#16508: Add Commutative graded differential algebras.
-------------------------------------+-------------------------------------
       Reporter:  mmarco             |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.4
      Component:  algebra            |   Resolution:
       Keywords:  sd58, sd59,        |    Merged in:
  algebras, nonconmutative, graded   |    Reviewers:  Travis Scrimshaw
        Authors:  Miguel Marco,      |  Work issues:
  John Palmieri                      |       Commit:
Report Upstream:  N/A                |  7b6f118fda2362a592f6d627c608674166ee5841
         Branch:                     |     Stopgaps:
  public/algebras/cdga-16508         |
   Dependencies:  #17224             |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Miguel Marco, John Palmieri', 'oldvalue': 
u'mmarco'}):

 * commit:  a4d5b24e4bd7b49d8fd838090b380f79704de5b5 =>
     7b6f118fda2362a592f6d627c608674166ee5841
 * dependencies:   => #17224
 * reviewer:   => Travis Scrimshaw
 * branch:  u/jhpalmieri/DGA_new => public/algebras/cdga-16508
 * author:  mmarco => Miguel Marco, John Palmieri


Comment:

 Okay here's my first big pass of review. I've reworked a bunch of things:

 - Differentials are linear, so they are in the category of modules
 morphisms.
 - Differentials now are endomorphisms of a `CGAlgebra`.
 - Implemented coercions between `GCAlgebra` and `CDGAlgebra`.
 - I put the `over {base_ring}` last for `CGAlgebra` to better follow the
 rest of Sage.

 There will be more changes and improvements coming, but I figured I should
 post what I have currently. In particular, I'm going to tweaks things
 around so that the differential specified for `CDGAlgebra` acts naturally
 on its elements rather than using the coercions. I'm also going to
 implement a method to create a differential morphism, in case someone has
 a use for that independently.

 Actually, that makes me ask this question. Should we put all of the chain
 complex implementations in the differentials? If so, should we have
 (decorator) class of `CDGAlgebra` call those functions (which would mainly
 be a shorthand) or remove that class all together?
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=cd59dbcc169779d10ac63963d8aa88845f22a7cf
 cd59dbc]||{{{Merge branch 'u/jhpalmieri/DGA_new' of trac.sagemath.org:sage
 into public/algebras/cdga-16508}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=619624ef1c07f2fc7035d0d602285fcb0429397e
 619624e]||{{{Merge branch 'u/jhpalmieri/DGA_new' of trac.sagemath.org:sage
 into public/algebras/cdga-16508}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=1b95a7e16d6daa9056971f5899a6c162323c8f23
 1b95a7e]||{{{First pass of reviewer changes: Various minor to moderate
 fixes.}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=7dd57c50f0b39d0fe078aedf8de6c45e21d26026
 7dd57c5]||{{{Some more minor tweaks.}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=13a552e4bc9fca71db81f6d2bd1a766f8d782e8f
 13a552e]||{{{Fix for pickling NC rings with weighted term order.}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=9aaf59119177639e9a0c8d063e0a8f1cf85241d8
 9aaf591]||{{{Merge branch 'public/pickling/term_order_NC_plural-17224'
 into public/algebras/cdga-16508}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=aae8f5b51bb4a26a5cc5a09e65c7206ffa543114
 aae8f5b]||{{{Merge branch 'u/jhpalmieri/DGA_new' of trac.sagemath.org:sage
 into public/algebras/cdga-16508}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=7b6f118fda2362a592f6d627c608674166ee5841
 7b6f118]||{{{Fixed doctests.}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/16508#comment:42>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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