**From:** Hans Aberg (*haberg-1@telia.com*)

**Date:** Mon Apr 18 2011 - 08:27:15 CDT

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Since one can add parenthesizes for emphasis, a purely semantic parsing method is probably not good. One would end up classifying mathematical constructs, and ways enabling/disabling them, as one may not want to always use them.

In addition to superscript and subscript characters, one would need grouping characters, which in TeX are '{' ... '}'. They do not display, but only show the logical grouping.

So then f^(i + j) with displayed parenthesizes would have to be written f^{(i + j)}, but it proves full control of what to put into the superscript.

If these grouping characters were integrated into the display of the text editor, one would see the superscript. So it would not be as illogical as when writing it inline.

Hans

On 18 Apr 2011, at 01:29, Philippe Verdy wrote:

*> 2011/4/15 Hans Aberg <haberg-1@telia.com>:
*

*>> 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.
*

*>>
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*> Actually when *extra* parentheses are used in a superscript (i.e.
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*> parentheses that are not needed to correctly evaluate the value of the
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*> inner expression which is already self-contained by the superscript),
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*> this gives a different semantic to those parentheses, which are not
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*> used for their function of grouping, but to change the semantic into a
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*> n-th derivative.
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*>
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*> If you transcribe such expression into plain-text only, without
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*> support for superscripts/exponent, you usually use the "^" symbol, but
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*> then nothing can help make the distinction between grouping
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*> parentheses and nth-derivative, because the inner expression is no
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*> longer self-contained. The only way to preserve this, is to use extra
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*> parentheses (exactly like for the case when superscripts are
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*> available). So you should write: f^((n)).
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*>
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*> If you write f^(n) only, it's not clear if this is the n-th exponent
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*> or the n-th derivative of function f. This may be implicit in some
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*> contexts, but specifying such formula without expliciting this context
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*> will cause problems. Notably when both interpretations are used in the
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*> same text (n-th derivatives and n-th exponentiations are heavily used
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*> concurrently, for example when working with limited developments, or
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*> with convergence of series, in probabilities...)
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*>
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*> I've seen also f^('n), where the prime is denoted by some single quote
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*> or apostrophe at the beginning of the inner expression. This preserves
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*> the parentheses for their usual grouping-only meaning. If the inner
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*> expression is simple enough (such as a single number or variable name,
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*> you can even remove these parentheses and write f^'n directly. This
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*> also preserves the distinction with f'^n (which denotes the n-th
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*> exponent of the first derivative of function f, because the prime
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*> operator is left-associative only).
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*>
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*> I've also seen the even shorter notation f('n), without any ^ symbol
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*> which then remains reserved to exponentiation only. (I will leave out
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*> of this discussion the choice of the "correct" character to use for
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*> the prime symbol, but it you cannot use true superscripts, then you're
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*> also likely to use basic text encoding. Other notations like f^[n] or
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*> f^{n} may be found (sometimes without the ^ symbol as well), provided
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*> that square brackets and braces are not used as alternative grouping
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*> parentheses to help reading complex formulas with multiple nesting
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*> levels, or to denote vectors/matrices, or value ranges and sets, or to
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*> denote indices/subscripts for terms of series.
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*>
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*> Philippe.
*

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