Set() should construct facade parents or use ElementWrapper

[mkoeppe]

Currently, Set(...) does not always construct an object with the full set of set operations.

sage: P = Set(Primes()); P
Set of all prime numbers: 2, 3, 5, 7, ...
sage: P.union
AttributeError: 'Primes_with_category' object has no attribute 'union'
sage: type(P)
<class 'sage.sets.primes.Primes_with_category'>

We change this so that users can rely on the methods provided by the mixins Set_base, Set_boolean_operators, Set_add_sub_operators being available.

When Set(...) does construct an instance of Set_object, this is a parent whose elements do not belong to it. We update the category so that it is in Sets().Facade().

We add the option Set(..., universe=...). This option will be handled like Sequence(..., universe=...): We convert the given elements to the given parent first. Via #34461, we register a "pointless" inclusion map from the set to the universe.

Finally, we add the option Set(..., facade=False). In this case, Set will use ElementWrappers.

Here on the ticket we ignore all issues of (1) sets of unhashable elements (#23324, #33932) and (2) abuses of Set and EnumeratedSets for multisets (#34389).

Depends on #34461

CC: @tscrim

Component: categories

Author: Matthias Koeppe

Branch/Commit: u/mkoeppe/set___should_construct_facade_parents @ 9cc1113

Issue created by migration from https://trac.sagemath.org/ticket/34387

[mkoeppe]

Branch: u/mkoeppe/set___should_construct_facade_parents

[mkoeppe]

Commit: 45245b1

[mkoeppe]

New commits:

b19a1ff	src/sage/sets/set.py: Accept and handle 'category' arguments
d461411	Update doctest outputs
df327b9	src/sage/sets/set.py: Refine categories of unions, intersections, differences
8a30493	src/sage/sets/set.py: Simplify category checks as suggested
141ebf1	src/sage/categories/sets_cat.py: Update doctest output
8aa274e	src/sage/categories/sets_cat.py: Fix doctest
402af5d	Merge #34376
45245b1	WIP Set_parent

[sagetrac-git]

Changed commit from 45245b1 to 6424fea

[sagetrac-git]

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

6424fea

Set: Always create facade sets

[sagetrac-git]

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

233da80

src/sage/sets/set.py: Pass keyword 'facade' to `__init__` methods

[sagetrac-git]

Changed commit from 6424fea to 233da80

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

Changed commit from 233da80 to c10ff34

[sagetrac-git]

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

c10ff34

src/sage/categories/homset.py: Remove outdated 'todo' in doctest

[sagetrac-git]

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

fbdda32

Update some doctest outputs

[sagetrac-git]

Changed commit from c10ff34 to fbdda32

[mkoeppe]

Changed dependencies from #34376 to #34376, #34461

[sagetrac-git]

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

5db7f09	src/sage/categories/morphism.pyx (FacadeInclusionMorphism): New
dc94887	Merge #34461
96b6b94	WIP use FacadeInclusionMorphism

[sagetrac-git]

Changed commit from fbdda32 to 96b6b94

[sagetrac-git]

Changed commit from 96b6b94 to 0965a16

[sagetrac-git]

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

fe22973	Merge tag '9.7.rc0' into t/34387/set___should_construct_facade_parents
62634bc	src/sage/sets/set.py (Set): If input is a parent, make use it as facade_for
0965a16	src/sage/sets/set.py: Add examples

[sagetrac-git]

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

83c5ec0

src/sage/sets/real_set.py (RealSet): Make it a subclass of Set_parent

[sagetrac-git]

Changed commit from 0965a16 to 83c5ec0

[sagetrac-git]

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

8d7518b

src/sage/sets/set.py (Set): Pass input through if it is a Set_parent of the right category

[sagetrac-git]

Changed commit from 83c5ec0 to 8d7518b

[sagetrac-git]

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

5890ff0	src/sage/sets/real_set.py (RealSet): Make it a facade parent
aade7d1	src/sage/sets/set.py: Add examples
c4f1cb5	src/sage/sets/real_set.py (RealSet): Make it a facade parent (fixup)
caae0b3	src/sage/sets/set.py (Set_object_enumerated): Do not require passed category to be a subcat
20c153d	src/sage/sets/set.py (Set_object._element_constructor_): New
9a789a9	RealSet._element_constructor_: Add example

[sagetrac-git]

Changed commit from 8d7518b to 9a789a9

[sagetrac-git]

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

203bb84	src/sage/categories/enumerated_sets.py: Update doctest output
cfb975e	src/sage/sets/set.py (Set_object._element_constructor_): When universe is given, convert to it

[sagetrac-git]

Changed commit from 9a789a9 to cfb975e

[sagetrac-git]

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

e86438b

src/sage/sets/set.py (Set): Handle generators of unhashables. Fixes part of #33932

[sagetrac-git]

Changed commit from cfb975e to e86438b

[sagetrac-git]

Changed commit from e86438b to 8c1212b

[sagetrac-git]

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

8c1212b

Set, Set_object_enumerated: Use both frozenset and tuple; remove methods duplicated from category

[sagetrac-git]

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

f117aa2

src/sage/sets/finite_set_map_cy.pyx: Do not use Set_object_enumerated directly

[sagetrac-git]

Changed commit from 8c1212b to f117aa2

[sagetrac-git]

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

9cc1113

src/sage/sets/{set,image_set,real_set}.py, src/sage/categories/[finite_]enumerated_sets.py: Update copyright according to git blame -w --date=format:%Y FILE | sort -k2

[sagetrac-git]

Changed commit from f117aa2 to 9cc1113

[mkoeppe]

Changed dependencies from #34376, #34461 to #34461