#18762: Create coercion between diagram algebras and the symmetric group algebra
-------------------------------------+-------------------------------------
       Reporter:  ghseeli            |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.10
      Component:  algebra            |   Resolution:
       Keywords:  diagram algebra,   |    Merged in:
  partition algebra, days65          |    Reviewers:  Travis Scrimshaw
        Authors:  George H.          |  Work issues:
  Seelinger                          |       Commit:
Report Upstream:  N/A                |  14f80d3624d95079c896cb5efe8f29988834e1ac
         Branch:                     |     Stopgaps:
  u/tscrim/diagram_algebras_SGA-18762|
   Dependencies:  #18720             |
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * status:  needs_work => needs_review
 * reviewer:   => Travis Scrimshaw
 * priority:  minor => major
 * branch:
u/ghseeli/create_coercion_between_diagram_algebras_and_the_symmetric_group_algebra
     => u/tscrim/diagram_algebras_SGA-18762
 * milestone:  sage-6.9 => sage-6.10
 * commit:  a4c199d2842865c6385e6938b67974f39ebd8876 =>
     14f80d3624d95079c896cb5efe8f29988834e1ac


Comment:

 Okay, so I figured out what was going on.

 <technical>What was happening was you were creating a coercion from a
 subalgebra to the ambient algebra, but the ambient algebra could be
 garbage collected because the morphism (which only holds a strong
 reference to the ''codomain'') could be collected and the subalgebra
 didn't have a strong reference to the ambient algebra. When the ambient
 algebra was recreated, the morphism was not, and so there was no coercion
 registered (which is done in the codomains). I reworked things so the lift
 morphism was strongly referenced, and hence the ambient algebra, by the
 subalgebra.</technical>

 I also reworked the morphisms to the Sage standard practice and expanded
 coercions to allow when there is also a coercion of base rings. There were
 also some other misc issues that I fixed as well.

 If you're happy with my changes, then you can set a positive review.
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=14f80d3624d95079c896cb5efe8f29988834e1ac
 14f80d3]||{{{Reviewer changes and fixing coercions.}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/18762#comment:26>
Sage <http://www.sagemath.org>
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