy/asymptoticExpression' into t/19068/asy/inversion
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106eacd | Merge branch 't/19068/asy/inversion' into t/19083/asy/prototype
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1108cfc | Merge branch 't/17716/asy/asymptoticExpression' into t/19048/asy/an_element
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3c2fa0c | Merge branch 't/19048/asy/an_element' into t/19083/asy/prototype
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1812a5e | rename doc-index-file
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0720b14 | fix doctests: update since TestSuite now checks for cardinality
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14f9a9a | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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9aba4b6 | make entry in reference/index
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70abf65 | include misc
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comment:36 Changed 4 years ago by
- Description modified (diff)
comment:37 Changed 4 years ago by
- Component changed from symbolics to asymptotic expansions
comment:38 Changed 4 years ago by
- Commit changed from 70abf65739587016ed71a953585ff56af33e325b to 2e4a415d7859d3968f612932b36c98318e1823d2
Branch pushed to git repo; I updated commit sha1. New commits:
2e4a415 | rename title
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comment:39 Changed 4 years ago by
- Commit changed from 2e4a415d7859d3968f612932b36c98318e1823d2 to b0e228b4870e49cfdc9594c5f85173bb889f6722
Branch pushed to git repo; I updated commit sha1. New commits:
cd17673 | Merge tag '6.9.beta6' into t/18182/18182-on-6.8
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3eefe25 | correct typo in AUTHORS
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5fe52e4 | fix doctests since name of cartesian product functor has changed
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60b9375 | revert changes in base_ring of category_object and adapt doctests
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8d6de43 | Merge remote-tracking branch 'trac/u/dkrenn/18182/pushout' into t/19073/asy/groups-coercion
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d50cc55 | Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log
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44fbccc | Merge remote-tracking branch 'origin/u/dkrenn/asy/ring-exp-log' into t/19094/asy/ring-exp-log
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09032ee | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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b0e228b | Merge remote-tracking branch 'origin/u/dkrenn/asy/prototype' into t/19083/asy/prototype
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comment:40 Changed 4 years ago by
- Commit changed from b0e228b4870e49cfdc9594c5f85173bb889f6722 to 1109ce002874d776617102f2ccc295b410e4a3b6
comment:41 Changed 4 years ago by
- Milestone changed from sage-6.6 to sage-6.9
comment:42 Changed 4 years ago by
- Description modified (diff)
- Summary changed from Meta-Ticket: Asymptotic Expansions in SageMath to Metaticket: Asymptotic Expansions in SageMath
comment:43 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269
comment:44 Changed 4 years ago by
- Description modified (diff)
comment:45 Changed 4 years ago by
- Description modified (diff)
comment:46 Changed 4 years ago by
- Description modified (diff)
comment:47 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300
- Description modified (diff)
comment:48 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306
- Description modified (diff)
- Summary changed from Metaticket: Asymptotic Expansions in SageMath to Meta ticket: Asymptotic Expansions in SageMath
comment:49 Changed 4 years ago by
- Description modified (diff)
comment:50 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316
- Description modified (diff)
comment:51 Changed 4 years ago by
- Commit changed from 1109ce002874d776617102f2ccc295b410e4a3b6 to 3ca2e9179d3bf8ad5a72df9b9b7a69cf25a0adb0
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
6d3e4f4 | Trac #18587: nicer output of one link target
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66759bb | Revert "remove unreachable ValueError (comment 2)"
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0642564 | doctest added
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7f209ea | improved error message (equal or disjoint var.)
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c49740a | Merge branch 'u/behackl/asy/growth-group-cartesian' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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4fe08b7 | rewrite a doctest to make it work (and mark original test as 'not tested')
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4acd110 | Merge branch 'u/dkrenn/asy/ring-exp-log' of trac.sagemath.org:sage into t/19083/asy/prototype
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45d0c03 | post-merge: fix imports
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f62f7cf | post-merge: fix doctests
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3ca2e91 | fix broken links
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comment:52 Changed 4 years ago by
- Commit changed from 3ca2e9179d3bf8ad5a72df9b9b7a69cf25a0adb0 to 7f4272375d6de89bbe7fe5457c11d9165d4622ff
comment:53 Changed 4 years ago by
- Commit changed from 7f4272375d6de89bbe7fe5457c11d9165d4622ff to ff90d7351b6d8c96c7ee077dcc6d0fd7e7cf98df
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
65ce848 | Merge branch 'asy/growth-group-cartesian' into asy/growthGroup-exponential and resolve merge conflicts
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bd93e37 | fix doctests
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7ec7e7d | fix indentation of one block
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e56459a | : --> ::
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0d469cd | Merge branch 'u/behackl/asy/growthGroup-exponential' of trac.sagemath.org:sage into t/19073/asy/groups-coercion
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e86db32 | Merge branch 'u/dkrenn/asy/asymptoticExpression' of trac.sagemath.org:sage into t/19073/asy/groups-coercion
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36e16a3 | fix doctests after merge
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dd82094 | fix duplicated docstring-parts
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ae300ad | Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log
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ff90d73 | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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comment:54 Changed 4 years ago by
- Commit changed from ff90d7351b6d8c96c7ee077dcc6d0fd7e7cf98df to c4cd7ed152db8651e0af80951dfe45ed598e4399
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
e8460b9 | improve docstring
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9e41be5 | doctest with infinite iterator inputs
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97cb59c | add seealso blocks
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17229c6 | extend AUTHROS
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e33703b | Merge branch 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:sage into t/19048/asy/an_element
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a529d4c | Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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ba99790 | use new product_cantor_pairing and delete old product_diagonal
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4a9d3d2 | Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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8204cfa | remove old product_diagonal (superseded by #19319)
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c4cd7ed | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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comment:55 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319
- Description modified (diff)
Last 10 new commits:
e8460b9 | improve docstring
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9e41be5 | doctest with infinite iterator inputs
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97cb59c | add seealso blocks
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17229c6 | extend AUTHROS
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e33703b | Merge branch 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:sage into t/19048/asy/an_element
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a529d4c | Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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ba99790 | use new product_cantor_pairing and delete old product_diagonal
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4a9d3d2 | Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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8204cfa | remove old product_diagonal (superseded by #19319)
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c4cd7ed | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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comment:56 Changed 4 years ago by
- Commit changed from c4cd7ed152db8651e0af80951dfe45ed598e4399 to 14941885df88ebdb20555268f193367e741fddb3
Branch pushed to git repo; I updated commit sha1. New commits:
88f0013 | adapt Trac #19073, comment 20, 1: add missing INPUT/OUTPUT block of combine_exceptions
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6659cee | adapt Trac #19073, comment 20, 4: missing INPUT/OUTPUT block of merge_overlapping and extend description
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2008f6b | adapt Trac #19073, comment 20, 4: cache keys
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1494188 | adapt Trac #19073, comment 20, 7: remove Poset category from AsymptoticRing
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comment:57 Changed 4 years ago by
- Commit changed from 14941885df88ebdb20555268f193367e741fddb3 to 60b93ab17ef80750fbd053c2219d9bd84fe22bc9
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
4a52a84 | Trac 19319: fix doctests
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3c5af3b | Trac #19319: fix typo
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c20bfe5 | Trac #19319: a.next() -> next(a) (Python3 compliance)
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1fee722 | Trac #19319: added a few blanks
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96c0366 | Trac 19319: return tuples + repeat argument
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ceb1db5 | Trac #19048: Merge #19319
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3fd53d6 | Trac #19048: rename product_cantor_pairing to cantor_product (see #19319)
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617c593 | Trac #19048: Fix doctests (order in cantor_product changed)
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9213baa | Merge branch 'u/cheuberg/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log
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60b93ab | Merge branch 'u/dkrenn/asy/ring-exp-log' of trac.sagemath.org:sage into t/19083/asy/prototype
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comment:58 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319
- Description modified (diff)
comment:59 Changed 4 years ago by
- Commit changed from 60b93ab17ef80750fbd053c2219d9bd84fe22bc9 to 2cba56bd14842af761cd4eb7eb1fb56a50424724
comment:60 Changed 4 years ago by
- Commit changed from 2cba56bd14842af761cd4eb7eb1fb56a50424724 to a39204c67440a804066b1877937cccdca7593e92
Branch pushed to git repo; I updated commit sha1. New commits:
2a80346 | Trac #19073: simplify signatures of helper functions in merge_overlapping
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1583ffc | Trac #19073: Reword and add doctest for _pushout_
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8a32f1f | correct PEP8-spacings in doctest
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05862f4 | Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log
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b160261 | forgotten changes of last merge
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d0c0f15 | Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype
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a39204c | changes part 2 (of 2) after comments of cheuberg
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comment:61 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399
- Description modified (diff)
comment:62 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400
- Description modified (diff)
comment:63 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412
- Description modified (diff)
comment:64 Changed 4 years ago by
- Commit changed from a39204c67440a804066b1877937cccdca7593e92 to e8ad893715b0dfc8a3907a05382b0c1cba57b818
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
0ca6efd | Trac #19094/#19083 comment 60, 11: correct wrong log and give log in errors a base
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71802da | Trac #19094/#19083 comment 60, 8: rename to _create_element_in_extension_
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e2285e7 | Trac #19094/#19083 comment 60, 8: rewrite description of _create_element_in_extension_
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4cb775f | Trac #19094/#19083 comment 60, 12: add doctest in _rpow_element to test parameter base
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51f796c | Trac #19094/#19083 comment 60, 12: document _rpow_element 2^x
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2f110db | Trac #19094/#19083 comment 60, 13: simplify ExponentialGrowthElement._repr_
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4c49d02 | Trac #19094/#19083 comment 60, 14: rewrite keyword arguments documentation of GrowthGroupFactory
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d2cc73a | add forgotten "EXAMPLES::" line
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498dbad | Trac #19094/#19083 comment 60, 15: add a doctest to GenericProduct._create_element_via_parent_
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e8ad893 | Trac #19094/#19083 comment 60, 16: delte misplaced statement in docstring
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comment:65 Changed 4 years ago by
- Description modified (diff)
comment:66 Changed 4 years ago by
- Commit changed from e8ad893715b0dfc8a3907a05382b0c1cba57b818 to b66497d7e1dfe12d486b0c50bef65547f28ed44f
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
c5dadf7 | Trac #19083: More interesting doctest by including a coefficient
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e2a0c6e | Trac #19083: minor language issues
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ac9d4bc | Trac #19083: ReSt errors
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b6ac6c1 | Trac #19083: abbreviate link
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b85176a | Trac #19083: break long lines
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6b45b79 | Trac #19083: mark one doctest as indirect
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0481cda | Trac #19083: simplify doctest
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5867787 | Trac #19083: o(1) instead of O(1) for use of taylor series
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2c60570 | Trac #19083: additional doctest and explanation
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b66497d | Merge remote-tracking branch 'origin/u/cheuberg/asy/prototype' into t/19083/asy/prototype
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comment:67 Changed 4 years ago by
- Commit changed from b66497d7e1dfe12d486b0c50bef65547f28ed44f to 3fdb4dcee28c67dd076a6552580c8ab15811924a
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
cacd890 | Trac #19094/#19083 comment 64, 28: test error in OTermMonoid._create_element_
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5219671 | Trac #19094/#19083 comment 64, 29: fix broken link
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d4a447f | Trac #19094/#19083 comment 64, 29: TermWithCoefficient._calculate_pow_: test ArithemticError
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086b62d | Trac #19094/#19083 comment 64, 30: TermMonoidFactory: note block to refer to instance TermMonoid
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7647952 | write docstrings for the factory instances
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7e4e823 | Trac #19094/#19083 comment 64, 30: more doctests in TermMonoidFactory
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8f57fa1 | Trac #19083: Insert external link
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6c00163 | Trac #19083: minor language issues
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51f699d | Trac #19083: fix dead link by explicitly naming GenericGrowthElement
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3fdb4dc | Merge branch 'u/cheuberg/asy/prototype' of trac.sagemath.org:sage into t/19083/asy/prototype
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comment:68 Changed 4 years ago by
- Commit changed from 3fdb4dcee28c67dd076a6552580c8ab15811924a to d582c1345a788d5b8eba1b5d6e0734378f4559c4
Branch pushed to git repo; I updated commit sha1. New commits:
728ccf9 | Trac #19094/#19083 comment 66, 30: document parameter convert
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a7f7faf | Trac #19094/#19083 comment 66, 31: test parameter convert
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7a27e68 | Trac #19094/#19083 comment 66, 31: Doctest error
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ad645aa | Trac #19094/#19083 comment 66, 32: change simplification check to "not exact term"
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d582c13 | Trac #19094/#19083 comment 66, 29: rename coefficient to new_coefficent (_calculate_pow_)
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comment:69 Changed 4 years ago by
- Commit changed from d582c1345a788d5b8eba1b5d6e0734378f4559c4 to 44b52d61e4c1e3229ee8f3ae7c2c375a67bbc247
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
7ca2b7f | Trac #19094/#19083 comment 66, 33: test errors in __invert__
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12e8e52 | Trac #19094/#19083 comment 66, 34: not tested in __pow__: refer to #19316
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0845655 | Trac #19094/#19083 comment 66, 34: __pow__ add error tests
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3fe96bf | sort maximal elements in error string
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5ca69ea | Trac #19094/#19083 comment 66, 35: doctest errors of log
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cb55faa | Trac #19094/#19083 comment 66, 35: improve speed of log
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d925157 | Trac #19094/#19083 comment 66, 36: rpow: decrease indention of ALGORITHM block
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57eb7cc | Trac #19083: Mention "GrowthGroup" in docstring of "GrowthGroupFactory"
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0042756 | Trac #19083: added doctest (comment 64.23)
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44b52d6 | Merge branch 'u/cheuberg/asy/prototype' of trac.sagemath.org:sage into t/19083/asy/prototype
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comment:70 Changed 4 years ago by
- Commit changed from 44b52d61e4c1e3229ee8f3ae7c2c375a67bbc247 to 80068372f79a2e804be5c864b51bac9a1c75498a
Branch pushed to git repo; I updated commit sha1. New commits:
2522bd0 | Trac #19094/#19083 comment 66, 36: add error test
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8cbacdf | Trac #19094/#19083 comment 66, 37: refer to #19424 in not tested doctest
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ec10395 | Trac #19094/#19083 comment 66, 39: extend description of old_parent (in
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36a48e4 | Trac #19094/#19083 comment 66, 39: _create_element_in_extension_ rewrite doctests and rename parameter to old_term_parent
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38a597b | Trac #19094/#19083 comment 66, 40: remove outdated NOTE block
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b927671 | Trac #19094/#19083 comment 66, 40: complete doctests of AsymptoticRing._element_constructor_
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7624627 | Trac #19094/#19083 comment 66, 40: refer to trac tickets at O-Term from SR todo
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1ceba10 | Trac #19094/#19083 comment 66, 40: test conversion from multivariate polynomial ring
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8006837 | Trac #19094/#19083 comment 66, 40: simplify test for empty data
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comment:71 Changed 4 years ago by
- Commit changed from 80068372f79a2e804be5c864b51bac9a1c75498a to a848139a35e95bfd67d9964fa7412743942de4a4
Branch pushed to git repo; I updated commit sha1. New commits:
4e5af11 | Trac #19094/#19083 comment 66, 36: delete ALGORITHM block
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cb083d4 | Trac #19094/#19083 comment 66, 41: delete _create_exact_summands_ since not needed
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cf228bb | Trac #19094/#19083 comment 66, 42: make creating of exact summand with growth but without coefficient impossible
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a848139 | Trac #19094/#19083 comment 66, 42: create_summands: add doctests for interesting `data`
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comment:72 Changed 4 years ago by
- Description modified (diff)
comment:73 Changed 4 years ago by
- Description modified (diff)
comment:74 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426
comment:75 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429
- Description modified (diff)
comment:76 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431
- Description modified (diff)
comment:77 Changed 4 years ago by
- Description modified (diff)
comment:78 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436
comment:79 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437
- Description modified (diff)
comment:80 Changed 4 years ago by
- Description modified (diff)
comment:81 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504
- Description modified (diff)
- Milestone changed from sage-6.9 to sage-6.10
comment:82 Changed 4 years ago by
- Description modified (diff)
comment:83 in reply to: ↑ 14 Changed 4 years ago by
Replying to cheuberg:
I rather think of it as a version of the
PowerSeriesRing
with additional features (non-integer exponents, several (not completely independent) variables).
Yes, and you could get a lot of leverage out of making that link more prominent. In fact, the appropriate concept would be "Puiseux series", which are Laurent series (with negative exponents allowed) in fractional powers of your variables.
For asymptotic expansions you have x+O(x(1/2)) = O(x(1/2)), which is consistent with Puiseux series in t=1/x.
The usual implementation for Puiseux series is as
[d,N,a[N],a[N+1],a[N+2],...,finite number of terms]
meaning
sum_{i=N..} a_i* x(i/d)
For arithmetic you just first bring series in common denominator "d" and then do power series arithmetic.
For multivariate series, the appropriate behaviour is caught by "local term orders". SingularLib might offer some useful things already.
Note that a series in n and log(n) can be treated as a bivariate series, with an appropriate term order on the variables signifying "n" and "log(n)", for asymptotic series probably again modelling these with X=1/n and Y= 1/log(n).
So I think this ticket can be realized by implementing "multivariate puiseux series", which would be useful in a lot of settings. It would be better if (the underlying ring) would also be called "multivariate puiseux series ring" because that would improve discoverability.
Searching the literature for these terms will probably also make it easier to find relevant algorithms.
comment:84 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510
- Description modified (diff)
comment:85 Changed 4 years ago by
- Description modified (diff)
comment:86 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521
comment:87 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521, #19528
- Description modified (diff)
comment:88 Changed 4 years ago by
- Description modified (diff)
comment:89 Changed 4 years ago by
- Dependencies changed from #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521, #19528 to #17600, #17693, #17715, #17716, #18182, #18222, #18223, #18586, #18587, #18930, #19017, #19028, #19047, #19048, #19068, #19073, #19079, #19083, #19088, #19094, #19110, #19259, #19269, #19300, #19305, #19306, #19316, #19319, #19399, #19400, #19411, #19412, #19420, #19421, #19423, #19424, #19425, #19426, #19429, #19431, #19436, #19437, #19504, #19510, #19521, #19532
- Description modified (diff)
#10519 might be of interest.