Extend PolyhedronRepresentation richcmp to a linear order, defining comparisons of representation objects of different types

[yzh]

Currently, the comparison is implemented only for two objects of the same type (vertex/ray/line or inequality/equation), as follows

if type(self) != type(other):
    return NotImplemented
return richcmp(self._vector*self._comparison_scalar(), other._vector*other._comparison_scalar(), op)

It might be good to extend the comparison to objects of different types, using the numeric values for the output of the type() method: INEQUALITY = 0; EQUATION = 1; VERTEX = 2; RAY = 3; LINE = 4. That is, instead of return NotImplemented, we return something like

richcmp((self.type(), self._vector*self._comparison_scalar()), (other.type(), other._vector*other._comparison_scalar()), op)

In this way, we will be able to sort a list of polyhedra according to their Vrepresentations.

sage: P = Polyhedron(vertices=[(0,0),(1,1)])                                       
sage: Q = Polyhedron(vertices=[(0,0)], rays=[(1,1)])                               
sage: sorted([Q, P], key=lambda p: p.Vrepresentation())                               
Traceback (most recent call 
...
TypeError: '<' not supported between instances of 'Ray' and 'Vertex'

[gh-kliem]

As long as you don't break #30954, it should be fine.

It is somehow inherited from vectors, which does lexicographic comparison. Indeed you can make this comparison consistent by using rich comparison on the types, if the types differ. I don't need it, but I don't mind it either.

I would consider it to be bad practice to rely on an NotImplementedError, because it is somehow a deprecation message by itself implicitly telling you "this might change in the future".

[mkoeppe]

New commits:

​2803d29

make PolyhedronRepresentation richcmp compare two representation objects with different types

[mkoeppe]

if you add author name and set it to "needs review", the patchbot will run it

[mkoeppe]

This needs doctests that illustrate the new behavior.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​2d57f41	add doctest for 31702
​7af9ebc	solve relint: commands failed

[mkoeppe]

The wording "Check :trac:31702" suggests that this is a test for a bug -- but this ticket adds a feature, rather than fixing a bug.

It would be better to reword it so that it becomes part of the documentation of the sorting order. There is no need to refer to a ticket number for non-bugfix tickets.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​48a8e8d

reword the doctest of richcmp

[mkoeppe]

The documentation only explains when two objects are equal.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​73e78e2

improve docstring of __richcmp__

[mkoeppe]

LGTM.