Improvements to ImageSet

[mkoeppe]

(split out from #34340)

We equip ImageSet with an _element_constructor_ and hence, with a membership test. (This needs a map with inverse.)

We also add a new parameter value is_injective='check'.

CC: @tscrim

Component: combinatorics

Author: Matthias Koeppe

Branch/Commit: 6aeab7d

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34377

[mkoeppe]

Branch: u/mkoeppe/improvements_to_imageset

[sagetrac-git]

Commit: 52f6ca6

[sagetrac-git]

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

52f6ca6

src/sage/sets/image_set.py: Improve example

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,2 +1,5 @@
 (split out from #34340)
 
+We equip `ImageSet` with an `_element_constructor_` and hence, with a membership test. (This needs a map with inverse.)
+
+We also add a new parameter value `is_injective='check'`.

[tscrim]

comment:4

I think you should try-except the call to self._inverse(x) as that could fail in many different ways (with the actual error getting lost in the noise). Subsequently, I am not sure of the utility of verifying that it is an inverse versus trusting the user did give an honest inverse.

There is also an infinite recursion that seems to be happening:

src/sage/categories/sets_cat.py  # 1 doctest failed

Also, calling len(list(self)) might run for forever if self is infinite. I think list(self) also does a __len__ check too. This is also probably related to the infinite recursion above.

[mkoeppe]

comment:5

Replying to @tscrim:

I think you should try-except the call to self._inverse(x) as that could fail in many different ways (with the actual error getting lost in the noise).

Yes, I think that's a good idea

Subsequently, I am not sure of the utility of verifying that it is an inverse versus trusting the user did give an honest inverse.

Mapping back is necessary to get an element that is in the correct parent.
The comparison is just a safety check there.

[tscrim]

comment:6

Replying to @mkoeppe:

Replying to @tscrim:

Subsequently, I am not sure of the utility of verifying that it is an inverse versus trusting the user did give an honest inverse.

Mapping back is necessary to get an element that is in the correct parent.
The comparison is just a safety check there.

Couldn't we just do self.codomain()(x) for this?

[mkoeppe]

comment:7

If it's an honest Map, yes, but this is supposed to work also for PoorManMap

[tscrim]

comment:8

Ah, right. Thanks.

[sagetrac-git]

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

9e8d023

ImageSubobject.cardinality: Handle infinite cardinalities explicitly

[sagetrac-git]

Changed commit from 52f6ca6 to 9e8d023

[mkoeppe]

comment:10

Bots are green now

[sagetrac-git]

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

6aeab7d

src/sage/sets/image_set.py: Clarify is_injective=False

[sagetrac-git]

Changed commit from 9e8d023 to 6aeab7d

[tscrim]

Reviewer: Travis Scrimshaw