My comment about the documentation refers to:

monoids.py line 39

    with product rule given by $a \times b = a$ for all $a, b$::

free_monoid.py line 54

    OUTPUT: free abelian monoid

A further comment is that I am struggling to avoid deprecated classes.
If I type CombinatorialClass? I am told this is deprecated and I should use 
EnumeratedSets and variations.
Then I type EnumeratedSets? and find this is deprecated and I should use 
Sets

Is AlgebrasWithBasis deprecated and how do I tell? and I expected 
AlgebrasWithFiniteBasis as well.

I will have a look at Element as I have not understood the need for this. I 
am guessing it is a place to put the class variables
so that the class methods have a uniform interface.



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