AsymptoticRing: inversion

[behackl]

This ticket implements the inversion (and division) of asymptotic expressions (elements of the AsymptoticRing, implemented in #17716).

This relies heavily on the expansion via geometric series. If the expansion of such a series does not stop (e.g. in the case 1/(1-x)), the series has to be truncated with an O-Term.

Depends on #17716

CC: @dkrenn

Component: asymptotic expansions

Keywords: gsoc15

Author: Benjamin Hackl

Branch: c7023dd

Reviewer: Daniel Krenn

Issue created by migration from https://trac.sagemath.org/ticket/19068

[behackl]

Branch: u/behackl/asy/inversion

[behackl]

Commit: d72a173

[behackl]

Last 10 new commits:

6456300	minor rewording in docstring
4e7b080	Merge branch 'u/dkrenn/asy/asymptoticExpression' into asy/asymptoticExpression and fixed some merge conflicts
bea6f0d	fixed negative powers of O-Terms
5d1d3c0	new property default_prec implemented
ab9ae6f	division implemented
095b987	inversion and truncation implemented
d258eb9	two types of equality for asymptotic expressions implemented;
f326e4f	fixed endless recursion in __eq__
8eb21a6	used correct type of equality in truncate
d72a173	fixed doctests

[sagetrac-git]

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

7b8c1a0	fixed a conversion issue for terms with coefficient
83f74d3	Merge branch 'asy/asymptoticTerm' into asy/asymptoticExpression
5113a73	Merge branch 'asy/asymptoticExpression' into asy/inversion

[sagetrac-git]

Changed commit from d72a173 to 5113a73

[sagetrac-git]

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

fec5796	_is_same_term_ moved to TermWithCoefficient
b8ccae1	documentation adapted
0346e60	refactored: is_same_term --> is_same
56e3816	added doctests for is_same
03c2833	doctests for `_div_` and `_invert_` improved
97f15e6	mentioned inversion in the module description

[sagetrac-git]

Changed commit from 5113a73 to 97f15e6

[dkrenn]

Changed branch from u/behackl/asy/inversion to u/dkrenn/asy/inversion

[sagetrac-git]

Changed commit from 97f15e6 to 51cfce6

[sagetrac-git]

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

caef9ea	term: is_same --> __eq__
5618385	rewrite has_same_summands to use iterators efficiently
51cfce6	adapt doc

[dkrenn]

Reviewer: Daniel Krenn

[dkrenn]

Author: Benjamin Hackl

[dkrenn]

comment:6

3 reviewer commits. Please cross check. Fine otherwise. From my side a conditional positive review (once #17716 is positive this can be set to positive as well).

[sagetrac-git]

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

1c81c12	language oddities fixed
032d8b8	Merge branch 'asy/growthGroup' into asy/growthGroup-factory
3a05be7	Merge tag '6.9.beta5' into t/17600/asy/growthGroup
58f931d	add asymptotic_expansions index
9d6f2da	Merge branch 't/17600/asy/growthGroup' into t/18930/asy/growthGroup-factory
6da5ade	Merge branch 't/18930/asy/growthGroup-factory' into t/17715/asy/asymptoticTerm
2c1c39d	Merge branch 't/17715/asy/asymptoticTerm' into t/17716/asy/asymptoticExpression
8894fce	Merge branch 't/17716/asy/asymptoticExpression' into t/19068/asy/inversion

[sagetrac-git]

Changed commit from 51cfce6 to 8894fce

[dkrenn]

comment:8

Merged 6.9.beta5

[behackl]

comment:10

Merged positively reviewed dependencies and fixed some merge conflicts.

---

Last 10 new commits:

b31fac8	rewrite a couple of one-line descriptions
17e921f	remove sorted_set_by_tuple
7af4b6b	remove reverse keyword from shells
a49a20d	add comment in code to make it clear what happens
89b8209	change left/right to self/other
1d52f6c	add a note to the set operations methods
3b3b2fb	object --> SageObject
572a95d	Merge branch 'asy/mutable-poset' into asy/asymptoticExpression
5f54aec	explicitly forbid coercion from MutablePoset into the AsymptoticRing
dc38b28	Merge branch 'asy/asymptoticExpression' into asy/inversion

[behackl]

Changed branch from u/dkrenn/asy/inversion to u/behackl/asy/inversion

[behackl]

Changed commit from 8894fce to dc38b28

[behackl]

comment:11

@Daniel: thank you for your review, I cross-checked your reviewer commits; LGTM. As soon as the dependencies are all positive (and after I've merged them into this branch) I'll set this to positive_review.

Benjamin

[dkrenn]

comment:12

Merge conflict with changed dependency.

[cheuberg]

comment:13

Please add a TODO: Once L-terms are implemented, this inversion here will give incorrect results.

[sagetrac-git]

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

dc00f95	improve documentation of _element_constructor_
abb08ff	improve _element_constructor_
78b9e96	Trac #17716: additional doctest
055e35b	Trac #17716: Fix ReSt error
e8e2501	make entry in reference/index
f0b759a	Merge branch 'asy/asymptoticExpression' into asy/inversion
b37740f	remove code duplicate
bfc460a	fix removed keyword 'default_prec'
fc9bcf2	add result to doctest
4edaa39	slightly improve __pow__

[sagetrac-git]

Changed commit from dc38b28 to 4edaa39

[sagetrac-git]

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

c7023dd

todo-block with remark w.r.t. L-terms added

[sagetrac-git]

Changed commit from 4edaa39 to c7023dd

[behackl]

comment:16

Daniel, do you want to cross-check the merge and the adaptions?

[dkrenn]

comment:17

Replying to @behackl:

Daniel, do you want to cross-check the merge and the adaptions?

Cross-checked...changes look good.

[vbraun]

Changed branch from u/behackl/asy/inversion to c7023dd

[jdemeyer]

comment:19

Why reinvent the coercion model? You don't need __div__ and _div_, the class MultiplicativeGroupElement already implements that for you...

I will fix this in #18578.

[jdemeyer]

Changed commit from c7023dd to none

[dkrenn]

comment:20

Replying to @jdemeyer:

Why reinvent the coercion model? You don't need __div__ and _div_, the class MultiplicativeGroupElement already implements that for you...

Seems to be a forgotten __div__; we got rid of them in the other files of this folder, but it seems we've forgotten it in the term monoids.

I will fix this in #18578.

Thank you.