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**To**:*math-font-discuss@cogs.susx.ac.uk***Subject**:**some thoughts on \nabla, Laplace and Quabla****From**:*vieth@convex.rz.uni-duesseldorf.de (Ulrik Vieth)***Date**: Wed, 18 Aug 93 12:28:54 +0200

Here are some thoughts on \nabla and the Laplace and d'Alembert operators needed in theoretical physics. I don't know if there are plans to include specific glyphs for the Laplace and d'Alembert operators that are missing in the present cm fonts. If there are, you can probably ignore the rest, if not, please read on and do something about them ... * \nabla and the Laplace operator I recently had a private discussion with J\"org Knappen concerning the apperarence of \nabla and the Laplace and d'Alembert operators in theoretical physics. Although there are no specific recommendations in the IUPAP standard (IUPAP = Intl. Union of Pure and Appl. Phys.), we seemingly both agree that \nabla and the Laplace operator should be visually compatible. While there is a perfectly suitable \nabla symbol in the present cmsy, there is *no* specific symbol for the Laplace operator. It is usually refered to as \Delta (upright), but that's unfortunate if uppercase greek letters (when used as identifiers) are set in math italics instead of math roman. I therefore suggests that we have a separate glyph reserved for the Laplace operator, especially to avoid unwanted dependencies between identifiers and symbols. \Laplace would be an obvious name for it, but if anyone has a better idea, just say so. A seperate glyph for \Laplace would also allow a type designer to replace \nabla and \Laplace by triangles of uniform line thickness withouth interfering with greek letters if it is desired. * the d'Alembert (or Quabla) operator Another symbol often needed in relativistic wave equations is the d'Alembert operator, sometimes refered to as Quabla. It basically looks like a square box, but the \Box from the lasy font is a bit too small. A sepearate symbol for \quabla, that is adjusted in size to match \nabla and \Laplace, would definitely be desirable. (In fact, I recall that there was a specific request to include the d'Alembert operator at the math font BOF with Norbert Schwarz that was held at the DANTE meeting 1992 in Hamburg. I don't know how much of the outcome has reached this working group as input.) In any case, I regard \nabla, \Laplace and \quabla as a group of symbols that should be dealt with together. They should match in size (btw: Is \Laplace = \Delta actually an upside-down \nabla or are there any differences?) and maybe also in stroke thickness (\Box has rather thin lines compared to the others), but that's a question of design and not of encoding. A need for these symbols is definitely there, as everyone in theoretical physics would probably agree. They are perhaps much more important than some of the other symbols under consideration. In case you have already decided to include \Laplace and \quabla please excuse my lenghty argument, but I didn't know what the current situation is. Please enlighten me! Greetings, Ulrik Vieth. P.S: A note on usage: I observed that American books or papers often use $\nabla^2$ where European papers usually use $\Delta$. I don't know if there's any deeper reason behind it, but I guess that this is probably the reason why there is only a \nabla in the cm fonts. For the same reasons (American typesetting conventions) uppercase greek letters are taken from math roman instead of math italics, which is also different from traditional European typography. We should try to allow more flexibility for national math typesetting conventions this time, shouldn't we?

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