TensorProductsCategory fails to work in 6.3

[cnassau]

The following code used to work in Sage 6.0 (up to Sage 6.2 possibly, but can't test it right now):

from sage.categories.category_types import Category_over_base_ring
from sage.categories.tensor import TensorProductsCategory, tensor

class TestCat(Category_over_base_ring):
    @cached_method
    def super_categories(self):
        return []
    class ParentMethods:
        def mytestmthd(self):
            return "ok"
    class TensorProducts(TensorProductsCategory):
        @cached_method
        def extra_super_categories(self):
            return [self.base_category()]
        class ParentMethods:
            def tenstestmthd(self):
                return "ok"

O=CombinatorialFreeModule(RDF,ZZ,category=(ModulesWithBasis(RDF),TestCat(RDF)))
print "O.cats=", O.categories()

OO=tensor((O,O))
print "OO.cats=", OO.categories()

C=O.category()
print C
#print TensorProductsCategory(C)

J=OO.category()
print "OO.category=",J

print O.mytestmthd()
print OO.mytestmthd()
print OO.tenstestmthd()

Here "works" means that the last three print statements produce an "ok".

It no longer works in Sage 6.3:

• the print TensorProductsCategory(C) raises an error in _repr_
• the tensor product OO is no longer in the TestCat.TensorProducts category

The _repr_ error seems to relate to the new Axiom-framework.

CC: @nthiery

Component: categories

Issue created by migration from https://trac.sagemath.org/ticket/16831

[cnassau]

comment:1

Here is the backtrace from print TensorProductsCategory(C):

ValueError                                Traceback (most recent call last)
<ipython-input-1-713356a36280> in <module>()
     25 C=O.category()
     26 print C
---> 27 print TensorProductsCategory(C)
     28 
     29 J=OO.category()

/waste/cn/sage-6.3/local/lib/python2.7/site-packages/sage/structure/sage_object.so in sage.structure.sage_object.SageObject.__repr__ (build/cythonized/sage/structure/sage_object.c:1999)()

/waste/cn/sage-6.3/local/lib/python2.7/site-packages/sage/categories/category.pyc in _repr_(self)
    609             Category of sets
    610         """
--> 611         return "Category of {}".format(self._repr_object_names())
    612 
    613     def _latex_(self):

/waste/cn/sage-6.3/local/lib/python2.7/site-packages/sage/categories/covariant_functorial_construction.pyc in _repr_object_names(self)
    421             Category of subquotients of semigroups
    422         """
--> 423         return "%s of %s"%(Category._repr_object_names(self), self.base_category()._repr_object_names())
    424 
    425     def _latex_(self):

/waste/cn/sage-6.3/local/lib/python2.7/site-packages/sage/categories/category.pyc in _repr_object_names(self)
   2860         """
   2861         from sage.categories.category_with_axiom import CategoryWithAxiom
-> 2862         return CategoryWithAxiom._repr_object_names_static(self._without_axioms(named=True), self.axioms())
   2863 
   2864     def _repr_(self, as_join = False):

/waste/cn/sage-6.3/local/lib/python2.7/site-packages/sage/categories/category.pyc in _without_axioms(self, named)
   2816             if category._with_axioms(axioms) is self:
   2817                 return category._without_axioms(named=named)
-> 2818         raise ValueError("This join category isn't built by adding axioms"
   2819                          " to a single category")
   2820 

ValueError: This join category isn't built by adding axioms to a single category

[cnassau]

comment:3

It turns out this problem can be circumvented by making TensorProducts a method, rather than a subclass:

class TestCat(Category_over_base_ring):
    @cached_method
    def super_categories(self):
        return []
    class ParentMethods:
        def mytestmthd(self):
            return "ok"
    def TensorProducts(self):
        return TestCat_TensorProducts(self)

class TestCat_TensorProducts(TensorProductsCategory):
        def _repr_(self):
            return "my tensor tst category" 
        @cached_method
        def extra_super_categories(self):
            return [self.base_category()]
        class ParentMethods:
            def tenstestmthd(self):
                return "ok"

Seems I've been hit by black-category-magic once again...

But even with this "fix" the TensorProductsCategory(C) still throws an error.