extra symbols: int with sum or Sigma

• To: math-font-discuss@cogs.susx.ac.uk
• Subject: extra symbols: int with sum or Sigma
• From: vieth@convex.rz.uni-duesseldorf.de (Ulrik Vieth)
• Date: Wed, 18 Aug 93 12:17:59 +0200


I'm probably somewhat late in responding to this, but anyway.
In a message on Thu 05 Aug Justin wrote:

> Here is a list of new symbols that *could* be included in the new encoding.
> Any comments are welcome. If you happen to know that some of the symbols
> are very much need, please say so. If you know where th metafont code can
> be found please say so. If you know of some fonts that actually have them

[stuff deleted]

> \item A single integral with on top a $\Sigma$:
>   $\displaystyle\int\!\!\!\!\!\!\textstyle\Sigma$ (J\"org)
^^^^^^^^^^^^ = six \!

Well, I certainly need such a symbol, although I think that \int
overlaid with \sum would be the more logical choice, since that's
the meaning of it: a combination of sum over discrete and integral
over continuous eigenvalues or eigenfunctions in QM.

My private macro definition looks like this:

\def\dsumint{\displaystyle\mathop{\int\mkern-21mu\sum\limits}}
^^^^^^^^^^ = seven \!

but that's probably not the best solution. The d' before sumint
actually means that I haven't found a suitable result in textstyle
and it's only good for use in displaystyle. Alas, I got by without
needing textstyle except for one line, which was luckily a single
line after a display and before a sectioning command, so I could
simply use displaystyle in that case.

The problems I see with such a sumint' symbol are these:

1. in textstyle the \int symbol doesn't stick out enough from
the \sum symbol, so the combination doesn't look right.
Maybe that's the reason why J\"org proposed using \Sigma,
but that again would be somewhat inconsistent.
Of course, a sumint' in textstyle would also need different
kerning than in displaystyle, but that's no real problem.
It's also a matter of taste, where the symbols should intersect.

2. in displaystye a problem arises as where to put the limits.
Since \int is the bigger symbol it would determine the height
and the placement of limits. However, this looks irritating
when sumint' appears right next to sum with limits (which
acutually occurs frequently in pertubation theory). I wonder
if there is any compromise between \sum and \int concerning
the placement of limits.

In any case, I definitely see a need for such a symbol (at least
in QM papers). I'm not sure if the problems mentioned above can
be solved by a symbol of its own or if it's sufficient to have
a standardized control sequence to access some macro construction.
However, I definitely think there should be some standardized way
to access it in the new math encoding.

If anyone has a proper solution that produces pleasing results
both in textstyle and in displaystyle, please tell me.

Greetings,

Ulrik Vieth.

P.S. If anyone is interested in my background: I'm a physics student
who has not yet started on a thesis, but I'm probably going into
theoretical plasma physics. The amount of symbols needed in that
area is rather modest (execpt for bold and sans for vectors and
tensors). However, I currently have a job typing theoretical physics
lecture manuscripts into TeX which includes lots of quantum mechanics.
Apart from some rather unsual notations for operators in QM used
by my professor, I've come across several special symbols I had to
construct myself (see above and next mail). I wonder if any of that
is a standard requirement or just the author's personal style.