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Also, currently I am writing a method to separate into matching and non-matching edges. This will help in building the staircases. After that it remains to add faces to get the actual staircases. For that I have the following thought, tell me if this is ok -
Say we have a non-matching pair $(a,b)$ from two paths, where $a$ is part of the leftmost geodesic $c_L$ and $b$ is part of the rightmost geodesic $c_R$ then $b.a^{-1}$ is the boundary of a staircase $S$. Also each face of the staircase should contain at least two edges from $b.a^{-1}$.
I do not remember what I wote. But some things to try are:
By the way, @Chinmaya-Kausik please address me here by my Gitter handle to maximize the chance I am alerted.
Copying the above with double dollars.
I do not remember what I wote. But some things to try are:
By the way, @Chinmaya-Kausik please address me here by my Gitter handle to maximize the chance I am alerted.
I do remember explaining my method (since there was no explicit algorithm in the paper and the algorithm in the paper referenced seemed a bit involved), but I'm not sure if its correctness was discussed at all.
the algorithm in the other paper referenced*
What we expect, I will work out and add soon.
Okay, I think I've double checked and the issue seems to hold, so we should not expect any answer from this algorithm. There is a much more involved algorithm in a paper by Lazarus and Rivaud, but I never tried to read it.
LazyList
of iterations.
However, you seem to suggest that the wrong answer is returned, which will not happen in an infinite loop unless @anotherArka put a safeguard for this situation which halts and gives an error or wrong answer.
It turns out that I coded in this algorithm and I actually just make it terminate after loopLength + 2 iterations.
@Chinmaya-Kausik Are you saying that we get into an infinite loop when we try to make things canonical?
When attempting to do this by hand, that is what seems to happen, yes.