Open behackl opened 9 years ago
Changed author from Benjamin Hackl, Clemens Heuberger, Daniel Krenn to Benjamin Hackl, Daniel Krenn
Description changed:
---
+++
@@ -53,8 +53,11 @@
* 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 ...)
-* Additional Dependencies:
+* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
- * #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
* #19110: QQ(0)^-1 raises SIGFPE (which is caught)
+* Other related Tickets:
+ * #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
+ * #19269: add category Posets to ZZ and QQ
+ * #19259: subrings of the symbolic ring
Changed dependencies 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
Description changed:
---
+++
@@ -1,16 +1,16 @@
-We intend to implement asymptotic expressions in Sage. We would like to do computations with simple expressions such as
+We intend to implement asymptotic expansions in [SageMath](../wiki/SageMath). We would like to do computations with simple expansions such as
n<sup>2</sup> + n<sup>3/2</sup> + O(n<sup>1/2</sup>),
-but also with expressions such as
+but also with expansions such as
2<sup>n</sup> * n + O(n*log(n))
-or even multivariate expressions such as
+or even multivariate expansions such as
3*k/n + O(k<sup>2</sup> / n<sup>2</sup>) with |k| <= n<sup>(1/2)</sup>.
-Of course, O(n) - O(n) = O(n) must hold and we want to perform various arithmetic operations with these asymptotic expressions. Eventually, specified O-constants shall also be supported.
+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.
---
@@ -24,24 +24,24 @@
* Implementing a minimal working example
* #17600 (AsymptoticGrowthElement): elements which handle the asymptotic growth. Such an element holds, e.g. n<sup>2</sup> 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 expressions. 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 expression.
- * #17716 (AsymptoticRing and AsymptoticExpression): sum of asymptotic terms.
+ * #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
- * #19028: More growth group implementations: exponential growth groups.
- * #18587: cartesian products for growth groups (allowing the construction of more complicated univariate as well as multivariate asymptotic expressions)
+ * #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 AsymptoticExpression
- * #19068: Implement Division for asymptotic Expressions.
- * #19094: Implement higher-order operations like `exp` and `log` for asymptotic expressions.
+* Extending the functionality of the AsymptoticRing and AsymptoticExpansion
* #19048: `AsymptoticRing.an_element()`
* #19047: `QQ.some_elements()`
+ * #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__`
+ * #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions.
* #19083: AsymptoticRing: cleanup, some improvements, documentation.
* Further plans
@@ -49,7 +49,7 @@
* implement dependencies like |k| <= n<sup>1/2</sup> for different growth group variables.
* growth groups with asymptotic at a non-infinity point
* other
- * Deal with comparison for asymptotic expressions.
+ * 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 ...)
Description changed:
---
+++
@@ -14,7 +14,7 @@
---
-See #17716 and #19083 for more examples and the documentation files there for a more detailed description. A working prototype can be found in branch u/dkrenn/asy/prototype (based on 6.9.beta5).
+See #17716 and #19083 for more examples and the documentation files there for a more detailed description. A working prototype can be found in branch `u/dkrenn/asy/prototype`.
---
Description changed:
---
+++
@@ -1,4 +1,4 @@
-We intend to implement asymptotic expansions in [SageMath](../wiki/SageMath). We would like to do computations with simple expansions such as
+We intend to implement asymptotic expansions in SageMath. We would like to do computations with simple expansions such as
n<sup>2</sup> + n<sup>3/2</sup> + O(n<sup>1/2</sup>),
@@ -55,7 +55,7 @@
* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
- * #19110: QQ(0)^-1 raises SIGFPE (which is caught)
+ * #19110: QQ(0)<sup>-1</sup> raises SIGFPE (which is caught)
* Other related Tickets:
* #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
Changed dependencies 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 changed:
---
+++
@@ -52,6 +52,7 @@
* 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 ...)
+ * Run benchmarks on `MutablePoset.remove` to decide between two algorithms: #19300.
* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
Changed dependencies 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 changed:
---
+++
@@ -52,7 +52,9 @@
* 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 ...)
- * Run benchmarks on `MutablePoset.remove` to decide between two algorithms: #19300.
+ * #19300: Run benchmarks on `MutablePoset.remove` to decide between two algorithms.
+ * #19305: substitution of asymptotic expansions
+ * #19306: common generators for asymptotic expansions
* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
Description changed:
---
+++
@@ -55,6 +55,7 @@
* #19300: Run benchmarks on `MutablePoset.remove` to decide between two algorithms.
* #19305: substitution of asymptotic expansions
* #19306: common generators for asymptotic expansions
+ * #19259: subrings of the symbolic ring
* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
@@ -63,4 +64,4 @@
* Other related Tickets:
* #18222: provide <=, <, >=, > for poset elements by the category (depends on #10130)
* #19269: add category Posets to ZZ and QQ
- * #19259: subrings of the symbolic ring
+
Description changed:
---
+++
@@ -56,6 +56,7 @@
* #19305: substitution of asymptotic expansions
* #19306: common generators for asymptotic expansions
* #19259: subrings of the symbolic ring
+ * #19316 compute asymptotic expansion to some rational directly
* Additional dependencies
* #19017: Easy access to the `O`-constructor in `big_oh.py`.
Changed dependencies 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
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 |
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 |
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 |
Description changed:
---
+++
@@ -37,6 +37,7 @@
* 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
Changed dependencies 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
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 |
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 |
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 |
Changed dependencies 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 changed:
---
+++
@@ -65,5 +65,6 @@
* 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
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 |
Description changed:
---
+++
@@ -45,6 +45,9 @@
* #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions.
* #19083: AsymptoticRing: cleanup, some improvements, documentation.
+* Bugs and minor Improvements
+ * #19399: let category of growth group be determined by input
+
* Further plans
* for growth groups
* implement dependencies like |k| <= n<sup>1/2</sup> for different growth group variables.
Changed dependencies 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
Changed dependencies 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 changed:
---
+++
@@ -44,6 +44,7 @@
* #19079: ConstructionFunctor: remove `__str__`
* #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions.
* #19083: AsymptoticRing: cleanup, some improvements, documentation.
+ * #19400: move code to sage.asymptotic
* Bugs and minor Improvements
* #19399: let category of growth group be determined by input
Description changed:
---
+++
@@ -46,8 +46,10 @@
* #19083: AsymptoticRing: cleanup, some improvements, documentation.
* #19400: move code to sage.asymptotic
-* Bugs and minor Improvements
+* 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
* Further plans
* for growth groups
Changed dependencies 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
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 |
Description changed:
---
+++
@@ -42,8 +42,8 @@
* #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__`
- * #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions.
- * #19083: AsymptoticRing: cleanup, some improvements, documentation.
+ * #19083: AsymptoticRing: `exp`, `log`, cleanup, some improvements, documentation.
+ * contains #19094: Implement higher-order operations like `exp` and `log` for asymptotic expansions
* #19400: move code to sage.asymptotic
* Bugs and minor improvements
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 |
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 |
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_) |
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(nlog(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
.Roadmap:
Implementing a minimal working example
17600 (AsymptoticGrowthElement): elements which handle the asymptotic growth. Such an element holds, e.g. n2 or k/n or n*log(n). This can compare, multiply etc., but has no coefficient; the order of magnitude is managed here. Concretely for this ticket: MonomialGrowthElement, implementation for powers.
18930: Factory for user-friendly generation of growth groups
17715 (AsymptoticTerm): a summand for asymptotic expansions. They contain the growth and additional information on the type of the summand. For starters, there will be big-Oh terms (e.g.
O(n)
and exact terms (e.g.3*n^2
).17693 (MutablePoset): data structure for storing asymptotic terms within an asymptotic expansions.
17716 (AsymptoticRing and AsymptoticExpansion): sum of asymptotic terms.
Extending the functionality of growth groups
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.exp
andlog
for asymptotic expansions19400: move documentation to sage.asymptotic
Additional dependencies
19017: Easy access to the
O
-constructor inbig_oh.py
.19110: QQ(0)-1 raises SIGFPE (which is caught)
We have a working prototype (made of the tickets above).
Arithmetic, categories and coercion (bugs and improvements)
19399: let category of growth group be determined by input
19316: compute asymptotic expansion to some rational directly
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
19423: AsymptoticExpansion: combine shared code of invert, log, exp
19577: performance improvement of mutable poset used for univariate asymptotic expansions
20000: sqrt of AsymptoticExpansion
20043: multiplication with zero fails
20044: calculate asymptotic expansions to some asymptotic expansions exponents directly
21665:
AsymptoticRing.substitute
fails with exponents in QQbar22396: AsymptoticRing default_prec lost with coercion
22414: check for subs of AsymptoticExpansion
Conversion (bugs and improvements)
19421: let asymptotic terms accept multivariate polynomials
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
19921: handle zero coefficients when converting asymptotic rings
19945: Asymptotic Ring: cannot construct (1/2)^n
19946: Asymptotic Ring: cannot construct 2n when coefficient ring is SR
19961: mention rpow of asymptotic ring in module doc/examples more prominently
19965: parent of exponent getting too large in exponentiation in asymptotic ring
19947: conversion SR to asymptotic ring
Other bugs and minor improvements
19300: Run benchmarks on
MutablePoset.remove
to decide between two algorithms.19424: enable TestSuite for AsymptoticRing
19504: better implementation of
AsymptoticExpansion.__hash__
19576: parentheses around coefficients of asymptotic expansions
19580: use
locals()
in growth group factory19981: implementation of
is_exact
for asymptotic expansions19987: LaTeX-representation of asymptotic expansions
19999: infinite recursion creating certain asymptotic expansion
20045: move wrongly imported series_precision in AsymptoticRing
22140: remove "import sage" from sage.rings.asymptotic.*
22340: coefficient of an AsymptoticExpansion
22395: ordering of (O-)terms: absolute values, real parts, etc.
22944: remove experimental warning of asymptotic ring
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
Singularity analysis
19532: generators related to singularity analysis
19969: enhancement of SA-generators: log-type singularities
19993: Arb: parse symbolic expressions
19944: singularity analysis
20020: singularity analysis (log-type) without renormalization
20040: singularity analysis method for log-type singularities
20049: singularity in formula in docstring of SingularityAnalysis-generator
20056: rename
AsymptoticRing.singularity_analysis
tocoefficients_of_generating_function
20051: speed up singularity analysis (log-type) without renormalization
20052: allow symbolic expressions
20053: allow singular expansions as input
20054: intelligent choice of precision
20055: non-integral exponents beta also outside of generators
21659:
coefficients_of_generating_function
: hardcoded exponents inQQ
22360: raise proper !OZero-exception (instead of AttributeError)
More features
19305: substitution of asymptotic expansions
19528:
map_coefficients
for asymptotic expansions19931: exact_part for asymptotic expansions
19540: factorial
19957: list plot comparing values
Further plans
20050: growth groups with asymptotic at a non-infinity point
20065: Asymptotic Expansions: adaptive precision
Other related tickets:
10519: analytic combinatorics: new code for computing asymptotics for multivariate generating functions
19989: asymptotics for multivariate generating functions: zero division error on last coordinate
18092: evaluating symbolic expressions
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
Depends on #17600 Depends on #17693 Depends on #17715 Depends on #17716 Depends on #18182 Depends on #18222 Depends on #18223 Depends on #18586 Depends on #18587 Depends on #18930 Depends on #19017 Depends on #19028 Depends on #19047 Depends on #19048 Depends on #19068 Depends on #19073 Depends on #19079 Depends on #19083 Depends on #19088 Depends on #19094 Depends on #19110 Depends on #19259 Depends on #19269 Depends on #19300 Depends on #19305 Depends on #19306 Depends on #19316 Depends on #19319 Depends on #19399 Depends on #19400 Depends on #19411 Depends on #19412 Depends on #19420 Depends on #19421 Depends on #19423 Depends on #19424 Depends on #19425 Depends on #19426 Depends on #19429 Depends on #19431 Depends on #19436 Depends on #19437 Depends on #19504 Depends on #19510 Depends on #19521 Depends on #19528 Depends on #19532 Depends on #19540 Depends on #19576 Depends on #19577 Depends on #19580 Depends on #19898 Depends on #19921 Depends on #19931 Depends on #19944 Depends on #19945 Depends on #19946 Depends on #19957 Depends on #19961 Depends on #19965 Depends on #19969 Depends on #19981 Depends on #19987 Depends on #19999 Depends on #20000 Depends on #20020 Depends on #20040 Depends on #20043 Depends on #20044 Depends on #20045 Depends on #20049 Depends on #20050 Depends on #20051 Depends on #20052 Depends on #20053 Depends on #20054 Depends on #20055 Depends on #20056 Depends on #20065 Depends on #21659 Depends on #21665 Depends on #22140 Depends on #22340 Depends on #22360 Depends on #22395 Depends on #22396 Depends on #22414 Depends on #22944
CC: @dkrenn @cheuberg @nathanncohen @videlec @malb @mezzarobba @rwst @kalvotom
Component: asymptotic expansions
Keywords: gsoc15
Author: Benjamin Hackl, Daniel Krenn, Clemens Heuberger
Branch/Commit: public/asy/trunk @
db96be9
Issue created by migration from https://trac.sagemath.org/ticket/17601