Hi Nicolas,

Here is the description of affine-E-nt.patch. Feel free to fold. If I
get to work more on this, I'll create a new patch.

 - Added UniqueRepresentation to the type E highest weight crystals
 - Factored out command abstract superclass for E6 and E7
 - Still failing tests in kirillov_reshetikhin.py
   - One that should be easy (rational number * weight lattice element)
   - One that sounds more tricky (failing assertion in
     highest_weight_dict in the construction of the KR_type_E6_order2
     crystal)

I folded the patches and fixed rational number doctest failure.
There are some problems with the experimental code, so I separated it out.

> By the way, I just realized that: isn't the cartan type information
> redundant? Shouldn't HighestWeightCrystal just take a weight as input?

Ok, in principle I agree.

From the programming point of view, how can this be done?
Currently there are only the optional inputs dominant_weight
or dominant_weights. For type E they are dealt with in
__classcall__ . Should this go into HighestWeightCrystal?
Otherwise, one cannot use
weight.parent().cartan_type()
to get the Cartan type and dispatch appropriately.

Applying the patch

crystal-energy-as.patch

there is an error running the tests, which I am not sure how to fix

sage -t  "4.3.1/devel/sage-combinat/sage/combinat/crystals/crystals.py"
**********************************************************************
File 
"/Applications/sage-4.3.1/devel/sage-combinat/sage/combinat/crystals/crystals.py",
 line 350:
    sage: f=T.crystal_morphism(g,acyclic = False)
Exception raised:
    Traceback (most recent call last):
      File "/Applications/sage/local/bin/ncadoctest.py", line 1231, in 
run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/Applications/sage/local/bin/sagedoctest.py", line 38, in 
run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, 
compileflags)
      File "/Applications/sage/local/bin/ncadoctest.py", line 1172, in 
run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_9[26]>", line 1, in <module>
        f=T.crystal_morphism(g,acyclic = False)###line 350:
    sage: f=T.crystal_morphism(g,acyclic = False)
      File 
"/Applications/sage/local/lib/python/site-packages/sage/combinat/crystals/crystals.py",
 line 437, in crystal_morphism
        return CachedFunction(morphism)
      File 
"/Applications/sage/local/lib/python/site-packages/sage/misc/cachefunc.py", 
line 59, in __init__
        self._argumentfixer = ArgumentFixer(f,classmethod=classmethod)
      File 
"/Applications/sage/local/lib/python/site-packages/sage/misc/function_mangling.py",
 line 109, in __init__
        defaults = f.func_defaults
    AttributeError: 'builtin_function_or_method' object has no attribute 
'func_defaults'

> Btw: most of the stuff in check(), is now handled in the generic tests
> of FiniteEnumeratedSets. So we could strip them out. For classical
> crystal we could keep a _test_fast_iter_ comparing the elements of
> list(self) and Crystal.list(self), since the algorithms are different,
> and we once had bug there.

Feel free to do that if you think it is worth it.

Cheers,

Anne

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