Braid Group construction misses some relations

[miguelmarco]

Braid Groups are constructed over a finitely presented group, but not all relations are present:

sage: B=BraidGroup('a,b,c')
sage: B
Braid group on 4 strands
sage: B.relations()
(a*b*a*b^-1*a^-1*b^-1,)

CC: @vbraun @nathanncohen @fchapoton

Component: group theory

Keywords: braid groups

Author: Miguel Marco

Reviewer: Travis Scrimshaw

Merged: sage-5.13.rc0

Issue created by migration from https://trac.sagemath.org/ticket/15505

[tscrim]

comment:2

The if statement is always true since range(a, b) is [a, a+1, ..., b-2, b-1] (or you can think of it as the integer points in th internal [a, b)). So I think this should work:

for i in range(1, n):
    rels.append(free_group([i, i+1, i, -i-1, -i, -i-1]))
    for j in range(i+2, n+1):
        rels.append(free_group([i, j, -i, -j]))

[miguelmarco]

comment:3

You are right. Here is a new patch.

[tscrim]

comment:4

Could you add a proper commit message? Once that's done, you can set this to positive review on my behalf. Thanks!

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed author from mmarco to Miguel Marco

[miguelmarco]

Attachment: 15505_braid_rels.patch.gz

[jdemeyer]

Merged: sage-5.13.rc0