If we change the name and nature of the objects a little bit, one can
actually write down examples where Robert D's interpretation is not so
outlandish.
For instance:
sage: var("D, x");
sage: f=D^2+D+1;
sage: f(x^3)
x^6 + x^3 + 1
In an article about differential operators, one would probably mean
that D= d/dx or something like that and then one would expect
f(x^3)=6*x+3*x^2+x^3
admittedly, multiplication (composition) of differential operators is
not commutative, so the symbolic ring would get that wrong as well
(one has D*x=x+1)
Allowing for such exotic interpretations in the symbolic ring would
probably ruin many conveniences for calculus, which I guess is still
the main application, so I would think that properly documenting the
current behaviour is probably the better way to go forward.
I think it also provides an argument for the explicit "var"
declaration: If you declare "D" to be a variable, it's pretty clear
that you shouldn't expect operator semantics, whereas if you're
allowed to use "D" without declaring anything about it, you could make
an argument that Sage was a little bit presumptuous in assuming that
it's not an operator.
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