Categories for Family

[mkoeppe]

Currently a LazyFamily is automatically in EnumeratedSets, so at most countable.

We add keyword category to the constructor Family and all implementation classes, so that the user can choose the correct category.

Moreover, we define a (non-full) subcategory of Sets named Families, which captures the additional structure (= the map from the keys onto the parent).

Follow-ups / related:

• If the function from indices to objects is a morphism, then the category can be taken from the codomain.
• category of lazy family wrong if infinite combinatorial class used as index #18849 category of lazy family wrong if infinite combinatorial class used as index
• Bug in Family constructor #8822 Bug in Family constructor

Depends on #34375

CC: @tscrim

Component: combinatorics

Work Issues: Add method "as_map"

Author: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/34340

[mkoeppe]

Branch: u/mkoeppe/lazyfamily__accept_category_keyword

[mkoeppe]

Commit: 6de0424

[mkoeppe]

New commits:

6de0424

Family: Pass keyword 'category' through to implementation classes

[sagetrac-git]

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

5809547

src/sage/sets/family.py: Expand doc, clarify relationship to collections.abc and the Sets() category

[sagetrac-git]

Changed commit from 6de0424 to 5809547

[sagetrac-git]

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

18937bb

src/sage/sets/family.py: Accept init arg 'category' in Family implementation classes

[sagetrac-git]

Changed commit from 5809547 to 18937bb

[sagetrac-git]

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

96dd8ca

src/sage/sets/family.py: Update copyright according to git blame -w --date=format:%Y FILE | sort -k2

[sagetrac-git]

Changed commit from 18937bb to 96dd8ca

[sagetrac-git]

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

9efef62

src/sage/sets/family.py: Improve some docstring markup

[sagetrac-git]

Changed commit from 96dd8ca to 9efef62

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

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

cdfb2db

src/sage/sets/family.py: Add example with an uncountable index set

[sagetrac-git]

Changed commit from 9efef62 to cdfb2db

[tscrim]

comment:14

The main part of your changes LGTM, it is good to have this extra flexibility. I just have some issues with the docstring you changed.

For the first paragraph, I am not a fan of giving implementation details to the more casual user in the docstring. If they care about such details, then they almost certainly are already looking at the code. I know it was there previously, but now it has been given more prominence. So I think the first paragraph about the function being a factory should go last (although I really would like to remove it altogether).

The second paragraph is good (I am not counting the one-line description as a paragraph).

I don't really understand the third paragraph, even what you are trying to say. My thought is that it will be far too technical and likely should be removed. Although it would be worthwhile to state that iterating through the object returns the values rather than the keys.

I don't understand the second part of the fourth paragraph. I think I know what you are trying to say, but that is not anything that belongs in this documentation. It seems like a code comment for within the category. I don't think the first sentence is even necessary (this is true for nearly every object in Sage).

I would change .. NOTE:: -> .. WARNING::.

[mkoeppe]

comment:15

It boils down to this: When the function is not injective, there is a subtle conflict between methods such as __len__ according to the collections.abc and cardinality from Sets.ParentMethods. Arguably, __len__ should return the number of keys, whereas cardinality definitely must return the cardinality of the set (values)

[sagetrac-git]

Changed commit from cdfb2db to 5fa0915

[sagetrac-git]

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

5fa0915

src/sage/sets/family.py: NOTE -> WARNING, talk about factory later

[tscrim]

comment:17

Unfortunately I don't see how that is in the documentation (beyond the .. WARNING::; also `iter` -> ``iter`` in there). Nor does that seem to be true that is is values():

sage: F = Family([1,1,1])
sage: F
Family (1, 1, 1)
sage: F.cardinality()
3

The __len__ also redirects from cardinality() by default (from the category). Or perhaps that is your point, that it is different than what you would expect as a set (of values). Since this is a mapping, it is a set of pairs (k, v), so the cardinality for me is consistent.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

b96983a	src/sage/algebras/yangian.py: Make GeneratorIndexingSet a Parent
75ea8bf	Merge #34375

[sagetrac-git]

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

993c9cc

src/doc/en/reference/categories/index.rst: Add new files

[sagetrac-git]

Changed commit from 75ea8bf to 993c9cc

[sagetrac-git]

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

f49dc8d

src/sage/sets/family.py: WIP facade families

[sagetrac-git]

Changed commit from 993c9cc to f49dc8d

[sagetrac-git]

Changed commit from f49dc8d to 7d7e23b

[sagetrac-git]

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

7d7e23b

src/sage/categories/families.py: Make all families facade

[sagetrac-git]

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

fa7accb	LazyFamily.__init__: Category when index set is infinite depends on is_injective
434932f	src/sage/categories/families.py: Update doctest output for facade sets
7569a95	src/sage/categories/finitely_enumerated_families.py: New

[sagetrac-git]

Changed commit from 7d7e23b to 7569a95

[mkoeppe]

Changed dependencies from #34375, #34377 to #34375, #34377, #30300

[mkoeppe]

Work Issues: Add method "as_map"

[mkoeppe]

Changed dependencies from #34375, #34377, #30300 to #34375

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

5be1bdf	src/sage/categories/families.py: New
bfab550	src/sage/categories/families.py: Add example
5857d9b	src/sage/categories/enumerated_families.py: New
af7aa99	src/sage/sets/family.py: Use category EnumeratedFamilies
dd48ffd	src/doc/en/reference/categories/index.rst: Add new files
22970fd	src/sage/sets/family.py: WIP facade families
fe3a7a4	src/sage/categories/families.py: Make all families facade
204c1e2	LazyFamily.__init__: Category when index set is infinite depends on is_injective
b8f5295	src/sage/categories/families.py: Update doctest output for facade sets
0b352a8	src/sage/categories/finitely_enumerated_families.py: New

[sagetrac-git]

Changed commit from 7569a95 to 0b352a8

[sagetrac-git]

Changed commit from 0b352a8 to 6bbbdb9

[sagetrac-git]

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

b4f413d	Replacing the indedxing set of the Yangian with cartesian_product.
a346bff	Fixing pyflakes for yangian.py.
abf1edc	Choosing smaller degree elements to run the test suite.
6bbbdb9	Merge #34375

[sagetrac-git]

Changed commit from 6bbbdb9 to f3cdfe8

[sagetrac-git]

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

e6c999f	src/sage/sets/family.py: Rephrase a sentence
f3cdfe8	src/sage/sets/family.py: Mention that families are immutable (fixes Trac #14124)

[mkoeppe]

comment:143

sage -t --random-seed=143738364655453723155583373959896127051 src/sage/combinat/root_system/type_G.py  # 1 doctest failed
sage -t --random-seed=143738364655453723155583373959896127051 src/sage/sets/family.py  # 6 doctests failed

[sagetrac-git]

Changed commit from f3cdfe8 to 192483d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

4b73142	src/sage/categories/enumerated_families.py: New
4bb87f6	src/sage/sets/family.py: Use category EnumeratedFamilies
533cadc	src/doc/en/reference/categories/index.rst: Add new files
c0ce059	src/sage/sets/family.py: WIP facade families
fcf8d99	src/sage/categories/families.py: Make all families facade
306c62a	LazyFamily.__init__: Category when index set is infinite depends on is_injective
13490f6	src/sage/categories/families.py: Update doctest output for facade sets
3bb3b53	src/sage/categories/finitely_enumerated_families.py: New
cd42510	src/sage/sets/family.py: Rephrase a sentence
192483d	src/sage/sets/family.py: Mention that families are immutable (fixes Trac #14124)

[mkoeppe]

Removed branch from issue description; replaced by PR #35175