#15309: Symmetric group algebra creating algebra generators using
_element_constructor_
------------------------------------+-----------------------------
       Reporter:  tscrim            |        Owner:  sage-combinat
           Type:  defect            |       Status:  needs_review
       Priority:  major             |    Milestone:  sage-5.13
      Component:  coercion          |   Resolution:
       Keywords:                    |    Merged in:
        Authors:  Travis Scrimshaw  |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:                    |     Stopgaps:
------------------------------------+-----------------------------

Old description:

> When calling the `algebra_generators()`, `SymmetricGroupAlgebra` ends up
> setting the `_coercions_used` flag to `True`. This prevents us from
> creating coercions dynamically.
>
> For example:
> {{{#!python
> sage: S3 = SymmetricGroupAlgebra(QQ, 3)
> sage: S3._coercions_used
> False
> sage: S3.algebra_generators()
> [[2, 1, 3], [2, 3, 1]]
> sage: S3._coercions_used
> True
> }}}

New description:

 When calling the `algebra_generators()`, `SymmetricGroupAlgebra` ends up
 setting the `_coercions_used` flag to `True`. This prevents us from
 creating coercions dynamically.

 For example:
 {{{#!python
 sage: S3 = SymmetricGroupAlgebra(QQ, 3)
 sage: S3._coercions_used
 False
 sage: S3.algebra_generators()
 [[2, 1, 3], [2, 3, 1]]
 sage: S3._coercions_used
 True
 }}}

 Apply: [attachment:trac_15309-sga_alg_gens_fix-ts.patch]

--

Comment (by tscrim):

 Hey Darij,

 I'm somewhat surprised I get a 2x speedup; that's good to know for future
 reference.

 I've folded in your review patch (it applied with some fuzz 2), but made
 one change. Instead of `return self.monomial(self._one)`, I changed it to
 `return self.one()`. If you're happy with the patch, then it's positive
 review.

 Best,[[BR]]
 Travis

 For patchbot:

 Apply: trac_15309-sga_alg_gens_fix-ts.patch

--
Ticket URL: <http://trac.sagemath.org/ticket/15309#comment:6>
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