Meta ticket: unified sequence/lazy list objects

[rwst]

Several (maybe specialized) implementations of lazy lists exist. This meta ticket can be considered closed when

• uncouple Sequence from categories #15852: uncouple sequence from categories (was earlier: the class Sequence has a parent from the category Sets implemented)
• class Sequence: maybe renaming to FiniteSequence
• lazy_list from various input data #16137: extend lazy_list: lazy_list from various input data
• extend lazy lists: various improvements and generalizations, new sublists #19895: extend lazy_list: various improvements and generalizations, new sublists
• (infinite) homogenous sequences #19896: implementation of class InfiniteSequence
• let both (class Sequence, class InfiniteSequence) use sage.misc.lazy_list
• catalog of sequences in SageMath #18565: catalog of sequences
• major improvements to lazy power series #15673: refactor code in combinat.species.*stream to use sage.misc.lazy_list
• if obsolete close formal/lazy/infinite powerseries #6800

Depends on #15852
Depends on #15673
Depends on #16137
Depends on #18565
Depends on #19895
Depends on #19896

CC: @MatthieuDien @videlec @nthiery @mantepse

Component: combinatorics

Keywords: days57, LazyPowerSeries

Issue created by migration from https://trac.sagemath.org/ticket/16107

[MatthieuDien]

Description changed:

[MatthieuDien]

comment:1

Fot the last point : I did a benchmark between it and the current implementation and [ticket:6800 #6800] was really slow (and have some bugs).

For now, I have to do a benchmark between [ticket:15673 #15673] and another implementation, so I willl look for look for other points

[MatthieuDien]

Changed keywords from none to days57

[MatthieuDien]

comment:5

After some tests, sage.misc.lazy_list seems to be faster than sage.structure.sequence and sage.combinat.species.*stream because it it cythonized.

We will try to do an implementation of sage.combinat.species.series_stream over sage.misc.lazy_list

[rwst]

Changed dependencies from #15852, #15673 to #15852, #15673, #16107

[rwst]

Description changed:

--- 
+++ 
@@ -2,8 +2,7 @@
 
 * the `class Sequence` has a parent from the category `Sets` implemented, maybe with renaming to `FiniteSequence` (#15852)
 * implementation of `class InfiniteSequence`
-* let both use `sage.misc.lazy_list` (as default implementation? do benchmark)
-* refactor code in `combinat.species.*stream` to use `Sequence`
-* how does the hypothetical `combinat.species.series.LazyPowerSeries` (#6800) fit in?
+* let both use `sage.misc.lazy_list`
+* refactor code in `combinat.species.*stream` to use `sage.misc.lazy_list` (#15673)
+* if obsolete close #6800
 
-Major improvements in `combinat.species.*stream` are planned in #15673.

[mantepse]

Changed dependencies from #15852, #15673, #16107 to #15852, #15673, #16137

[mantepse]

comment:8

I think you meant to add #16137, since #16107 is this ticket.