Opened 5 years ago
Last modified 3 years ago
#17601 new enhancement
Meta ticket: Asymptotic Expansions in SageMath — at Version 106
Reported by:  behackl  Owned by:  

Priority:  major  Milestone:  sage7.4 
Component:  asymptotic expansions  Keywords:  asymptotics, gsoc15 
Cc:  dkrenn, cheuberg, ncohen, vdelecroix, malb, mmezzarobba, rws, kalvotom  Merged in:  
Authors:  Benjamin Hackl, Daniel Krenn, Clemens Heuberger  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  public/asy/trunk (Commits)  Commit:  d4359563e8159993e8f32edb127c4285d3c3b944 
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, #19528, #19532, #19540, #19576, #19577, #19580  Stopgaps: 
Description (last modified by )
We intend to implement asymptotic expansions in SageMath. We would like to do computations with simple expansions such as
n^{2} + n^{3/2} + O(n^{1/2}),
but also with expansions such as
2^{n} * n + O(n*log(n))
or even multivariate expansions such as
3*k/n + O(k^{2} / n^{2}) 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 Oconstants shall also be supported.
See the documentation files for a more examples and a detailed description. A working prototype is include in SageMath 6.10 and a version
containing all features can be found in branch public/asy/trunk
.
Roadmap:
 Implementing a minimal working example
 #17600 (AsymptoticGrowthElement): elements which handle the asymptotic growth. Such an element holds, e.g. n^{2} 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 userfriendly 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 bigOh 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 higherorder operations like
exp
andlog
for asymptotic expansions
 contains #19094: Implement higherorder 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__
 #19576: parentheses around coefficients of asymptotic expansions
 #19577: performance improvement of mutable poset used for univariate asymptotic expansions
 #19580: use
locals()
in growth group factory
 Generators for asymptotic expansions
 #19306: common generators for asymptotic expansions
 #19259: subrings of the symbolic ring
 #19510: generator for binomial(kn, n)
 #19521: wrong inverse action when using
ConstructionFunctor.coercion_reversed
 #19521: wrong inverse action when using
 #19898: generator for expansion of harmonic number
 #19532: generators related to singularity analysis
 #19306: common generators for asymptotic expansions
 More features
 Further plans
 for growth groups
 implement dependencies like k <= n^{1/2} for different growth group variables.
 growth groups with asymptotic at a noninfinity point
 MultivariatePuiseuxSeriesRing
 other
 Deal with comparison for asymptotic expansions.
 Check and improve the performance of computations in the AsymptoticRing.
 Implementation of more types of asymptotic terms (littleoh terms, omegaterms, variations of bigOh terms ...)
 #19300: Run benchmarks on
MutablePoset.remove
to decide between two algorithms.  #19316 compute asymptotic expansion to some rational directly
 for growth groups
 Additional dependencies
Change History (106)
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 followup: ↓ 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/lnabs.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 sage6.5 to sage6.6
comment:13 followup: ↓ 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 ; followup: ↓ 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 (noninteger 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 5 years ago by
 Description modified (diff)
 Keywords gsoc15 added
comment:19 Changed 5 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 MetaTicket: Asymptotic Expressions in Sage to MetaTicket: 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/ringexplog' into t/19083/asy/prototype

8894fce  Merge branch 't/17716/asy/asymptoticExpression' into t/19068/asy/inversion

106eacd  Merge branch 't/19068/asy/inversion' into t/19083/asy/prototype

1108cfc  Merge branch 't/17716/asy/asymptoticExpression' into t/19048/asy/an_element

3c2fa0c  Merge branch 't/19048/asy/an_element' into t/19083/asy/prototype

1812a5e  rename docindexfile

0720b14  fix doctests: update since TestSuite now checks for cardinality

14f9a9a  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

9aba4b6  make entry in reference/index

70abf65  include misc

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

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/18182/18182on6.8

3eefe25  correct typo in AUTHORS

5fe52e4  fix doctests since name of cartesian product functor has changed

60b9375  revert changes in base_ring of category_object and adapt doctests

8d6de43  Merge remotetracking branch 'trac/u/dkrenn/18182/pushout' into t/19073/asy/groupscoercion

d50cc55  Merge branch 't/19073/asy/groupscoercion' into t/19094/asy/ringexplog

44fbccc  Merge remotetracking branch 'origin/u/dkrenn/asy/ringexplog' into t/19094/asy/ringexplog

09032ee  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

b0e228b  Merge remotetracking branch 'origin/u/dkrenn/asy/prototype' into t/19083/asy/prototype

comment:40 Changed 4 years ago by
 Commit changed from b0e228b4870e49cfdc9594c5f85173bb889f6722 to 1109ce002874d776617102f2ccc295b410e4a3b6
comment:41 Changed 4 years ago by
 Milestone changed from sage6.6 to sage6.9
comment:42 Changed 4 years ago by
 Description modified (diff)
 Summary changed from MetaTicket: 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

66759bb  Revert "remove unreachable ValueError (comment 2)"

0642564  doctest added

7f209ea  improved error message (equal or disjoint var.)

c49740a  Merge branch 'u/behackl/asy/growthgroupcartesian' of trac.sagemath.org:sage into t/19094/asy/ringexplog

4fe08b7  rewrite a doctest to make it work (and mark original test as 'not tested')

4acd110  Merge branch 'u/dkrenn/asy/ringexplog' of trac.sagemath.org:sage into t/19083/asy/prototype

45d0c03  postmerge: fix imports

f62f7cf  postmerge: fix doctests

3ca2e91  fix broken links

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/growthgroupcartesian' into asy/growthGroupexponential and resolve merge conflicts

bd93e37  fix doctests

7ec7e7d  fix indentation of one block

e56459a  : > ::

0d469cd  Merge branch 'u/behackl/asy/growthGroupexponential' of trac.sagemath.org:sage into t/19073/asy/groupscoercion

e86db32  Merge branch 'u/dkrenn/asy/asymptoticExpression' of trac.sagemath.org:sage into t/19073/asy/groupscoercion

36e16a3  fix doctests after merge

dd82094  fix duplicated docstringparts

ae300ad  Merge branch 't/19073/asy/groupscoercion' into t/19094/asy/ringexplog

ff90d73  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

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

9e41be5  doctest with infinite iterator inputs

97cb59c  add seealso blocks

17229c6  extend AUTHROS

e33703b  Merge branch 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:sage into t/19048/asy/an_element

a529d4c  Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ringexplog

ba99790  use new product_cantor_pairing and delete old product_diagonal

4a9d3d2  Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ringexplog

8204cfa  remove old product_diagonal (superseded by #19319)

c4cd7ed  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

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

9e41be5  doctest with infinite iterator inputs

97cb59c  add seealso blocks

17229c6  extend AUTHROS

e33703b  Merge branch 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:sage into t/19048/asy/an_element

a529d4c  Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ringexplog

ba99790  use new product_cantor_pairing and delete old product_diagonal

4a9d3d2  Merge branch 'u/dkrenn/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ringexplog

8204cfa  remove old product_diagonal (superseded by #19319)

c4cd7ed  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

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

6659cee  adapt Trac #19073, comment 20, 4: missing INPUT/OUTPUT block of merge_overlapping and extend description

2008f6b  adapt Trac #19073, comment 20, 4: cache keys

1494188  adapt Trac #19073, comment 20, 7: remove Poset category from AsymptoticRing

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

3c5af3b  Trac #19319: fix typo

c20bfe5  Trac #19319: a.next() > next(a) (Python3 compliance)

1fee722  Trac #19319: added a few blanks

96c0366  Trac 19319: return tuples + repeat argument

ceb1db5  Trac #19048: Merge #19319

3fd53d6  Trac #19048: rename product_cantor_pairing to cantor_product (see #19319)

617c593  Trac #19048: Fix doctests (order in cantor_product changed)

9213baa  Merge branch 'u/cheuberg/asy/an_element' of trac.sagemath.org:sage into t/19094/asy/ringexplog

60b93ab  Merge branch 'u/dkrenn/asy/ringexplog' of trac.sagemath.org:sage into t/19083/asy/prototype

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

1583ffc  Trac #19073: Reword and add doctest for _pushout_

8a32f1f  correct PEP8spacings in doctest

05862f4  Merge branch 't/19073/asy/groupscoercion' into t/19094/asy/ringexplog

b160261  forgotten changes of last merge

d0c0f15  Merge branch 't/19094/asy/ringexplog' into t/19083/asy/prototype

a39204c  changes part 2 (of 2) after comments of cheuberg

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

71802da  Trac #19094/#19083 comment 60, 8: rename to _create_element_in_extension_

e2285e7  Trac #19094/#19083 comment 60, 8: rewrite description of _create_element_in_extension_

4cb775f  Trac #19094/#19083 comment 60, 12: add doctest in _rpow_element to test parameter base

51f796c  Trac #19094/#19083 comment 60, 12: document _rpow_element 2^x

2f110db  Trac #19094/#19083 comment 60, 13: simplify ExponentialGrowthElement._repr_

4c49d02  Trac #19094/#19083 comment 60, 14: rewrite keyword arguments documentation of GrowthGroupFactory

d2cc73a  add forgotten "EXAMPLES::" line

498dbad  Trac #19094/#19083 comment 60, 15: add a doctest to GenericProduct._create_element_via_parent_

e8ad893  Trac #19094/#19083 comment 60, 16: delte misplaced statement in docstring

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

e2a0c6e  Trac #19083: minor language issues

ac9d4bc  Trac #19083: ReSt errors

b6ac6c1  Trac #19083: abbreviate link

b85176a  Trac #19083: break long lines

6b45b79  Trac #19083: mark one doctest as indirect

0481cda  Trac #19083: simplify doctest

5867787  Trac #19083: o(1) instead of O(1) for use of taylor series

2c60570  Trac #19083: additional doctest and explanation

b66497d  Merge remotetracking branch 'origin/u/cheuberg/asy/prototype' into t/19083/asy/prototype

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_

5219671  Trac #19094/#19083 comment 64, 29: fix broken link

d4a447f  Trac #19094/#19083 comment 64, 29: TermWithCoefficient._calculate_pow_: test ArithemticError

086b62d  Trac #19094/#19083 comment 64, 30: TermMonoidFactory: note block to refer to instance TermMonoid

7647952  write docstrings for the factory instances

7e4e823  Trac #19094/#19083 comment 64, 30: more doctests in TermMonoidFactory

8f57fa1  Trac #19083: Insert external link

6c00163  Trac #19083: minor language issues

51f699d  Trac #19083: fix dead link by explicitly naming GenericGrowthElement

3fdb4dc  Merge branch 'u/cheuberg/asy/prototype' of trac.sagemath.org:sage into t/19083/asy/prototype

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

a7f7faf  Trac #19094/#19083 comment 66, 31: test parameter convert

7a27e68  Trac #19094/#19083 comment 66, 31: Doctest error

ad645aa  Trac #19094/#19083 comment 66, 32: change simplification check to "not exact term"

d582c13  Trac #19094/#19083 comment 66, 29: rename coefficient to new_coefficent (_calculate_pow_)

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__

12e8e52  Trac #19094/#19083 comment 66, 34: not tested in __pow__: refer to #19316

0845655  Trac #19094/#19083 comment 66, 34: __pow__ add error tests

3fe96bf  sort maximal elements in error string

5ca69ea  Trac #19094/#19083 comment 66, 35: doctest errors of log

cb55faa  Trac #19094/#19083 comment 66, 35: improve speed of log

d925157  Trac #19094/#19083 comment 66, 36: rpow: decrease indention of ALGORITHM block

57eb7cc  Trac #19083: Mention "GrowthGroup" in docstring of "GrowthGroupFactory"

0042756  Trac #19083: added doctest (comment 64.23)

44b52d6  Merge branch 'u/cheuberg/asy/prototype' of trac.sagemath.org:sage into t/19083/asy/prototype

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

8cbacdf  Trac #19094/#19083 comment 66, 37: refer to #19424 in not tested doctest

ec10395  Trac #19094/#19083 comment 66, 39: extend description of old_parent (in

36a48e4  Trac #19094/#19083 comment 66, 39: _create_element_in_extension_ rewrite doctests and rename parameter to old_term_parent

38a597b  Trac #19094/#19083 comment 66, 40: remove outdated NOTE block

b927671  Trac #19094/#19083 comment 66, 40: complete doctests of AsymptoticRing._element_constructor_

7624627  Trac #19094/#19083 comment 66, 40: refer to trac tickets at OTerm from SR todo

1ceba10  Trac #19094/#19083 comment 66, 40: test conversion from multivariate polynomial ring

8006837  Trac #19094/#19083 comment 66, 40: simplify test for empty data

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

cb083d4  Trac #19094/#19083 comment 66, 41: delete _create_exact_summands_ since not needed

cf228bb  Trac #19094/#19083 comment 66, 42: make creating of exact summand with growth but without coefficient impossible

a848139  Trac #19094/#19083 comment 66, 42: create_summands: add doctests for interesting `data`

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 sage6.9 to sage6.10
comment:82 Changed 4 years ago by
 Description modified (diff)
comment:83 in reply to: ↑ 14 ; followup: ↓ 101 Changed 4 years ago by
Replying to cheuberg:
I rather think of it as a version of the
PowerSeriesRing
with additional features (noninteger 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)
comment:90 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, #19532 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, #19532
 Description modified (diff)
comment:91 Changed 4 years ago by
 Description modified (diff)
comment:92 Changed 4 years ago by
 Branch changed from u/dkrenn/asy/prototype to public/asy/trunk
 Commit changed from a848139a35e95bfd67d9964fa7412743942de4a4 to b859e5d29e5cbcd84bb7be98496e8d6d558e1783
Last 10 new commits:
e93ce46  simplify coefficients automatically and use the faster algorithm per default

f468de6  docu

4a27e66  result over QQ if skipparameter given

e59c71f  toc entry (at top of file)

39936e5  Merge branch 'u/dkrenn/asy/generatorsbinomial' of trac.sagemath.org:sage into asy/trunk

e06f8ae  Merge branch 'u/jdemeyer/symbolic/subvar' of trac.sagemath.org:sage into asy/singularityanalysis

f2573a9  calculate coefficients of singularity analysis (pole type)

b2e375f  generator SingularityAnalysis (pole type)

3214c83  explicitly specify a default defaultprecision

b859e5d  Merge branch 'u/dkrenn/asy/singularityanalysis' of trac.sagemath.org:sage into asy/trunk

comment:93 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, #19532 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, #19532, #19540
 Description modified (diff)
comment:94 Changed 4 years ago by
 Commit changed from b859e5d29e5cbcd84bb7be98496e8d6d558e1783 to 9e17c568a4cabe53417188ba43f8b0eae4ec4514
Branch pushed to git repo; I updated commit sha1. New commits:
15865eb  Merge branches 'coerce/inverseaction' and 'asy/map_coefficients' into t/19306/asy/generators

94f003a  factorial

5cbabc1  seealso and links

8858983  correct :meth: > :func:

0ec9795  Merge branch 'u/dkrenn/asy/factorial' of trac.sagemath.org:sage into asy/trunk

ea3dd35  small bugfix

9e17c56  Merge branch 'u/dkrenn/asy/generatorsbinomial' of trac.sagemath.org:sage into asy/trunk

comment:95 Changed 4 years ago by
 Commit changed from 9e17c568a4cabe53417188ba43f8b0eae4ec4514 to b2ac9aad4fdb59f351c4b0c3e4ad416db62c6d72
comment:96 Changed 4 years ago by
 Commit changed from b2ac9aad4fdb59f351c4b0c3e4ad416db62c6d72 to bf0a3fe65bb917df15ab1c59e3868a7dc3a7f97d
comment:97 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, #19532, #19540 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, #19532, #19540, #19576, #19577
 Description modified (diff)
comment:98 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, #19532, #19540, #19576, #19577 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, #19532, #19540, #19576, #19577, #19580
 Description modified (diff)
comment:99 Changed 4 years ago by
 Commit changed from bf0a3fe65bb917df15ab1c59e3868a7dc3a7f97d to 2af8888cad7403af8b396a406713d23dab6a0150
Branch pushed to git repo; I updated commit sha1. New commits:
8989602  function locals_of_caller

2a57f15  use locals in repr_short_to_parent

39af603  allow locals in GrowthGroupFactory

d4bbc88  locals during construction of an asymptotic ring

81e5453  locals in change_parameter

c264579  Merge branch 'asy/map_coefficients' into asy/locals

5f884c5  complete merge

2af8888  Merge branch 'asy/locals' into asy/trunk

comment:100 Changed 4 years ago by
 Description modified (diff)
comment:101 in reply to: ↑ 83 ; followup: ↓ 103 Changed 4 years ago by
Replying to nbruin:
Replying to cheuberg:
I rather think of it as a version of the
PowerSeriesRing
with additional features (noninteger exponents, several (not completely independent) variables).Yes, and you could get a lot of leverage out of making that link more prominent.
We've planned to do so, once asymptotic expansions at 0
are implemented (currently everything is only at oo
).
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) }
We are aware of Puiseux series.
The restrictions imposed by Puiseux series are that they cannot handle nonrational exponents like sqrt(2)
or symbolic constants. However, we'd like to be able to handle these.
Moreover, we can work with terms like exp(x+O(1))=O(exp(x))
.
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).
In addition to the relation between n
and log(n)
, our asymptotic expansions will be able to handle dependencies between the variables as well, e.g. x <= sqrt(y)
.
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.
As mentioned above, once we have expansions at 0
, we have a MultivariatePuiseuxSeriesRing as a special case; renaming it now is not expedient.
comment:102 Changed 4 years ago by
 Description modified (diff)
comment:103 in reply to: ↑ 101 Changed 4 years ago by
Replying to dkrenn:
Replying to nbruin:
In fact, the appropriate concept would be "Puiseux series", which are Laurent series (with negative exponents allowed) in fractional powers of your variables. [...] 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.
As mentioned above, once we have expansions at
0
, we have a MultivariatePuiseuxSeriesRing as a special case; renaming it now is not expedient.
We've added MultivariatePuiseuxSeriesRing to our roadmap above.
comment:104 Changed 4 years ago by
 Description modified (diff)
comment:105 Changed 4 years ago by
 Commit changed from 2af8888cad7403af8b396a406713d23dab6a0150 to d4359563e8159993e8f32edb127c4285d3c3b944
Branch pushed to git repo; I updated commit sha1. New commits:
153a23f  Merge tag '7.0.rc1' into asy/trunk

cc256c8  Trac #19306: remove old code

31e4dc4  Trac #19306: other variables than n

a3fad56  Trac #19306: fix error terms for low precision

a4c3f9d  Trac #19306: Fix low precision for Stirling

46ef12f  Merge branch 'u/cheuberg/asy/generators' of git://trac.sagemath.org/sage into asy/trunk

4c58608  Trac #19898: Generator for expansion of harmonic number

adae74b  Trac #19898: Merge #19510 to resolve conflicts

d435956  Merge branch 'u/cheuberg/asy/harmonicnumber' of git://trac.sagemath.org/sage into asy/trunk

comment:106 Changed 4 years ago by
 Description modified (diff)
 Milestone changed from sage6.10 to sage7.0
New commits:
153a23f  Merge tag '7.0.rc1' into asy/trunk

cc256c8  Trac #19306: remove old code

31e4dc4  Trac #19306: other variables than n

a3fad56  Trac #19306: fix error terms for low precision

a4c3f9d  Trac #19306: Fix low precision for Stirling

46ef12f  Merge branch 'u/cheuberg/asy/generators' of git://trac.sagemath.org/sage into asy/trunk

4c58608  Trac #19898: Generator for expansion of harmonic number

adae74b  Trac #19898: Merge #19510 to resolve conflicts

d435956  Merge branch 'u/cheuberg/asy/harmonicnumber' of git://trac.sagemath.org/sage into asy/trunk

#10519 might be of interest.