Fix connected sum of knots

[miguelmarco]

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

CC: @slel

Component: algebraic topology

Keywords: connected_sum, knot

Author: Miguel Marco

Branch/Commit: d8cb5c1

Reviewer: Samuel Lelièvre

Issue created by migration from https://trac.sagemath.org/ticket/25159

[miguelmarco]

Branch: u/mmarco/connected_sum_of_knots_is_incorrect

[miguelmarco]

Commit: d8cb5c1

[miguelmarco]

New commits:

d8cb5c1

Compute the connected sum from the oriented gauss code

[slel]

comment:3

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

[slel]

Changed keywords from none to connected_sum, knot

[fchapoton]

Reviewer: ​Samuel Lelièvre

[miguelmarco]

comment:8

Why hasn't this been merged?

[vbraun]

Changed reviewer from ​Samuel Lelièvre to Samuel Lelièvre

[vbraun]

comment:9

There was an invisible unicode in the reviewer name

[vbraun]

Changed branch from u/mmarco/connected_sum_of_knots_is_incorrect to d8cb5c1