Re: Operator precedence

Kaz Kylheku <643-408-1753@kylheku.com> writes:

Now in the C grammar, we have multiplication also occuping a
precedence rung between unary plus/minus and additive expressions.
>
Thus -A*B means (-A)*B, whereas X - A*B means X-(A*B).
>
In this case it doesn't matter because the unary minus is
a kind of product. -A can be regarded as a shorthand for (-1)*A.
>
More importantly the identity (-A)*B = -(A*B) holds.
>
This creates a problem if we naively wedge exponentiation into
the grammar, by sticking it into a precedence level above
multiplication, but below unary.
>
The identity does not hold in exponentiation: (-A)**B
is not -(A**B).

Very nice explanation, many thanks. I will likely pass it to a friend
(geodesist), who had a heated argument with the math teacher of her son
about whether

    2
  -3

is -9 or +9. I think the mathematical conventions are clear (and
probably established for centuries), but the teacher might be confused
and think Excel is the reference, see

  https://en.wikipedia.org/wiki/Order_of_operations#Unary_minus_sign

It would be interesting to learn about the motivation for spreadsheets
and "bc" to deviate from the mathematical convention.

Best regards

Axel