#13074: Implementation of TableauTuples
--------------------------------------------+-------------------------------
Reporter: andrew.mathas | Owner: Andrew Mathas
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-pending
Component: combinatorics | Resolution:
Keywords: Tableaux, PartitionTuple | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Andrew Mathas | Merged in:
Dependencies: #13072 | Stopgaps:
--------------------------------------------+-------------------------------
Description changed by andrew.mathas:
Old description:
> Implements (standard) tableaux of shape a !PartitionTuple. That is,
> tableau with shape a tuple of partitions, together with standard
> functions for these objects. These objects arise naturally in algebraic
> combinatorics, such as in the representation theory of the cyclotomic
> Hecke algebras of type G(r,1,n) and (hence) in the categorification of
> the irreducible highest weight representations (and their canonical
> bases) of the (quantum) affine special linear groups.[[BR]][[BR]]This
> patch implements !TableauTuples and !StandardTableauTuples and basic
> methods for them. The idea is that these classes should naturally extend
> the corresponding Tableaux classes, which are in bijection with 1-tuples
> of tableaux. As with !PartitionTuples, the !TableauTuple classes return
> honest Tableaux whilst still recognising them as being !TableauTuples.
> Both Tableaux and !TableauTuples classes have a component() method which
> returns the list of components which allows loops such as
>
> {{{
> for s in t.components():
> do X
> }}}
> where t is a !TableauTuple (or Tableau). With this modification is it
> possible to write code which will behave the same for both classes.
> Whenever they were meaningful, I have implemented existing functions for
> tableaux for the tableau tuples. For example, there are iterators for
> !StandardTableauTuples, you conjugate !TableauTuples, take teir shape
> and size, compute words, act on them....[[BR]][[BR]]The patch implements
> the following classes:[[BR]] *
> !TableauTuples(!UniqueRepresentation, Parent):[[BR]] *
> !TableauTuples_all(!TableauTuples):[[BR]] *
> !TableauTuples_level(!TableauTuples):[[BR]] *
> !TableauTuples_size(!TableauTuples):[[BR]] *
> !TableauTuples_level_size(!TableauTuples):[[BR]] *
> !StandardTableauTuples(!TableauTuples):[[BR]] *
> !StandardTableauTuples_all(!StandardTableauTuples):[[BR]] *
> !StandardTableauTuples_level(!StandardTableauTuples):[[BR]] *
> !StandardTableauTuples_size(!StandardTableauTuples):[[BR]] *
> !StandardTableauTuples_level_size(!StandardTableauTuples):[[BR]] *
> !StandardTableauTuples_shape(!StandardTableauTuples):[[BR]][[BR]]Unfortunately,
> I haven't been able to up[load the patch to the patch server. When I
> tried something when wrong. Will keep trying...
New description:
Implements (standard) tableaux of shape a !PartitionTuple. That is,
tableau with shape a tuple of partitions, together with standard functions
for these objects. These objects arise naturally in algebraic
combinatorics, such as in the representation theory of the cyclotomic
Hecke algebras of type G(r,1,n) and (hence) in the categorification of the
irreducible highest weight representations (and their canonical bases) of
the (quantum) affine special linear groups.[[BR]][[BR]]This patch
implements !TableauTuples and !StandardTableauTuples and basic methods for
them. The idea is that these classes should naturally extend the
corresponding Tableaux classes, which are in bijection with 1-tuples of
tableaux. As with !PartitionTuples, the !TableauTuple classes return
honest Tableaux whilst still recognising them as being !TableauTuples.
Both Tableaux and !TableauTuples classes have a component() method which
returns the list of components which allows loops such as
{{{
for s in t.components():
do X
}}}
where t is a !TableauTuple (or Tableau). With this modification is it
possible to write code which will behave the same for both classes.
Whenever they were meaningful, I have implemented existing functions for
tableaux for the tableau tuples. For example, there are iterators for
!StandardTableauTuples, you conjugate !TableauTuples, take teir shape and
size, compute words, act on them....[[BR]][[BR]]The patch implements the
following classes:[[BR]] * !TableauTuples(!UniqueRepresentation,
Parent):[[BR]] * !TableauTuples_all(!TableauTuples):[[BR]] *
!TableauTuples_level(!TableauTuples):[[BR]] *
!TableauTuples_size(!TableauTuples):[[BR]] *
!TableauTuples_level_size(!TableauTuples):[[BR]] *
!StandardTableauTuples(!TableauTuples):[[BR]] *
!StandardTableauTuples_all(!StandardTableauTuples):[[BR]] *
!StandardTableauTuples_level(!StandardTableauTuples):[[BR]] *
!StandardTableauTuples_size(!StandardTableauTuples):[[BR]] *
!StandardTableauTuples_level_size(!StandardTableauTuples):[[BR]] *
!StandardTableauTuples_shape(!StandardTableauTuples):[[BR]]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13074#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
