Opened 7 years ago

Closed 7 years ago

#15505 closed defect (fixed)

Braid Group construction misses some relations

Reported by: mmarco Owned by:
Priority: major Milestone: sage-5.13
Component: group theory Keywords: braid groups
Cc: vbraun, ncohen, chapoton Merged in: sage-5.13.rc0
Authors: Miguel Marco Reviewers: Travis Scrimshaw
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

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,)

Attachments (1)

15505_braid_rels.patch (4.4 KB) - added by mmarco 7 years ago.

Download all attachments as: .zip

Change History (7)

comment:1 Changed 7 years ago by ncohen

  • Status changed from new to needs_review

comment:2 Changed 7 years ago by tscrim

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]))
Last edited 7 years ago by tscrim (previous) (diff)

comment:3 Changed 7 years ago by mmarco

You are right. Here is a new patch.

comment:4 Changed 7 years ago by tscrim

  • Authors changed from mmarco to Miguel Marco
  • Reviewers set to Travis Scrimshaw

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

Changed 7 years ago by mmarco

comment:5 Changed 7 years ago by mmarco

  • Status changed from needs_review to positive_review

comment:6 Changed 7 years ago by jdemeyer

  • Merged in set to sage-5.13.rc0
  • Resolution set to fixed
  • Status changed from positive_review to closed
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