From: Hans Aberg (haberg-1@telia.com)
Date: Fri Apr 15 2011 - 15:29:23 CDT
On 15 Apr 2011, at 21:46, John W Kennedy wrote:
>>> For example, a/b might be written like that, but it might be written (still inline) with 'a' over 'b' and a horizontal stroke between. In addition, there is "a over b" which does not have such a stroke (but normally parenthesizes). So one might have a character telling that two parts should be grouped over each other.
>>
>> Just FYI, that distinction is presentational, not semantic, where fractions are concerned.
>
> Actually, it's semantic:
>
> a+b
> ---
> c+d
>
> is not equal to:
>
> a+b/c+d
This last one should be written (a+b)/(c+d). When using a two-dimensional layout, one reduces on the number of parenthesizes needed, which is an advantage, making it more readable. When parsing a formula in computer language, one typically constructs an AST (abstract syntax or semantic tree), and from that, it is not difficult to figure to render it with a minimal number of parenthesizes. Parenthesizes can be semantic, for example f^(k) (f superscripted with (k)) might denote the n-th derivative, while f^k the n-th composite or power of f.
If one does not want automatically the minimal number of parenthesizes, then one needs some other way to indicate groupings.
Hans
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