HOMFLY polynomial of links. #20719

miguelmarco · 2016-05-30T15:59:15Z

This branch adds a method for computing the HOMFLY polynomial of links. It deppends on #18057 and #18047.

Depends on #18057
Depends on #18047

CC: @vbraun @kcrisman @sagetrac-amitjadagni @sagetrac-fugelde @tscrim

Component: algebraic topology

Keywords: days74

Author: Miguel Marco

Branch/Commit: ee2cf38

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/20719

The text was updated successfully, but these errors were encountered:

miguelmarco · 2016-05-30T15:59:59Z

Dependencies: #18057, #18047

miguelmarco · 2016-05-30T17:53:16Z

Branch: u/mmarco/homfly_polynomial_of_links_

miguelmarco · 2016-05-30T17:54:27Z

New commits:

`05edf9c`	`Added homfly_polynomial method.`

miguelmarco · 2016-05-30T17:54:27Z

Commit: 05edf9c

sagetrac-git · 2016-05-31T15:25:04Z

Changed commit from 05edf9c to b641799

sagetrac-git · 2016-05-31T15:25:04Z

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

`b641799`	`Adapted to the new interface by dicts.`

tscrim · 2016-05-31T22:34:38Z

Changed commit from b641799 to da53581

tscrim · 2016-05-31T22:34:38Z

comment:5

I've made some tweaks. We should also test other examples, such as two unknots and the Boromean rings (since those are the (lib)homfly examples).

New commits:

`da53581`	`Some reviewer changes.`

tscrim · 2016-05-31T22:34:38Z

Changed branch from u/mmarco/homfly_polynomial_of_links_ to u/tscrim/homfly_polynomial-20719

tscrim · 2016-05-31T22:34:38Z

Reviewer: Travis Scrimshaw

sagetrac-git · 2016-06-01T13:06:49Z

Changed commit from da53581 to 6c45265

sagetrac-git · 2016-06-01T13:06:49Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`0f880bc`	`set doctests as optional`
`86b9a43`	`Cython interface to libhomfly`
`d3e96fc`	`set doctests as optional`
`69ec550`	`Merge branch 'u/mmarco/libhomfly_interface' of git://trac.sagemath.org/sage into t/18057/libhomfly_interface`
`2019b9d`	`Moved dependency to cysignals`
`53ad4bf`	`Adapted to the new interface with functions for strings and dict`
`eeda425`	`Removing commented out code and making OptionalExtension.`
`b4c923c`	`Marked all tests as optional, because they all depend on libhomfly.`
`a4add26`	`Merge branch 'u/tscrim/libhomfly_cython_interface-18057' of trac.sagemath.org:sage into u/tscrim/homfly_polynomial-20719`
`6c45265`	`Adding some more doctests.`

tscrim · 2016-06-01T13:08:38Z

comment:7

We might have a problem:

sage: B = BraidGroup(3)
sage: K = Knot(B([-1,-1,-1,-1,-1,-1,-2,1,-2,-2]))  # Knot 9_6
L^10*M^4 - L^8*M^6 - 3*L^10*M^2 + 4*L^8*M^4 + L^6*M^6 + L^10 - 3*L^8*M^2 - 5*L^6*M^4 - L^8 + 7*L^6*M^2 - 3*L^6

Some of the signs are wrong in this example. Nathan is thinking it might possibly by a variable a = -i M and/or b = -i L, but still...

Also, I will add a description of the polynomial after the above issue gets resolved.

miguelmarco · 2016-06-01T13:46:05Z

comment:8

The problem is that there are many equivalent definitions of the homfly polynomial. All of them are related by a change of variables.

The homfly program, which we adapted to libhomfly, uses the one where the variables are called L and M. There are at least other two definitions that use the variables \alpha and z and x, y and z respectively.

In particular, the first two variables are related by multiplying the variables by I, as you said.

It is true that we should clarify which are the coordinates we take.

miguelmarco · 2016-06-01T15:15:47Z

Changed branch from u/tscrim/homfly_polynomial-20719 to u/mmarco/homfly_polynomial-20719

miguelmarco · 2016-06-01T15:16:48Z

comment:10

I think this basicallys solves the problem. If you compare the output with normalization = 'az' to the results shown in knot atlas, they should match.

miguelmarco · 2016-06-01T15:16:48Z

Changed branch from u/mmarco/homfly_polynomial-20719 to u/tscrim/homfly_polynomial-20719

tscrim · 2016-06-01T15:22:06Z

Changed commit from 6c45265 to a468291

tscrim · 2016-06-01T15:22:06Z

Changed branch from u/tscrim/homfly_polynomial-20719 to u/mmarco/homfly_polynomial-20719

tscrim · 2016-06-01T15:22:06Z

New commits:

`df0eef1`	`Handle the other usual normalization.`
`a468291`	`Correct writing of doctest`

tscrim · 2016-06-01T15:44:10Z

Changed branch from u/mmarco/homfly_polynomial-20719 to u/tscrim/homfly_polynomial-20719

tscrim · 2016-06-01T15:44:10Z

comment:12

Great; thank you. I've added a note about the normalizations. I've fixed it so this didn't cause a segfault when there is more than one isolated component. I also added the extra little doc I wanted. If you're happy with my changes, then you can set a positive review.

New commits:

`5c54442`	`Fixing issue with isolated components.`
`dd21a96`	`Adding a little bit more documentation.`

tscrim · 2016-06-01T15:44:10Z

Changed commit from a468291 to dd21a96

tscrim · 2016-06-01T19:58:42Z

Changed branch from u/tscrim/homfly_polynomial-20719 to u/mmarco/homfly_polynomial-20719

tscrim · 2016-06-01T19:58:42Z

New commits:

`62f87a8`	`Handle several isolated components`

tscrim · 2016-06-01T20:00:21Z

comment:18

Other than a trailing ] here: http://mathworld.wolfram.com/HOMFLYPolynomial.html] LGTM. Thank you.

tscrim · 2016-06-02T07:17:10Z

Changed commit from 62f87a8 to dcdf428

tscrim · 2016-06-02T07:17:10Z

Changed branch from u/mmarco/homfly_polynomial-20719 to u/tscrim/homfly_polynomial-20719

tscrim · 2016-06-02T07:17:10Z

comment:19

Okay, I made some last little doc tweaks. If you're okay with my changes, then you can set a positive review.

New commits:

`cd786cb`	`Fixing docbuild issue.`
`5d9bc87`	`Merge branch 'u/tscrim/libhomfly_cython_interface-18057' into u/tscrim/homfly_polynomial-20719`
`3b4a5de`	`Merge branch 'u/mmarco/homfly_polynomial-20719' of trac.sagemath.org:sage into u/tscrim/homfly_polynomial-20719`
`dcdf428`	`Some last little doc fixes.`

miguelmarco · 2016-06-02T08:22:26Z

Changed branch from u/tscrim/homfly_polynomial-20719 to u/mmarco/homfly_polynomial-20719

miguelmarco · 2016-06-02T08:26:27Z

Changed branch from u/mmarco/homfly_polynomial-20719 to u/tscrim/homfly_polynomial-20719

miguelmarco · 2016-06-02T08:26:27Z

comment:21

Ups, wrong push, sorry.

miguelmarco · 2016-06-02T09:01:36Z

comment:22

I get an error when building documentation. Working on it.

tscrim · 2016-06-02T09:07:50Z

comment:23

Probably this: L ^{-1}, which needs to be L^{-1} (and similar for a).

tscrim · 2016-06-02T09:09:04Z

comment:24

Oh and the indentation is wrong:

         - ``normalization`` -- (default: ``lm``) the system of coordinates
-            and can be one of the following:
+          and can be one of the following:

(and for the rest of the block).

miguelmarco · 2016-06-02T09:15:50Z

comment:25

Ok, checking it now. If it builds, I will push the branch with the correction and give a positive review.

tscrim · 2016-06-02T09:16:16Z

comment:26

Replying to @miguelmarco:

Ok, checking it now. If it builds, I will push the branch with the correction and give a positive review.

Sounds good. Thank you.

miguelmarco · 2016-06-02T12:00:30Z

Changed branch from u/tscrim/homfly_polynomial-20719 to u/mmarco/homfly_polynomial-20719

miguelmarco · 2016-06-02T12:01:10Z

Changed commit from dcdf428 to c9d0987

miguelmarco · 2016-06-02T12:01:10Z

New commits:

`c9d0987`	`Fixed docstring`

tscrim · 2016-06-02T12:02:20Z

comment:29

There's a few things in the doc I need to tweak.

tscrim · 2016-06-02T12:09:37Z

Changed commit from c9d0987 to ee2cf38

tscrim · 2016-06-02T12:09:37Z

comment:30

Okay, that will do it. Thank you for all your work on this.

New commits:

`ee2cf38`	`Last little fixes in the doc.`

tscrim · 2016-06-02T12:09:37Z

Changed branch from u/mmarco/homfly_polynomial-20719 to u/tscrim/homfly_polynomial-20719

vbraun · 2016-06-03T21:49:31Z

Changed branch from u/tscrim/homfly_polynomial-20719 to ee2cf38

miguelmarco added this to the sage-7.3 milestone May 30, 2016

miguelmarco added c: algebraic topology labels May 30, 2016

miguelmarco added the t: enhancement label May 30, 2016

miguelmarco added the s: needs review label May 30, 2016

tscrim added s: needs info and removed s: needs review labels Jun 1, 2016

miguelmarco added s: positive review and removed s: needs review labels Jun 2, 2016

tscrim added s: needs work and removed s: positive review labels Jun 2, 2016

tscrim added s: positive review and removed s: needs work labels Jun 2, 2016

vbraun removed the s: positive review label Jun 3, 2016

vbraun closed this as completed in acb5cc7 Jun 3, 2016

HOMFLY polynomial of links. #20719

HOMFLY polynomial of links. #20719

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