Opened 10 years ago

Last modified 9 years ago

## #11943 closed enhancement

# The category graph should comply with Python's method resolution order — at Initial Version

Reported by: | SimonKing | Owned by: | nthiery |
---|---|---|---|

Priority: | major | Milestone: | sage-5.1 |

Component: | categories | Keywords: | category graph, method resolution order |

Cc: | hivert, mderickx | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description

Let C be a category. `C.all_super_categories()`

starts with `C.super_categories()`

and finds all super categories inductively.

Unfortunately, the algorithm of `C.all_super_categories()`

does not comply with the C3 algorithm, that is used by Python to determine the method resolution order for `C.parent_class`

and `C.element_class`

.

The aim of this ticket is to be more consistent. Eventually, for any category C (perhaps with modifications for hom categories), one should have

sage: C.parent_class.mro() == [X.parent_class for X in C.all_super_categories()] + [object] True sage: C.element_class.mro() == [X.element_class for X in C.all_super_categories()] + [object] True

and that test should become part of the test suite.

At #11900, the implementation of `all_super_categories()`

has been changed, so, work should rely on #11900.

Unfortunately, it seems that the C3 algorithm can not simply be imported from Python, even though Python uses it internally, namely in `Objects/typeobject.c`

. Looking at the implementation, it requires that one gets a list of types, while we want to use it on a list of objects.

Therefore, we need to implement C3 from scratch. Implementing C3 is easy, but if it shall be fast, one needs to be careful.

In particular, one needs to be able to `L.pop(0)`

quickly, where L is a list. Unfortunately, `L.pop(0)`

is slow, even in Cython. I found that, if the lists are not too long, it is best to revert L and do `L.pop()`

instead, which is optimized in Cython. See the discussion at sage-devel.

My plan is:

- Provide the C3 algorithm in a new extension module
`sage.misc.c3`

- Use it to compute
`all_super_categories()`

- Add a test
`_test_category_graph`

, asserting that`self.parent_class.mro()`

and`self.all_super_categories()`

are compatible.

First tests indicate that the change of order on `C.all_super_categories()`

is fine (sage does not crash, and most tests in sage.categories pass. However, one really needs to look at the performance.

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