irreducibility of generalized permutation

[videlec]

The irreducibility of generalized permutation does not work

sage: p = iet.GeneralizedPermutation('1 2 2 3 3','1 4 4')
sage: p.is_irreducible()
True

But it should returns False.

The patch corrects this behavior. The implementation is a bit modified and many doctests are added.

Component: combinatorics

Keywords: permutation, quadratic differentials

Author: Vincent Delecroix

Reviewer: Frédéric Chapoton

Merged: sage-5.3.beta0

Issue created by migration from https://trac.sagemath.org/ticket/12643

[fchapoton]

comment:2

This looks good, as far as I can tell, because I am not able to check the algorithms..

And the bot is happy. Two minor comments :

• One should say "There exists a decomposition" (instead of "exist")

• The reference to "Boissy-Lanneau" is not complete (journal, etc)

[fchapoton]

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 The irreducibility of generalized permutation does not work
 
 ```
-sage: p = iet.GeneralizedPermutation('1 2 2 3 3','1 4 4)
+sage: p = iet.GeneralizedPermutation('1 2 2 3 3','1 4 4')
 sage: p.is_irreducible()
 True
 ```

[videlec]

comment:4

Hello,

Thank you Frederic for your relecture. Do you think I need to add a proof for the algorithm within the documentation?

I made the modification (and remove one r for corrrects in the description of the ticket).

[videlec]

Description changed:

--- 
+++ 
@@ -7,4 +7,4 @@
 ```
 But it should returns False.
 
-The patch corrrects this behavior. The implementation is a bit modified and many doctests are added.
+The patch corrects this behavior. The implementation is a bit modified and many doctests are added.

[fchapoton]

comment:5

Well, I was just saying that I do not understand the underlying mathematics, so that I cannot check if the given examples are indeed irreducible or not. I do not think that it is necessary to add a proof.

Is there an easy place where I can try to understand the meaning of

iet.GeneralizedPermutation('a a b','b c c') ?

or

GP('1 2 3 4 5 1','5 6 6 4 3 2')

Maybe I can just give a positive review without understanding, but I would prefer if I can be just slightly more serious.

[videlec]

comment:6

but I would prefer if I can be just slightly more serious.

Me too ;-)

Is there an easy place where I can try to understand the meaning of

iet.GeneralizedPermutation('a a b','b c c') ?

or

GP('1 2 3 4 5 1','5 6 6 4 3 2')

You have to think as the standard two lines notation for permutations. For example, the permutation

p(1) = 2, p(2) = 1, p(3) = 3

would be denoted

1 2 3
2 1 3

Then iet.Permutation('1 2 3', '2 1 3') is just a version of the permutation above. But we are interested in the so called interval exchange transformations (see Figure 1 p. 8 of [BL]) and it is better to have two order of labels instead of a permutation. The object iet.Permutation is two lines of symbols where each symbol appears once in the first line and once in the second.

Generalized Permutations encode the combinatorics of more complicated maps called linear involution (see Figure 6 p 16 of [BL]). The object iet.GeneralizedPermutation is two lines of symbols where each symbol appear twice.

.. [BL] Boissy-Lanneau http://arxiv.org/abs/0710.5614

[fchapoton]

comment:7

I think I almost understand now, even if I am a bit puzzled by the lack of symmetry between left and right. Anyway, I will give a positive review, provided you correct

Test reducible permutations with two left corner empty

into

Test reducible permutations with two left corners empty

and same with right instead of left.

[fchapoton]

comment:8

Hello, is there anybody out there ? just make these 2 small changes, and I will give a positive review !

[videlec]

comment:9

Replying to @fchapoton:

Hello, is there anybody out there ? just make these 2 small changes, and I will give a positive review !

done