On Apr 1, 11:06 am, Nils Bruin <nbr...@sfu.ca> wrote:
> On Apr 1, 4:56 am, Harald Schilly <harald.schi...@gmail.com> wrote:
>
> > > sage: D[0](f)(x, y)/x + D[0, 1](f)(x, y)
>
> > For me, this just looks quite awkward.
>
> OK, some reasons *for* the notation then.
>
> 1) It's how sage prints the expression. It's very desirable to ensure
> that output is also valid input.
>

Yes.

I agree completely about the usefulness of arithmetic on differential
operators.  Another necessary feature is some way to extract
coefficients of the various D operators.  For example the following
breaks with 'diff' or 'D' queries:

sage: a=f.diff(x,2)*x*x
sage: a
x^2*D[0, 0](f)(x)
sage: a.coeffs(x)
[[D[0, 0](f)(x), 2]]
sage: a.coeffs(diff(f,x))
/home/jlh/wrk/sage-5.0.beta11/local/lib/python2.7/site-packages/
IPython/iplib.py:2260: DeprecationWarning: Substitution using function-
call syntax and unnamed arguments is deprecated and will be removed
from a future release of Sage; you can use named arguments instead,
like EXPR(x=..., y=...)
  exec code_obj in self.user_global_ns, self.user_ns
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call
last)
...
ValueError: The name "D[0](f)(x)" is not a valid Python identifier.
sage:

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