Indeed, it looks like it was implemented in 
https://trac.sagemath.org/ticket/24129 which was merged in Sage 8.3.beta0.


On Thursday, August 9, 2018 at 3:02:42 PM UTC-7, John H Palmieri wrote:
>
> This works for me in Sage 8.3 but not in Sage 8.2. It must have been 
> implemented relatively recently. What version of Sage are you using? (It 
> looks like it's on Mac OS X; is that right?)
>
>
> On Thursday, August 9, 2018 at 2:43:35 PM UTC-7, Gabriel Frieden wrote:
>>
>> The following three methods in the Permutation class don't seem to work:
>> foata_bijection_inverse()
>> fundamental_transformation()
>> fundamental_transformation_inverse()
>>
>> Here is an example:
>>
>> sage: S = Permutations(3)
>> sage: S[0].foata_bijection()
>> [1, 2, 3]
>> sage: S[0].foata_bijection_inverse()
>>
>> ---------------------------------------------------------------------------
>> AttributeError                            Traceback (most recent call 
>> last)
>> <ipython-input-31-c8ef4d7624be> in <module>()
>> ----> 1 S[Integer(0)].foata_bijection_inverse()
>>
>> /Applications/SageMath/src/sage/structure/element.pyx in 
>> sage.structure.element.Element.__getattr__ 
>> (/Applications/SageMath/src/build/cythonized/sage/structure/element.c:4649)()
>>     411             dummy_error_message.name = name
>>     412             raise dummy_attribute_error
>> --> 413         return getattr_from_other_class(self, 
>> P._abstract_element_class, name)
>>     414 
>>     415     def __dir__(self):
>>
>> /Applications/SageMath/src/sage/structure/misc.pyx in 
>> sage.structure.misc.getattr_from_other_class 
>> (/Applications/SageMath/src/build/cythonized/sage/structure/misc.c:1763)()
>>     251         dummy_error_message.cls = type(self)
>>     252         dummy_error_message.name = name
>> --> 253         raise dummy_attribute_error
>>     254     try:
>>     255         attribute = getattr(cls, name)
>>
>> AttributeError: 'StandardPermutations_n_with_category.element_class' 
>> object has no attribute 'foata_bijection_inverse'
>>
>>

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