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  • Aug 10 2021 05:06
    siddhartha-gadgil opened #99
  • Aug 10 2021 04:50
    siddhartha-gadgil closed #94
  • Aug 10 2021 04:49
    siddhartha-gadgil closed #96
  • Aug 07 2021 03:43

    siddhartha-gadgil on master

    helpers for timing (compare)

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    helpers for curves being pants … (compare)

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    siddhartha-gadgil on master

    Updates to function shortPathsD… Merge pull request #98 from sha… (compare)

  • Jul 16 2021 06:40
    siddhartha-gadgil closed #98
  • Jul 16 2021 06:38
    shabarishch opened #98
  • Jul 16 2021 05:21
    siddhartha-gadgil closed #97
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    siddhartha-gadgil on master

    introducing compact types More compact types Merge pull request #97 from sha… (compare)

  • Jul 16 2021 05:16
    shabarishch opened #97
  • Jul 05 2021 10:55
    siddhartha-gadgil commented #96
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    siddhartha-gadgil on master

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  • Jul 05 2021 10:16
    siddhartha-gadgil commented #94
Siddhartha Gadgil
@siddhartha-gadgil
That is, when we make stuff canonical as paths, it fails to be canonical at the basepoint
And making it canonical at basepoint causes the whole process to loop.
If this is the case, we should check the paper if canonical as paths is enough.
At least if that is what they claim.
Chinmaya Kausik
@Chinmaya-Kausik

And making it canonical at basepoint causes the whole process to loop.

Yes, that's exactly what seems to happen here.

If this is the case, we should check the paper if canonical as paths is enough.

I'll take a look

And making it canonical at basepoint causes the whole process to loop.

Yes, that's exactly what seems to happen here.

To clarify - there are only two (adjacent) edges and two vertices and a right turn on the basepoint is a left turn on the other vertex and a left on the basepoint is a right on the other vertex.

Siddhartha Gadgil
@siddhartha-gadgil
That is a good example - simple enough that one can see what is happening. The only question is whether intersection numbers are correct when we take canonical as paths
Arka Ghosh
@anotherArka
What if in the cases where canonicising does not end, we create a list of loops it generates and stop when it generates one loop twice. Then take the intersection number between all such possible pairs of loops then take the minimum of them. Will it be same as the GIN?
Chinmaya Kausik
@Chinmaya-Kausik

That is a good example - simple enough that one can see what is happening. The only question is whether intersection numbers are correct when we take canonical as paths

I checked Erickson and Whittlesey's definition of canonical forms - they seem to require that the cyclic sequence of turns is canonical, so that the curve is canonical as a loop.

What if in the cases where canonicising does not end, we create a list of loops it generates and stop when it generates one loop twice. Then take the intersection number between all such possible pairs of loops then take the minimum of them. Will it be same as the GIN?

Yes, such details I'm not sure of - I don't know if the proofs themselves allow for things to work out. Also, a bigger issue is that the algorithm they describe sounds very similar to ours (to me it seems that it's merely a different way of organizing what we are doing), and they seem to claim that it works.

Chinmaya Kausik
@Chinmaya-Kausik
I should clarify - by "they" in the latest message I mean Erickson and Whittlesey
Siddhartha Gadgil
@siddhartha-gadgil
It seems we should carefully look at canonical in the sense of Erikson and Whittesley. At least the canonical form should exist
Chinmaya Kausik
@Chinmaya-Kausik
I took a look and it seems that our case is one of the (non-+) * cases with s = 0.
Chinmaya Kausik
@Chinmaya-Kausik
Their notation (in terms of turn cycles) and pictures are slightly ambiguous about what happens when s = 0, but even if one were to just plug in the numbers, x+2 is actually a right turn in our case.
It's funny that they just assumed that x+2 != -1 mod (degree)
Chinmaya Kausik
@Chinmaya-Kausik
Oh nvm - I see that x = -3 is a separate case
Chinmaya Kausik
@Chinmaya-Kausik
I still don't see how that's canonical when s= 0, t= 0
If I'm not wrong, there are only two geodesics representing "a1!" and both are non-canonical.
Siddhartha Gadgil
@siddhartha-gadgil
Perhaps we should just replace the curve by its inverse.
If only special ones fail to be non- canonical, one may always work
After all, we do have to pass to primitive curves in a similar way
Chinmaya Kausik
@Chinmaya-Kausik
It turns out that while checking things by hand, I had missed a case by ignoring the possibility of conjugation in free homotopies. The curve "4 to basepoint to 1" on the octagon diagram, representing the loop "b1!a1!b1" based at "4=1" is a canonical curve representing "a1!"
But I'm not sure how one would reach this curve by the algorithm we had discussed in class and implemented
Chinmaya Kausik
@Chinmaya-Kausik
Ah I think I see at least part of the issue. If two edges on a curve are in two quadrilaterals, then there are two ways to shift rightwards.
shabarishch
@shabarishch
Are you active here, @siddhartha-gadgil ?
gadgil
@gadgil:matrix.org
[m]
Just signed in. Wanted to test Latex: $x^2 + 2$
Or is it x2+2x^2 + 2
Just enabled: try $x^2 + 1$ and x3+yx^3 + y
It worked with single dollar.