How to parse f(x) as a Function?

[Paul Royik]

I want to parse something like `f(x) - 2 sin 3x`.

If I use `parse_expr` without `implicit_multiplication_application`, then `f(x)` is parsed correctly, but not `2 sin 3x`.

If I include `implicit_multiplication_application`, then `f(x)` is parsed as `fx`.

Is this a bug?

[Paul Royik]

I've found the following piece of code in _implicit_multiplication

elif (isinstance(tok, AppliedFunction) and
nextTok[0] == OP and nextTok[1] == '('):
# Applied function followed by an open parenthesis
if tok.function[1] == "Function":
result[-1].function = (result[-1].function[0], 'Symbol')
result.append((OP, '*'))

Is there any reason to substitute a Function with a Symbol?

[Aaron Meurer]

I'm not sure what that line of code is doing. You'd have to trace
through to see exactly what sequence of tokens can lead to it being
run.

However, I will say in general that it would make sense to me to split
out implicit multiplication via a space and implicit multiplication
via parentheses. It's only the latter that is ambiguous with function
application. Unfortunately, this is a general ambiguity that is
inherent in mathematical notation. Does x(y + z) mean x is a function
of y + z or does it mean xy + xz? There's no way to know from the
notation alone.

Aaron Meurer

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[Paul Royik]

You're correct. But symbols of the length one like f(x) are certaily function calls.