#939 subscripted additive functions should be additive on ( ) arguments, not [ ]

[Barton Willis]

(%i1) declare(f,additive)$

(%i2) f[a+b](x);
Improper name or value in functional position:
f[b]+f[a]

Yeechs! The function 'f' is additive in its
subscript:

(%i3) f[a+b];
(%o3) f[b]+f[a]

Surely, a subscripted additive function shouldn't be
additive in its subscript.

Barton

[Robert Dodier]

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I agree that subscripted functions should not be additive in
their subscripts, but in Maxima the same notation is used
for subscripted functions as for memoizing functions, and
there's no reason to rule out additive memoizing functions.
(Or is there?)

I suppose F[a + b](x + y) must be a subscripted function
call, but F[a + b] could be either a memoizing function
call, or a subscripted function. Even in the case of F[a +
b](x + y) could be the return value of a memoizing function
applied to x + y.

[Robert Dodier]

Thinking about this one again. At this point I am leaning towards saying that declare(f, something) make f[whatever] inherit the something property. Assuming that, that means f[a + b](x) should be f[a + b](x), and f[a + b](x + y) should be f[a + b](x) + f[a + b](y), i.e., I've come around to agreeing with Barton's original comment above.