#15927: What are the requirements on super_categories?
--------------------------+----------------------------------
Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.2
Component: categories | Keywords: C3, categories
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
--------------------------+----------------------------------
I've started this discussion on #10963 and that's also where the fix
should probably be done (if only to avoid some ugly mergery), but since
it's a separate issue I'm opening a new ticket for it.
The Sage categories primer (`src/sage/categories/primer.py`) says that,
when you specify a category,
{{{
``C.super_categories()`` *must* return a list of categories, namely
the *immediate* super categories of `C`.
}}}
I asked whether this means that it is FORBIDDEN to provide non-immediate
supercategories (i.e., categories which are redundant because they are
forced by transitivity using the rest of the list). If so, it means that
creating a category is harder than the tutorial implies, because not only
does one have to ensure that one has added all new relations to the poset
of categories, but one also must get rid of all the old relations that
have become redundant through the new relations created.
I have done some tests. Apparently there *is* some need for irredundancy:
{{{
sage: class Gggps(Category):
def super_categories(self):
return [Groups(), Groups(), Groups()]
....:
sage: Gggps()
---------------------------------------------------------------------------
KeyError Traceback (most recent call
last)
<ipython-input-38-ef76ba7c6662> in <module>()
----> 1 Gggps()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/classcall_metaclass.so in
sage.misc.classcall_metaclass.ClasscallMetaclass.__call__
(sage/misc/classcall_metaclass.c:1282)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in __classcall__(cls, *args,
**options)
463 if isinstance(cls, DynamicMetaclass):
464 cls = cls.__base__
--> 465 return super(Category, cls).__classcall__(cls, *args,
**options)
466
467 def __init__(self, s=None):
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/cachefunc.so in
sage.misc.cachefunc.WeakCachedFunction.__call__
(sage/misc/cachefunc.c:6182)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/structure/unique_representation.pyc in __classcall__(cls,
*args, **options)
1019 True
1020 """
-> 1021 instance = typecall(cls, *args, **options)
1022 assert isinstance( instance, cls )
1023 if instance.__class__.__reduce__ ==
CachedRepresentation.__reduce__:
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/classcall_metaclass.so in
sage.misc.classcall_metaclass.typecall
(sage/misc/classcall_metaclass.c:1665)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in __init__(self, s)
502 raise TypeError, "Argument string must be a
string."
503 self.__class__ =
dynamic_class("%s_with_category"%self.__class__.__name__,
--> 504 (self.__class__,
self.subcategory_class, ),
505 cache = False, reduction =
None,
506 doccls=self.__class__)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in subcategory_class(self)
1288 """
1289 return self._make_named_class('subcategory_class',
'SubcategoryMethods',
-> 1290 cache=False,
picklable=False)
1291
1292 @lazy_attribute
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in _make_named_class(self, name,
method_provider, cache, picklable)
1244 reduction = None
1245 return dynamic_class(class_name,
-> 1246 tuple(getattr(cat,name) for cat in
self._super_categories_for_classes),
1247 method_provider_cls,
prepend_cls_bases = False, doccls = doccls,
1248 reduction = reduction, cache = cache)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in
_super_categories_for_classes(self)
1038 [Category of rngs, Category of semirings]
1039 """
-> 1040 self._all_super_categories
1041 return self._super_categories_for_classes
1042
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in _all_super_categories(self)
885 for cat in
self._super_categories] +
886
[self._super_categories],
--> 887 category_sort_key)
888 if not sorted(result, key = category_sort_key,
reverse=True) == result:
889 warn("Inconsistent sorting results for all super
categories of %s"%self.__class__)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/c3_controlled.so in
sage.misc.c3_controlled.C3_sorted_merge (sage/misc/c3_controlled.c:4459)()
KeyError: (28672, 99)
}}}
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/classcall_metaclass.so in
sage.misc.classcall_metaclass.ClasscallMetaclass.__call__
(sage/misc/classcall_metaclass.c:1282)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in __classcall__(cls, *args,
**options)
463 if isinstance(cls, DynamicMetaclass):
464 cls = cls.__base__
--> 465 return super(Category, cls).__classcall__(cls, *args,
**options)
466
467 def __init__(self, s=None):
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/cachefunc.so in
sage.misc.cachefunc.WeakCachedFunction.__call__
(sage/misc/cachefunc.c:6182)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/structure/unique_representation.pyc in __classcall__(cls,
*args, **options)
1019 True
1020 """
-> 1021 instance = typecall(cls, *args, **options)
1022 assert isinstance( instance, cls )
1023 if instance.__class__.__reduce__ ==
CachedRepresentation.__reduce__:
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/classcall_metaclass.so in
sage.misc.classcall_metaclass.typecall
(sage/misc/classcall_metaclass.c:1665)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in __init__(self, s)
502 raise TypeError, "Argument string must be a
string."
503 self.__class__ =
dynamic_class("%s_with_category"%self.__class__.__name__,
--> 504 (self.__class__,
self.subcategory_class, ),
505 cache = False, reduction =
None,
506 doccls=self.__class__)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in subcategory_class(self)
1288 """
1289 return self._make_named_class('subcategory_class',
'SubcategoryMethods',
-> 1290 cache=False,
picklable=False)
1291
1292 @lazy_attribute
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in _make_named_class(self, name,
method_provider, cache, picklable)
1244 reduction = None
1245 return dynamic_class(class_name,
-> 1246 tuple(getattr(cat,name) for cat in
self._super_categories_for_classes),
1247 method_provider_cls,
prepend_cls_bases = False, doccls = doccls,
1248 reduction = reduction, cache = cache)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in
_super_categories_for_classes(self)
1038 [Category of rngs, Category of semirings]
1039 """
-> 1040 self._all_super_categories
1041 return self._super_categories_for_classes
1042
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/lazy_attribute.so in
sage.misc.lazy_attribute._lazy_attribute.__get__
(sage/misc/lazy_attribute.c:1357)()
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/category.pyc in _all_super_categories(self)
885 for cat in
self._super_categories] +
886
[self._super_categories],
--> 887 category_sort_key)
888 if not sorted(result, key = category_sort_key,
reverse=True) == result:
889 warn("Inconsistent sorting results for all super
categories of %s"%self.__class__)
/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/c3_controlled.so in
sage.misc.c3_controlled.C3_sorted_merge (sage/misc/c3_controlled.c:4459)()
KeyError: (28672, 99)
}}}
With only two `Groups()` it works. Now I'm wondering if this is a
consequence of the algorithm not being intended for redundant input, or
some unrelated C3 bug just showing up here. Either way, I'd prefer to see
it fixed because ensuring irredundancy seems to be a pain not many
category authors will want to inflict upon themselves.
--
Ticket URL: <http://trac.sagemath.org/ticket/15927>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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