Opened 5 years ago

Meta ticket: Asymptotic Expansions in SageMath — at Version 114

Reported by: Owned by: behackl major sage-7.4 asymptotic expansions asymptotics, gsoc15 dkrenn, cheuberg, ncohen, vdelecroix, malb, mmezzarobba, rws, kalvotom Benjamin Hackl, Daniel Krenn, Clemens Heuberger N/A public/asy/trunk (Commits) e107b79b7acc8440e33780d0cf268b5dce2b20d7 #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, #19898, #19921, #19931, #19944, #19945, #19946

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 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.

• 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
• #18587: cartesian products for growth groups (allowing the construction of more complicated univariate as well as multivariate asymptotic expansions)
• #18223: cartesian products with orders
• #18586: passing on parameters and extra_category for cartesian products
• #19028: More growth group implementations: exponential growth groups.
• Extending the functionality of the AsymptoticRing and AsymptoticExpansion
• #19048: AsymptoticRing.an_element()
• #19047: QQ.some_elements()
• #19319: iterator over pairs on diagonals a la Cantor pairing
• #19068: Implement Division for asymptotic expansions.
• #19073: categorial constructions, pushout and coercions (extended) for asymptotic ring and growth groups
• #18182: pushout construction and finding common parents for/including cartesian products
• #19079: ConstructionFunctor: remove __str__
• #19083: AsymptoticRing: exp, log, cleanup, some improvements, documentation.
• contains #19094: Implement higher-order operations like exp and log for asymptotic expansions
• #19400: move documentation to sage.asymptotic
• 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
• #19436: fixup of #19431
• #19437: SR.symbol: correct parent in inherting classes of SymbolicRing
• #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
• #19921: handle zero coefficients when converting asymptotic rings
• #19931: exact_part for asymptotic expansions
• #19945: Asymptotic Ring: cannot construct (1/2)n
• #19946: Asymptotic Ring: cannot construct 2n when coefficient ring is SR
• 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
• #19898: generator for expansion of harmonic number
• #19532: generators related to singularity analysis
• More features
• #19305: substitution of asymptotic expansions
• #19528: map_coefficients for asymptotic expansions
• #19540: factorial
• #19944: singularity analysis
• 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
• 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 (little-oh terms, omega-terms, variations of big-Oh terms ...)
• #19300: Run benchmarks on MutablePoset.remove to decide between two algorithms.
• #19316 compute asymptotic expansion to some rational directly
• #19110: QQ(0)-1 raises SIGFPE (which is caught)
• Other related Tickets:
• #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
• #19088: multi-line doctests fail when using angle notation (preparser)
• #19269: add category Posets to ZZ and QQ

comment:1 Changed 5 years ago by behackl

• Dependencies set to 17600

comment:2 Changed 5 years ago by behackl

• Dependencies changed from 17600 to #17600

comment:3 follow-up: ↓ 4 Changed 5 years ago by tscrim

#10519 might be of interest.

comment:4 in reply to: ↑ 3 Changed 5 years ago by dkrenn

#10519 might be of interest.

Thanks---I'm involved in both tickets ;)

At the moment both are independent, but when the asymptotic expressions are created, one can use them in the calculations (or at least as a possible output format) in #10519.

comment:6 Changed 5 years ago by dkrenn

• Dependencies changed from #17600 to #17600, #17693
• Description modified (diff)

comment:8 Changed 5 years ago by behackl

• Dependencies changed from #17600, #17693 to #17600, #17693, #17715, #17716
• Description modified (diff)

comment:11 Changed 5 years ago by fredrik.johansson

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 rws

• Milestone changed from sage-6.5 to sage-6.6

comment:13 follow-up: ↓ 14 Changed 5 years ago by vdelecroix

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 cheuberg

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:16 Changed 5 years ago by dkrenn

• 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 dkrenn

• 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 behackl

• Description modified (diff)

comment:19 Changed 5 years ago by behackl

• 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 5 years ago by behackl

• Description modified (diff)

comment:21 Changed 5 years ago by behackl

• 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 5 years ago by dkrenn

• Description modified (diff)

comment:23 Changed 5 years ago by dkrenn

• 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 5 years ago by dkrenn

• Description modified (diff)

comment:25 Changed 5 years ago by behackl

• 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 5 years ago by dkrenn

• 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 5 years ago by dkrenn

• 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 5 years ago by dkrenn

• Description modified (diff)

comment:29 Changed 5 years ago by dkrenn

• 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 5 years ago by behackl

• 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 5 years ago by dkrenn

• 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 5 years ago by dkrenn

• Summary changed from Meta-Ticket: Asymptotic Expressions in Sage to Meta-Ticket: Asymptotic Expansions in SageMath

comment:33 Changed 5 years ago by dkrenn

• Description modified (diff)

comment:34 Changed 5 years ago by dkrenn

• Description modified (diff)

comment:35 Changed 5 years ago by dkrenn

• 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 ​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 doc-index-file ​0720b14 fix doctests: update since TestSuite now checks for cardinality ​14f9a9a Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype ​9aba4b6 make entry in reference/index ​70abf65 include misc

comment:36 Changed 5 years ago by dkrenn

• Description modified (diff)

comment:37 Changed 5 years ago by dkrenn

• Component changed from symbolics to asymptotic expansions

comment:38 Changed 5 years ago by git

• Commit changed from 70abf65739587016ed71a953585ff56af33e325b to 2e4a415d7859d3968f612932b36c98318e1823d2

Branch pushed to git repo; I updated commit sha1. New commits:

 ​2e4a415 rename title

comment:39 Changed 5 years ago by git

• 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 ​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 remote-tracking branch 'trac/u/dkrenn/18182/pushout' into t/19073/asy/groups-coercion ​d50cc55 Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log ​44fbccc Merge remote-tracking branch 'origin/u/dkrenn/asy/ring-exp-log' into t/19094/asy/ring-exp-log ​09032ee Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype ​b0e228b Merge remote-tracking branch 'origin/u/dkrenn/asy/prototype' into t/19083/asy/prototype

comment:40 Changed 5 years ago by git

• Commit changed from b0e228b4870e49cfdc9594c5f85173bb889f6722 to 1109ce002874d776617102f2ccc295b410e4a3b6

Branch pushed to git repo; I updated commit sha1. New commits:

 ​c16587c fix bug (tower has only one entry which is None) ​1109ce0 Merge branch 'u/dkrenn/18182/pushout' of trac.sagemath.org:sage into t/19083/asy/prototype

comment:41 Changed 5 years ago by cheuberg

• Authors changed from Benjamin Hackl, Clemens Heuberger, Daniel Krenn to Benjamin Hackl, Daniel Krenn
• Milestone changed from sage-6.6 to sage-6.9

comment:42 Changed 5 years ago by dkrenn

• Description modified (diff)
• Summary changed from Meta-Ticket: Asymptotic Expansions in SageMath to Metaticket: Asymptotic Expansions in SageMath

comment:43 Changed 5 years ago by dkrenn

• 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 5 years ago by dkrenn

• Description modified (diff)

comment:45 Changed 5 years ago by dkrenn

• Description modified (diff)

comment:46 Changed 5 years ago by slelievre

• Description modified (diff)

comment:47 Changed 5 years ago by cheuberg

• 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 5 years ago by dkrenn

• 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 dkrenn

• Description modified (diff)

comment:50 Changed 4 years ago by dkrenn

• 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 git

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/growth-group-cartesian' of trac.sagemath.org:sage into t/19094/asy/ring-exp-log ​4fe08b7 rewrite a doctest to make it work (and mark original test as 'not tested') ​4acd110 Merge branch 'u/dkrenn/asy/ring-exp-log' of trac.sagemath.org:sage into t/19083/asy/prototype ​45d0c03 post-merge: fix imports ​f62f7cf post-merge: fix doctests ​3ca2e91 fix broken links

comment:52 Changed 4 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​03f3621 fix duplicated docstring-parts ​7f42723 update AUTHORS (new style)

comment:53 Changed 4 years ago by git

• 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 ​bd93e37 fix doctests ​7ec7e7d fix indentation of one block ​e56459a : --> :: ​0d469cd Merge branch 'u/behackl/asy/growthGroup-exponential' of trac.sagemath.org:sage into t/19073/asy/groups-coercion ​e86db32 Merge branch 'u/dkrenn/asy/asymptoticExpression' of trac.sagemath.org:sage into t/19073/asy/groups-coercion ​36e16a3 fix doctests after merge ​dd82094 fix duplicated docstring-parts ​ae300ad Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log ​ff90d73 Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype

comment:54 Changed 4 years ago by git

• 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/ring-exp-log ​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/ring-exp-log ​8204cfa remove old product_diagonal (superseded by #19319) ​c4cd7ed Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype

comment:55 Changed 4 years ago by dkrenn

• 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/ring-exp-log ​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/ring-exp-log ​8204cfa remove old product_diagonal (superseded by #19319) ​c4cd7ed Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype

comment:56 Changed 4 years ago by git

• 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 git

• 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/ring-exp-log ​60b93ab Merge branch 'u/dkrenn/asy/ring-exp-log' of trac.sagemath.org:sage into t/19083/asy/prototype

comment:58 Changed 4 years ago by dkrenn

• 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 git

• Commit changed from 60b93ab17ef80750fbd053c2219d9bd84fe22bc9 to 2cba56bd14842af761cd4eb7eb1fb56a50424724

Branch pushed to git repo; I updated commit sha1. New commits:

 ​a33daf9 changes part 1 after comments of cheuberg ​2cba56b rewrite informal description of growth elements and explain description strings

comment:60 Changed 4 years ago by git

• 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 PEP8-spacings in doctest ​05862f4 Merge branch 't/19073/asy/groups-coercion' into t/19094/asy/ring-exp-log ​b160261 forgotten changes of last merge ​d0c0f15 Merge branch 't/19094/asy/ring-exp-log' into t/19083/asy/prototype ​a39204c changes part 2 (of 2) after comments of cheuberg

comment:61 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 dkrenn

• 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 git

• 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 cheuberg

• Description modified (diff)

comment:66 Changed 4 years ago by git

• 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 remote-tracking branch 'origin/u/cheuberg/asy/prototype' into t/19083/asy/prototype

comment:67 Changed 4 years ago by git

• 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 git

• 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 git

• 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 git

• 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 O-Term 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 git

• 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 dkrenn

• Description modified (diff)

comment:73 Changed 4 years ago by dkrenn

• Description modified (diff)

comment:74 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 dkrenn

• 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 dkrenn

• Description modified (diff)

comment:78 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 dkrenn

• Description modified (diff)

comment:81 Changed 4 years ago by cheuberg

• 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 dkrenn

• Description modified (diff)

comment:83 in reply to: ↑ 14 ; follow-up: ↓ 101 Changed 4 years ago by nbruin

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.

Last edited 4 years ago by vdelecroix (previous) (diff)

comment:84 Changed 4 years ago by dkrenn

• 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 dkrenn

• Description modified (diff)

comment:86 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 dkrenn

• Description modified (diff)

comment:89 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 dkrenn

• Description modified (diff)

comment:92 Changed 4 years ago by dkrenn

• 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 skip-parameter given ​e59c71f toc entry (at top of file) ​39936e5 Merge branch 'u/dkrenn/asy/generators-binomial' of trac.sagemath.org:sage into asy/trunk ​e06f8ae Merge branch 'u/jdemeyer/symbolic/sub-var' of trac.sagemath.org:sage into asy/singularity-analysis ​f2573a9 calculate coefficients of singularity analysis (pole type) ​b2e375f generator SingularityAnalysis (pole type) ​3214c83 explicitly specify a default default-precision ​b859e5d Merge branch 'u/dkrenn/asy/singularity-analysis' of trac.sagemath.org:sage into asy/trunk

comment:93 Changed 4 years ago by dkrenn

• 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 git

• Commit changed from b859e5d29e5cbcd84bb7be98496e8d6d558e1783 to 9e17c568a4cabe53417188ba43f8b0eae4ec4514

Branch pushed to git repo; I updated commit sha1. New commits:

 ​15865eb Merge branches 'coerce/inverse-action' 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/generators-binomial' of trac.sagemath.org:sage into asy/trunk

comment:95 Changed 4 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​8ec2dfd fix docstring ​b2ac9aa Merge branch 'u/dkrenn/asy/singularity-analysis' of trac.sagemath.org:sage into asy/trunk

comment:96 Changed 4 years ago by git

Branch pushed to git repo; I updated commit sha1. New commits:

 ​b2af8aa test whether sorting is needed in topological iteration ​bf0a3fe Merge branch 'asy/speed-topo-iter' into asy/trunk

comment:97 Changed 4 years ago by dkrenn

• 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 dkrenn

• 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 git

• 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 dkrenn

• Description modified (diff)

comment:101 in reply to: ↑ 83 ; follow-up: ↓ 103 Changed 4 years ago by dkrenn

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.

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 non-rational 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.

Last edited 4 years ago by dkrenn (previous) (diff)

comment:102 Changed 4 years ago by dkrenn

• Description modified (diff)

comment:103 in reply to: ↑ 101 Changed 4 years ago by dkrenn

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.

comment:104 Changed 4 years ago by dkrenn

• Description modified (diff)

comment:105 Changed 4 years ago by git

• 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/harmonic-number' of git://trac.sagemath.org/sage into asy/trunk

comment:106 Changed 4 years ago by cheuberg

• Authors changed from Benjamin Hackl, Daniel Krenn to Benjamin Hackl, Daniel Krenn, Clemens Heuberger
• Description modified (diff)
• Milestone changed from sage-6.10 to sage-7.0

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/harmonic-number' of git://trac.sagemath.org/sage into asy/trunk

comment:107 Changed 4 years ago by cheuberg

• 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, #19580 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, #19898

comment:108 Changed 4 years ago by cheuberg

• 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, #19580, #19898 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, #19898, #19921
• Description modified (diff)
• Milestone changed from sage-7.0 to sage-7.1

comment:109 Changed 4 years ago by cheuberg

• 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, #19580, #19898, #19921 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, #19898, #19921, #19931
• Description modified (diff)

comment:110 Changed 4 years ago by git

• Commit changed from d4359563e8159993e8f32edb127c4285d3c3b944 to 81935c9007f423e4a3bf28c515fddabb3ca05ebf

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

 ​4d80eb3 Trac #19306: sage.rings.arith -> sage.arith.all (after #19879) ​ef9cb08 Trac #19898: Merge #19306 (due to #19879) ​e193ac1 Trac #19898: sage.rings.arith -> sage.arith.all (after #19879) ​b565ca4 Merge branch 't/19898/asy/harmonic-number' into t/17601/public/asy/trunk ​a27bd0b Trac #19532: Merge #19306 (due to #19879) ​25cd5b3 Trac #19532: sage.rings.arith -> sage.arith.all (after #19879) ​64c8a2d Merge branch 't/19532/asy/singularity-analysis' into t/17601/public/asy/trunk ​ab1cd26 Trac #19532: Merge #19576 to fix doctest ​9796508 Trac #19532: fix doctest ​81935c9 Merge branch 't/19532/asy/singularity-analysis' into t/17601/public/asy/trunk

comment:111 Changed 4 years ago by git

• Commit changed from 81935c9007f423e4a3bf28c515fddabb3ca05ebf to 3e23a35abd3a24f3022b1b80cbd78233865ea1a3

Branch pushed to git repo; I updated commit sha1. New commits:

 ​f114f9e Trac #19532: Add to table of contents ​ede5173 Trac #19532: Minor documentation fixes ​267718d Trac #19532: Additional tests ​0860173 Trac #19532: List log log factors, document missing implementations ​a3a6dfd Trac #19532: Add references ​3e23a35 Merge branch 't/19532/asy/singularity-analysis' into t/17601/public/asy/trunk

comment:112 Changed 4 years ago by git

• Commit changed from 3e23a35abd3a24f3022b1b80cbd78233865ea1a3 to e107b79b7acc8440e33780d0cf268b5dce2b20d7

Branch pushed to git repo; I updated commit sha1. New commits:

 ​bedd23a Trac #19898: rename harmonic_number to HarmonicNumber ​e107b79 Merge branch 't/19898/asy/harmonic-number' into t/17601/public/asy/trunk

comment:113 Changed 4 years ago by behackl

• 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, #19580, #19898, #19921, #19931 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, #19898, #19921, #19931, #19944
• Description modified (diff)

comment:114 Changed 4 years ago by cheuberg

• 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, #19580, #19898, #19921, #19931, #19944 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, #19898, #19921, #19931, #19944, #19945, #19946
• Description modified (diff)
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