Some Homset are not unique parents

[xcaruso]

I guess it is a bug:

sage: k = GF(5) 
sage: H = Hom(k,k)
sage: H2 = Hom(k,k)
sage: H is H2
False

I don't know what is the correct way to fix this problem.

More precisely, in sage.categories.homset (l. 223-227), one can read:

try:
    # Apparently X._Hom_ is supposed to be cached
    return X._Hom_(Y, category)
except (AttributeError, TypeError):
     pass

However, in this particular case, k.Hom is apparently not cached. IMHO, caching should be the job of sage.categories.homset.Hom is all cases, but I might be wrong.

---

Apply

1. attachment: trac_13184_sage_5.9.beta.patch

Depends on #14159

CC: @xcaruso @simon-king-jena @nbruin

Component: categories

Keywords: homset unique parent

Author: Xavier Caruso, Frédéric Chapoton

Reviewer: Travis Scrimshaw

Merged: sage-5.10.beta0

Issue created by migration from https://trac.sagemath.org/ticket/13184

[xcaruso]

comment:1

Attachment: trac_13184_homset_unique_parent.gz

I've attached a small patch fixing the problem.

[jdemeyer]

comment:4

Please fill in your real name as Author.

[xcaruso]

Author: Xavier Caruso

[saraedum]

Attachment: trac_13184.patch.gz

added .patch to the existing patch so the patchbot picks it up

[saraedum]

Description changed:

--- 
+++ 
@@ -21,3 +21,11 @@
 ```
 
 However, in this particular case, k._Hom_ is apparently not cached. IMHO, caching should be the job of sage.categories.homset.Hom is all cases, but I might be wrong.
+
+---
+
+Apply
+
+1. [attachment: trac_13184.patch](https://github.com/sagemath/sage-prod/files/10655866/trac_13184.patch.gz)
+
+to the sage library.

[tscrim]

comment:7

Sage does not run with the patch applied:

/home/travis/sage-5.5.rc0/local/lib/python2.7/site-packages/sage/categories/homset.pyc in Hom(X, Y, category)
    239         # To be investigated
    240         H = X._Hom_(Y,category)
--> 241         _cache[key] = weakref.ref(H)
    242         return H
    243     except (AttributeError, TypeError):

NameError: global name 'weakref' is not defined
Error importing ipy_profile_sage - perhaps you should run %upgrade?
WARNING: Loading of ipy_profile_sage failed.

[xcaruso]

Description changed:

--- 
+++ 
@@ -26,6 +26,6 @@
 
 Apply
 
-1. [attachment: trac_13184.patch](https://github.com/sagemath/sage-prod/files/10655866/trac_13184.patch.gz)
+1. [attachment: trac_13184_sage.5.5.0.beta.patch](https://github.com/sagemath/sage/files/ticket13184/trac_13184_sage.5.5.0.beta.patch.gz)
 
-to the sage library.
+to the sage library (version >= 5.5.0.beta)