[texhax] problems with circumflex

[Uwe Lück]

At 09:14 28.02.09, Benjamin Sambale wrote:
>I wonder about the difference between $^x \operatorname{N}$ and
>$\operatorname{N}^x$. Here, I use \operatorname only to write it
>upright. Apart from that it doesn't play a role. The problem is that the
>space between ^x and N is larger than the space between N and ^x.
>Another problem is that ^x in front of N lies lower than ^x after N. I
>want that both ^x look exactly the same. If I use
>$^x{\operatorname{N}}$, then the space reduces a bit, but it is still to
>large. The space in $^x\!\operatorname{N}$ looks also better, but I
>think this is not the best solution.

At 14:56 28.02.09, Benjamin Sambale wrote:
>The problem is not to write it upright. But you're right,
>$\operatorname{N}^x$ and $\mathrm{N}^x$ are different. In fact I want to
>use N as an mathematical operator. But even if you use $^xN$ and $N^x$,
>the spaces between ^x and N are different.

The TeXbook explains horizontal spacing in math formulas on, say, pp. 
154ff., 158f., 168ff. ...

[I think to have learnt:]

The circumflex attaches a superscript to something *previous*.

"left superscript" (as in non-standard analysis or ...!?) is not supported 
by TeX (from scratch, tried tricks, don't remember). "Symmetry" between 
left and right superscripts is not intended and occurs "by chance" if it does.

`^x \operatorname ...' yields a space because there is a space between an 
operator and something previous (to which the superscript is attributed).

With \mathrm{N}, there is the symmetry! ("by chance")

With $^xN$ and $N^x$ there is some symmetry again, but the "left 
superscript" is somewhat unable to account for the italics shift of the 
`N', while a "right superscript" does account for the italcs shift. There 
is no space between the "left supercript" and the *box* enclosing `N'. 
There is only some (apparent) space between the "left superscript" and the 
upper part of the `N'.

Before working at "superscript symmetry", one might reason whether it 
really is needed and worth it.

-- Uwe.