#15577: Making braid groups independent on the global option for order of
permutations
-------------------------+-------------------------------------------------
   Reporter:  darij      |            Owner:
       Type:  defect     |           Status:  new
   Priority:  major      |        Milestone:  sage-6.1
  Component:  group      |         Keywords:  groups, combinat, braid
  theory                 |  group, permutations
  Merged in:             |          Authors:  Darij Grinbrg
  Reviewers:             |  Report Upstream:  N/A
Work issues:             |           Branch:
     Commit:             |     Dependencies:
   Stopgaps:             |
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 <boilerplate>
 As detailed in #14885, it is not healthy for code to rely on the `__mul__`
 operation on permutations, since this operation depends on the
 `Permutations().global_options()['mul']` variable which can change at
 runtime. It is better to use the `left_action_product` and
 `right_action_product` methods introduced in #15174 (formerly known as
 `_left_to_right_multiply_on_left` and `_left_to_right_multiply_on_right`).
 </boilerplate>

 The branch I'll attach later today sets out to solve this issue in
 `sage/groups/braid.py`. In all methods whose result depends on the `mult`
 global variable, the user can now set a local variable `mult` to override
 the global one, and this is explicited in the docstrings. (Also, some
 speedups have been achieved, most noticeably in the `permutation()` method
 which now runs about 8 times faster since permutations are being composed
 by list operations rather than multiplied as permutations.)

 **WARNING:** Please read the TODO part I left in the comments to the
 sourcecode of the `_left_normal_form_perm_` method. I am not sure of my
 fix there and would prefer someone who knows what this method does to look
 over it (and document the method while at that).

--
Ticket URL: <http://trac.sagemath.org/ticket/15577>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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