Simplicity test

[Oscfon]

No description provided.

[videlec]

For walks on an OrientedMap, I think it would make sense to have a class Walk. The version of your code at commit 80ed422 introduces a class Walk for quad systems only (in quad_system.py) which has an additional _geodesic attributes.

The advantage of a well named class Walk is that we could then have Walk.geodesic_representative, Walk.self_intersection, Walk.has_simple_lift, etc A little drawback is that concatenation or accessing edges will be slower. But we could make the class so that the underlying data structure of the half-edge list is easily accessed (as we do with OrientedMap._vp).

To construct a walk, the entry point should just be OrientedMap.walk(self, ...).

[videlec]

Your function tree_contraction would better be a class that would return a morphism between the original OrientedMap and the one you obtain by doing some tree/co-tree contraction. A morphism is convenient to pass around objects on the OrientedMap (vertex, edge, walks, homotopy classe, homology classes, etc). In this particular case, you just want morphisms that contracts/deletes edges.

[videlec]

You should not use function names that start with test_ for anything but tests.

[videlec]

At #10, I introduced a word.pyx to implement at C level some operations on words (including free group elements). The underlying data structure is a Python array.

[videlec]

In #10 I finished the implementation of geometric intersection for OrientedMap with a single vertex and all faces punctured. It is currently in a separate file geometric_intersection.py but will hopefully be a method of Walk in the future. In order to handle the general case, I need to be able to

• have a way to contract a spanning tree and a co-forest (in the punctured case)
• implement reducing triangulations (for closed surfaces)

To me, it seems that we should do in order

1. merge the one-vertex-all-face-punctured geometric intersection Geometric Intersection #10
2. discuss the general interface for "map reductions" and adapt Simplicity test #11
3. merge Simplicity test #11
4. do geometric intersection in all cases.

What do you think?

[Oscfon]

There is already some works to contract spanning tree and co-tree in #11. We may adapt it.
I agree that it would be nice to have a common interface for all map reductions (Quadsystems and reducing triangulations).