#25159 closed defect (fixed)

Fix connected sum of knots

Reported by: mmarco Owned by:
Priority: major Milestone: sage-8.3
Component: algebraic topology Keywords: connected_sum, knot
Cc: slelievre Merged in:
Authors: Miguel Marco Reviewers: Samuel Lelièvre
Report Upstream: N/A Work issues:
Branch: d8cb5c1 (Commits) Commit: d8cb5c1fd9b25a4b9d5c089dddca1c9db4010245
Dependencies: Stopgaps:

Description (last modified by slelievre)

As pointed in https://ask.sagemath.org/question/41985/connected-sum-of-knots/ the connected sum of knots is not correctly computed.

Before this ticket, the connected sum of the trefoil knot with itself is incorrect, and computing the connected sum with a third trefoil knot fails:

sage: c = Knot.connected_sum
sage: B = BraidGroup(2)
sage: t = Knot(B([1, 1, 1])); t
Knot represented by 3 crossings
sage: tt = c(t, t); tt
Knot represented by 7 crossings
sage: tt_t = c(tt, t); tt_t
Traceback (most recent call last)
...
ValueError: the input has more than 1 connected component
sage: t_tt = c(t, tt); t_tt
Traceback (most recent call last)
...
ValueError: generators not in the group

After this ticket, these problems are fixed:

sage: c = Knot.connected_sum
sage: B = BraidGroup(2)
sage: t = Knot(B([1, 1, 1])); t
Knot represented by 3 crossings
sage: tt = c(t, t); tt
Knot represented by 6 crossings
sage: t_tt = c(t, tt); t_tt
Knot represented by 9 crossings
sage: tt_t = c(tt, t); tt_t
Knot represented by 9 crossings
sage: t_tt = tt_t
True

Change History (10)

comment:1 Changed 14 months ago by mmarco

  • Branch set to u/mmarco/connected_sum_of_knots_is_incorrect

comment:2 Changed 14 months ago by mmarco

  • Commit set to d8cb5c1fd9b25a4b9d5c089dddca1c9db4010245
  • Status changed from new to needs_review

New commits:

d8cb5c1Compute the connected sum from the oriented gauss code

comment:3 Changed 14 months ago by slelievre

  • Keywords connected_sum knot added
  • Status changed from needs_review to positive_review

This makes connected_sum correct (and a little faster it seems!).

comment:4 Changed 14 months ago by slelievre

  • Description modified (diff)
  • Summary changed from Connected sum of knots is incorrect to Fix connected sum of knots

comment:5 Changed 14 months ago by slelievre

  • Description modified (diff)

comment:6 Changed 14 months ago by chapoton

  • Reviewers set to ​Samuel Lelièvre

comment:7 Changed 13 months ago by davidloeffler

  • Milestone changed from sage-8.2 to sage-8.3

comment:8 Changed 13 months ago by mmarco

Why hasn't this been merged?

comment:9 Changed 13 months ago by vbraun

  • Reviewers changed from ​Samuel Lelièvre to Samuel Lelièvre

There was an invisible unicode in the reviewer name

comment:10 Changed 13 months ago by vbraun

  • Branch changed from u/mmarco/connected_sum_of_knots_is_incorrect to d8cb5c1fd9b25a4b9d5c089dddca1c9db4010245
  • Resolution set to fixed
  • Status changed from positive_review to closed
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