Where communities thrive

• Join over 1.5M+ people
• Join over 100K+ communities
• Free without limits
Activity
• Aug 10 2021 05:06
• Aug 10 2021 04:50
• Aug 10 2021 04:49
• Aug 07 2021 03:43

helpers for timing (compare)

• Aug 06 2021 05:19

"require" correction slight refactoring (compare)

• Aug 05 2021 05:22

helpers for curves being pants … (compare)

• Aug 05 2021 02:47

figures for pants length 2 (compare)

• Aug 04 2021 10:33

reduced laziness to run in REPL (compare)

• Aug 04 2021 09:50

segment lengths 1 and 2 bound (compare)

• Aug 04 2021 05:26

parallel normal path enumeration (compare)

• Aug 03 2021 10:41

margulis constant corrected (compare)

• Jul 16 2021 06:40

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

• Jul 16 2021 06:40
• Jul 16 2021 06:38
shabarishch opened #98
• Jul 16 2021 05:21
• Jul 16 2021 05:21

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
• Jul 05 2021 10:52

speedup by memoizing hash (compare)

• Jul 05 2021 10:16
The region $\Delta$ is the region bounded by $c_R$ and $c_L$. I am not sure of the traversed path statement, but in any case it is cleaner to just deduce it from the two boundary curves.
Namely, the paths $c_L$ and $c_R$ can be decomposed into coinciding segments and segments that are boundaries of stairs.
One can make a structure for a stair, and such a decomposition. Then define a recursively defined function computing this.
If the curves $c_L$ and $c_R$ start with a non-trivial coinciding segment, we find a maximal one and then recurse.
Otherwise we find the first staircase, which is bounded by the segments of the curves $c_L$ and $c_R$ between the initial point and the second point where they agree. Again we recurse.
Arka Ghosh
@anotherArka
I think the traversed path statement should follow as the region $\Delta$ is an annulus and if any of the spokes are skipped then the outer and inter boundaries, which are $c_L$ and $c_R$ can not be homotopic. But, maybe I am oversimplifying.
But is there anything gained by that?
Arka Ghosh
@anotherArka
It can give a possible method to calculate $\Delta$. But your algorithm is simpler I think.
Arka Ghosh
@anotherArka
While pattern matching in scala, is there a way to assert that certain patterns are unreachable.
For what reason?
I mean, why do you want to show this. Is it to avoid compiler warnings?
Arka Ghosh
@anotherArka
Compiler warnings is an issue but I was curious in general.
Arka Ghosh
@anotherArka

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 $b.a^{-1}$.

Yes, that is correct.
You have to decide which kind of staircase it is, and then the spokes just join vertices with index differinb by 1
Arka Ghosh
@anotherArka

Compiler warnings is an issue but I was curious in general.

The compiler is reasonably smart about this, but can only work with type information. If the missed case is based on object level, there is no way you can tell the compiler.
The practice I follow is have a match for the missed case and throw an exception with information of why that match should never have been reached (helps in debugging, but also serves as documentation)
Chinmaya Kausik
@Chinmaya-Kausik
Okay, to get to examples - would writing out the ones you mentioned in the email the first time we worked on GIN be good, Prof. Gadgil?
Arka Ghosh
@anotherArka
Do note that I have only written the code for primitive curves.

I do not remember what I wote. But some things to try are:

• Various pairs of intersections of generators $\alpha_i$ and $\beta_j$ and also their slef-intersections.
• Self-intersections of $\alpha_1\alpha_2$ and $\alpha_1\bar{\alpha_2}$ to check one is 0 and the other is not.
• Generate families such as $\alpha_1\beta_1^n$ and look for intersection numbers of pairs in these.
• Intersection number of the commutator $[alpha_1, \beta_1]$ with $\alpha_1\alpha_2$.

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:

• Various pairs of intersections of generators $\alpha_i$ and $\beta_j$ and also their slef-intersections.
• Self-intersections of $\alpha_1\alpha_2$ and $\alpha_1\bar{\alpha_2}$ to check one is 0 and the other is not.
• Generate families such as $\alpha_1\beta_1^n$ and look for intersection numbers of pairs in these.
• Intersection number of the commutator $[alpha_1, \beta_1]$ with $\alpha_1\alpha_2$.

By the way, @Chinmaya-Kausik please address me here by my Gitter handle to maximize the chance I am alerted.

Chinmaya Kausik
@Chinmaya-Kausik
In that case @anotherArka will you have the time to implement the code for non-primitive loops too? I'll write some examples but the tests obviously won't compile without that.
I'll do some primitive ones right now, of course.
Arka Ghosh
@anotherArka
I will try to do it. But I have a presentation tomorrow so I can't gurantee.
Chinmaya Kausik
@Chinmaya-Kausik
Oh definitely, no problem. I'll do the primitive ones for now.
Arka Ghosh
@anotherArka
I have uploaded a code to break a loop into primitive loops. I think the logic is correct but the code can be optimized slightly.
Unfortunately my laptop is out of charge and it's stormy outside so I can't charge it.
Chinmaya Kausik
@Chinmaya-Kausik

I have uploaded a code to break a loop into primitive loops. I think the logic is correct but the code can be optimized slightly.

Ah thanks a lot!

Chinmaya Kausik
@Chinmaya-Kausik
Running the tests I wrote, it seems like there's a flaw in the canonicization code, and it's very souped up and I can't quite figure out what it is.
Had anyone independently checked the general reasoning behind the code (the use of turn indices and rightward shifts)?
Chinmaya Kausik
@Chinmaya-Kausik
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.
Chinmaya Kausik
@Chinmaya-Kausik
I have made a pull request with the code I added for tests so far, which has been commented out though since the tests crashed due to some problem with canonicization.

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*

Chinmaya Kausik
@Chinmaya-Kausik

Had anyone independently checked the general reasoning behind the code (the use of turn indices and rightward shifts)?

Though I guess it's mostly what Prof. Gadgil told us to do, so it should ideally be correct.

@Chinmaya-Kausik can you clarify and narrow the error - do you mean the problem is hanging, presumably an infinite loop, or giving the wrong answer, and what minimal triggers this, and make an issue with this.
Chinmaya Kausik
@Chinmaya-Kausik
Oh okay, yes I can specify what is going wrong. The "why" is what I'm having trouble with.
So the loop "a1!" in genus2 does not canonicize correctly.
I'm trying to trace the algorithm by hand right now.
Make an issue first. That way we can all work on it.
Thanks. But can you add another comment for "does not canonicalize correctly" clarifying this - e.g. when we canonicalize we obtain ... which is incorrect (we expect ...).
Chinmaya Kausik
@Chinmaya-Kausik
What we expect, I will work out and add soon.
Chinmaya Kausik
@Chinmaya-Kausik
Oh this seems to be a theoretical issue. That doubt I once had about how canonicising at one basepoint make it non-canonical at the other seems to follow.
Chinmaya Kausik
@Chinmaya-Kausik
I'm not entirely sure yet (haven't double checked so far), but this is my current guess.
Chinmaya Kausik
@Chinmaya-Kausik

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.