Incorrect long element for signed permutations

[tscrim]

The long element is wrong:

sage: SP = SignedPermutations(5)
sage: SP.long_element()
[-5, -4, -3, -2, -1]

It should be

[-1, -2, -3, -4, -5]

CC: @sagetrac-sage-combinat @darijgr @fchapoton @stumpc5 @kevindilks

Component: combinatorics

Keywords: signed permutations

Author: Travis Scrimshaw

Branch/Commit: 7f2989d

Reviewer: Frédéric Chapoton, Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/25200

[tscrim]

Branch: public/combinat/fix_long_element_signed_permutations-25200

[tscrim]

Commit: 486febd

[tscrim]

Changed keywords from none to signed permutations

[tscrim]

comment:1

Simple fix.

---

New commits:

486febd

Fixing SignedPermutation.long_element().

[jplab]

comment:2

It would be nice if the test would be against the theoretical known value.

I mean, if such a mistake was there, maybe the longest expression is not even the real longest element. After all, we know the length, so why not check against that value?

[sagetrac-git]

Changed commit from 486febd to 7f2989d

[sagetrac-git]

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

7f2989d

Added length test against the number of positive roots.

[tscrim]

comment:4

Replying to @jplab:

It would be nice if the test would be against the theoretical known value.

I mean, if such a mistake was there, maybe the longest expression is not even the real longest element. After all, we know the length, so why not check against that value?

Good idea. I added a more systematic test.

[fchapoton]

comment:5

ok

maybe one should add that test to finite Coxeter groups, in some later ticket

[fchapoton]

Reviewer: Frédéric Chapoton, Jean-Philippe Labbé

[jplab]

comment:6

Nice! Thanks!

[vbraun]

Changed branch from public/combinat/fix_long_element_signed_permutations-25200 to 7f2989d