On Wednesday, August 17, 2016 at 3:25:31 PM UTC-7, Bill Page wrote:
>
>
> It turns out that a solution is now "hidden away" in plain sight: 
>
> https://trac.sagemath.org/ticket/18640 
>
> http://sagemanifolds.obspm.fr/doc/18640/reference/manifolds/sage/manifolds/utilities.html
>  
>
>
And also note the warning that's in the documentation there already: (*)
""" 
Note that D[1](g)(x, f(x,y)) is rendered as d(g)/d(f(x, y)). 
"""
How is that unambiguous?

Maple internally uses the same representation for derivatives as Pynac does 
(as far as I can tell) and it has a reasonable heuristic:

The expression:

D[i](f)(x1,...,xn)

can be rendered as (df/dxi)(x1,...,xn) if x1,...,xn are *distinct* pure 
variables or if n=1. Otherwise, render it D[i](f)(x1,...,xn). This is 
something that the standard expression renderer could do. It just requires 
a bit more work because "function application rendering" would need to 
inspect its function for the presence of an FDerivativeOperator.

The situation for topological manifolds is slightly different, because 
expressions there live in the context of a chart, where a specific 
correspondence between variable name and parameter position has been 
imposed. That makes it plausible that in the context of charts, one can get 
away with possible ambiguities a little easier. That said, I find it hard 
to not consider the example (*) an outright bug.

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