This example is dumb because it does not give any real benefit but it will
do. On the command line you could run something like

sage: B = matrix()
sage: B.T.roo<Tab>

and get

sage: B.T.rook_vector

but 

sage: sage: B.transpose().roo<tab>

will complete to useless stuff.

Now as I said this does not make a lot of sense with matrices. On the other
hand suppose you have a mathematical structure A endowed with building blocks
S and a pointer to the current block. Suppose also that each building block
has some method defined. Then properties allow to autocomplete things like

sage: A.current_S.some_method()

The same example does not work if A.current_S is a method itself and not a 
property.

By this I do not imply that properties should be preserved in sage. I am only
answering your question on which benefit is there in omitting the
parenthesis.

Best
S.



* Johan S. R. Nielsen <santaph...@gmail.com> [2016-04-27 13:46:08]:

> > One advantage of properties over methods is that they autocomplete
> 
> I don't understand? Tab-completion covers both methods and properties in
> all IDEs I'm aware of.
> 
> Best,
> Johan
> 
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