Lazy Taylor Series

[mantepse]

We implement (multivariate) Taylor series.

Note that there is no easy well-defined notion of multivariate Laurent series, which is why we create a new class.

Depends on #32309
Depends on #34330

CC: @tscrim @tejasvicsr1 @slel

Component: combinatorics

Keywords: LazyPowerSeries, FormalSeries

Author: Martin Rubey

Branch/Commit: e780472

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32324

[mantepse]

Branch: u/mantepse/lazy_taylor_series

[mantepse]

Last 10 new commits:

e5c89c9	Started moving eventually_geometric to exact. There are still many issues left.
799e22c	CS_eventually_geometric is now CS_exact
f450bbd	Merge branch 'u/gh-tejasvicsr1/dense_lls-31897' of git://trac.sagemath.org/sage into t/32309/lazy_dirichlet_series
97bb021	fix doctests
d904d6d	Merge branch 'u/mantepse/dense_lls-31897' of git://trac.sagemath.org/sage into t/32309/lazy_dirichlet_series
a5e5aea	fix doctests
65210a3	factor out add
346e2b6	factor out _lmul_
2015cfe	factor out remaining common methods
ca73f84	initial version, wip

[mantepse]

Dependencies: #32309

[mantepse]

Commit: ca73f84

[mantepse]

Changed keywords from none to LazyPowerSeries, FormalSeries

[mantepse]

Author: Martin Rubey

[sagetrac-git]

Changed commit from ca73f84 to 5b62ddb

[sagetrac-git]

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

5b62ddb

fix doctests

[sagetrac-git]

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

12e127c	backport code factorization from #32309
42cdf7a	Added CS_recursive method, fixed the apply_coeff method, and corrected some documentation.
ed3e8a4	Merge branch 'u/gh-tejasvicsr1/dense_lls-31897' of git://trac.sagemath.org/sage into t/32309/lazy_dirichlet_series
6e66a2a	Merge branch 'u/mantepse/lazy_dirichlet_series' of git://trac.sagemath.org/sage into t/32324/lazy_taylor_series

[sagetrac-git]

Changed commit from 5b62ddb to 6e66a2a

[sagetrac-git]

Changed commit from 6e66a2a to 428a4bb

[sagetrac-git]

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

ee9d593	Fixed tiny bug in composition code
2be305d	Small error fixed, typos fixed.
0726785	Merge branch 'u/gh-tejasvicsr1/dense_lls-31897' of git://trac.sagemath.org/sage into u/tscrim/dense_lls-31897
e31b75e	Fixing bug in CS_apply_coeff.
d75d44c	Refactoring out the CS_exact polynomial creation and doc fixes.
e0328c8	Changing `_an_element_`, printing O(z^k), and added global option.
3db49f1	Improving documentation and partially resurrecting series().
bbc1668	Removing CS_recursion.
5d856df	Merge branch 'u/tscrim/dense_lls-31897' of git://trac.sagemath.org/sage into t/32309/lazy_dirichlet_series
428a4bb	Merge branch 'u/mantepse/lazy_dirichlet_series' of git://trac.sagemath.org/sage into t/32324/lazy_taylor_series

[sagetrac-git]

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

c4852ba

factor mul, div, pow, invert into Cauchy class

[sagetrac-git]

Changed commit from 428a4bb to c4852ba

[sagetrac-git]

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

a12571d

remove dead code

[sagetrac-git]

Changed commit from c4852ba to a12571d

[sagetrac-git]

Changed commit from a12571d to 362a99e

[sagetrac-git]

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

362a99e

improve repr, add monomial

[sagetrac-git]

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

2d5285b

improve repr, fix doctests

[sagetrac-git]

Changed commit from 362a99e to 2d5285b

[sagetrac-git]

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

117022d

check for nonzero constant in multivariate Taylor series

[sagetrac-git]

Changed commit from 2d5285b to 117022d

[sagetrac-git]

Changed commit from 117022d to 174b601

[sagetrac-git]

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

b11e9e0	optionally check coeffcients in Taylor series
174b601	initial implementation of composition for Taylor series

[fchapoton]

comment:117

hey, guys, the linter is not GREEN !

sage/rings/lazy_series.py:3472:9: E306 expected 1 blank line before a nested definition, found 0
1       E306 expected 1 blank line before a nested definition, found 0

[sagetrac-git]

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

e780472

Addressing the linter complaint.

[sagetrac-git]

Changed commit from 4e03fee to e780472

[tscrim]

comment:119

Frédéric, while I appreciate what you have done standardizing the code within Sage and trying to keep it consistent, I don't think this should warrant reverting a positive review for adding one blankline that, IMO, makes the code less readable because it disassociates the internal function definition from the use. Nevertheless, I have made the change requested.

[fchapoton]

comment:120

oops, sorry for the inconvenience, apologies

I understand your point of view ; maybe we are going too far with the linter and should be more careful in choosing what to check.

My point is that the linter is going to be useful if and only if every single ticket makes sure not to break it again and again.

[tscrim]

comment:121

I broadly agree, but we should allow a certain amount of discretion to the ticket authors/reviewers. I really do not like that blankline required by the linter as it strongly affects the logical grouping of the code blocks.

[mantepse]

comment:122

On sage-devel several people were in favour of replacing Taylor with Power. While I a do not have a preference concerning the name, I would prefer a replacement to happen before the ticket is merged.

[tscrim]

comment:123

IMO that is best done as two separate tickets as the replacement might introduce bugs that are separate from this ticket. That ticket will also issue a formal deprecation of the LFPS.

[mantepse]

comment:124

Ok, But I d rather not go through a deprecation of lazy Taylor series

[tscrim]

comment:125

We can keep the alias since you want it )well, in the global namespace we would actually have LazyPowerSeriesRing be an alias for LazyTaylorSeriesRing). I have no objections to that (I am definitely not going to propose changing the class name in the file).

[mantepse]

comment:126

No, i do not want to keep an alias. I just do not want deprecations

[vbraun]

Changed branch from public/rings/lazy_talyor_series-32324 to e780472