id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,work_issues,upstream,reviewer,author,merged,dependencies,stopgaps
12914,Representation theory of finite semigroups,nthiery,sage-combinat,"Add support for representation theory of finite semigroups. Quite some
stuff is available in the sage-combinat queue.

* Required discussions about the current features:
 * What to merge now ; what to merge later
 * How to specify an indexing of the J-classes
 * Should JTrivial / ... be adjectives?
 * Should representation theory questions be asked to the semigroup or its algebra?
   * S.character_ring(QQ, ZZ) or S.algebra(QQ).character_ring(ZZ) ?
   * S.simple_modules(QQ) or S.algebra(QQ).simple_modules()?
 * Character rings
  * Should this be called Character ring?
  * How to specify the two base rings (for the representations / for the character ring)?
  * Should left and right characters live in the same space (with realizations)?
    e.g.:
    * Should there be coercions or conversions between the basis of left-class modules and right-class modules?
    * Should the basis of simple modules on the left and on the right be identified?
  * How to handle subspaces (like for projective modules when the Cartan matrix is not invertible)
 * If we discover that a semigroup is J-trivial, how to propagate this information to its algebra, character ring, ...?

* Features that remain to be implemented:
 * is_r_trivial + _test_r_trivial and friends
 * Group of a regular J-class
 * Character table for any monoid
 * Cartan matrix for any monoid
 * Group of a non regular J-class
 * Cartan matrix by J-classes
 * Radical filtration of a module
 * Recursive construction of a triangular basis of the radical

",task,new,major,sage-5.10,combinatorics,,,sage-combinat,,N/A,,,,"#11111,#12919",