Actually, I get the error:

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-10-6078cc2f8a98> in <module>()
----> 1 det = matrix.determinant(); show(det)

/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.pyx
 in sage.matrix.matrix2.Matrix.determinant 
(build/cythonized/sage/matrix/matrix2.c:15032)()
   1675         if algorithm is None:
   1676             try:
-> 1677                 R_is_field_attempt = R.is_field()
   1678             except NotImplementedError:
   1679                 R_is_field_attempt = False

/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/structure/category_object.pyx
 in sage.structure.category_object.CategoryObject.__getattr__ 
(build/cythonized/sage/structure/category_object.c:6865)()
    832             AttributeError: 'PrimeNumbers_with_category' object has no 
attribute 'sadfasdf'
    833         """
--> 834         return self.getattr_from_category(name)
    835 
    836     cdef getattr_from_category(self, name):

/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/structure/category_object.pyx
 in sage.structure.category_object.CategoryObject.getattr_from_category 
(build/cythonized/sage/structure/category_object.c:7028)()
    847                 cls = self._category.parent_class
    848 
--> 849             attr = getattr_from_other_class(self, cls, name)
    850             self.__cached_methods[name] = attr
    851             return attr

/home/michi/GitProjects/sage/local/lib/python2.7/site-packages/sage/cpython/getattr.pyx
 in sage.cpython.getattr.getattr_from_other_class 
(build/cythonized/sage/cpython/getattr.c:2540)()
    387         dummy_error_message.cls = type(self)
    388         dummy_error_message.name = name
--> 389         raise AttributeError(dummy_error_message)
    390     cdef PyObject* attr = instance_getattr(cls, name)
    391     if attr is NULL:

AttributeError: 'MixedFormAlgebra_with_category' object has no attribute 
'is_field'


However, the interesting part for me is the commutative subalgebra of even 
mixed forms which I could certainly implement. But I am not sure whether 
this will work due to the error message above...

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