[OS X TeX] A little help needed (math formula problem)
Claus Gerhardt
gerhardt at math.uni-heidelberg.de
Sat Dec 19 09:46:18 EST 2009
There is general rule when typesetting mathematics that variables are set in italics and operators, especially commonly known operators, are set in normal font with a few exceptions which are mainly dictated by aesthetics and sometimes by historical conventions.
Linear operators are usually denoted by $A, B, \ldots$ and typeset in italics, the trace operator however looks best when it is abbreviated by the upright symbol tr such that trace of A is
$\tr (A)$ where \tr is defined as
\DeclareMathOperator{\tr}{tr}
(I am using the conventions of the AMS in case of doubt. Since I always use the classes amsart resp amsbook, I cannot distinguish between generic Latex commands and those of AMS-Latex.)
The linear differential operator (partial derivative with respect to the real variable $x^k$ is usually denoted by $D_k$, i.e. both in italics and $D_ku$ looks fine to me. Similarly $Du$ for gradient of u is also alright, however, in $\grad u$ \grad should be defined by
\DeclareMathOperator{\grad}{grad}
The d in the symbol dx at the end of integral is not a linear operator, since dt is a symbol for an infinitesimal increment dt ~\varDelta t~ (t_2-t_1), and an upright d in this context is both illogical as well as silly looking. When there is no confusion I am usually omitting this increment in an integral such as in
$\int_\Omega f(x)$
Thus, when typesetting mathematics you should be guided by a few general rules, historical conventions, logic, and your own aesthetics, the latter, however, could be problematic in some cases.
Claus
On Dec 18, 2009, at 0:51, Ross Moore wrote:
> Hi Pete and Joe,
>
> On 18/12/2009, at 8:17 AM, Peter Dyballa wrote:
>
>> --
>> Greetings
>>
>> Pete
>>
>> There's something the technicians need to learn from the artists. If it isn't aesthetically pleasing, it's probably wrong.
>
>
> You couldn't have said it better.
> It especially applies to examples like on Joe's page,
> which people may refer to and copy.
> So let's get them right, both technically and aesthetically.
>
> A glaring example is: sphere_volume.tex
> where there are aesthetic errors (to my mind) on every line.
>
> line 1. the variable name Volume should be \mathrm{Volume} .
>
>
> line 2. the 'differential d' at the end of the integrals could be
> made upright (e.g. \,\phi\mathrm{d}\phi )
> The MathML rendering does it this way.
> BTW, it's good to see that preceding thinspace.
>
>
> line 3.
> A. the "evaluation-bars" after integration are far too large
> instead of \biggl| use \Bigr| .
> (the 'l' is technically wrong, as this is a closing fence
> around the integrated expression, and may result in too
> little space before it)
>
> B. \frac{\rho^3}{3} would look better as (\tfrac13 \rho^3)
> which also reduces the size needed for the evaluation-bar.
>
>
> line 4. Using just a space for implicit multiplication starts to
> look very cumbersome when if forces a need for lots of
> parentheses. Personally I'd write this line as:
>
> 2\pi \times 2 \times \tfrac13 R^3
>
> which is both shorter and clearer in the source,
> as well as producing a cleaner, more readable rendering
> which saves on vertical space as a bonus.
>
>
> line 5. the fraction 4/3 dominates the final result,
> yet it is the least meaningful term in that expression
> of a physical quantity.
> Use: \tfrac43 \pi R^3
>
> The attached image allows you to see the difference
> between your coding, and with these modifications.
>
> <texshop_image.jpeg>
>
> Note that expressions like \tfrac13 are equivalent to \tfrac{1}{3}
> which some LaTeX purists would say you should use.
> I disagree, since within your source \tfrac13 looks much more
> like a single simple entity --- especially when you put a space
> between quantities that are to be multiplied --- which it *is*
> logically. That is, it is the fraction one-third, rather than
> being primarily a representation of a division operation.
>
> To my mind, \tfrac{1}{3} is significantly less readable in the
> LaTeX source. Furthermore, a translation to MathML might well
> produce the single character at position U+2153 .
> (I'm not advocating this, as I actually prefer the text-style
> fraction form. Is there an OT font that has small text-style
> vertical fractions with bar, rather than using a slanted solidus?)
>
>
> The use of text-style fractions for d/dt in the "Differentiable
> Manifold (Tangent vector)" is another common (double) error.
> These should be using:
> \dfrac{\mathrm{d}}{\mathrm{d}t} .
>
> Of course that is rather cumbersome to write, so I usually define
> macros, as follows:
>
> \newcommand{\ddd}{\mathrm{d}}% differential d (upright)
> \newcommand{\dd}{\,\ddd}% differential closing an integral
> \newcommand{\Dd}[1]{\ddd#1}
> \newcommand{\ddx}{\Dd{x}}
> \newcommand{\ddt}{\Dd{t}}
> etc.
>
> Now derivatives look like:
> \dfrac{\ddx}{\ddt} or \dfrac{\Dd{}}{\ddt}
> and integrals like:
> \int_0^{\pi} \sin\theta \dd\theta
>
>
>
> These are primarily my opinions, but I know that many are
> shared. Also, now that software can do much more, (much faster
> than previously and the MathML standards/recommendations are
> being implemented) then there is going to be a need to have
> sets of examples that do everything in the best possible way.
>
>
> Hope this helps,
>
> Ross
>
> ------------------------------------------------------------------------
> Ross Moore ross at maths.mq.edu.au
> Mathematics Department office: E7A-419
> Macquarie University tel: +61 (0)2 9850 8955
> Sydney, Australia 2109 fax: +61 (0)2 9850 8114
> ------------------------------------------------------------------------
>
>
>
> ----------- Please Consult the Following Before Posting -----------
> TeX FAQ: http://www.tex.ac.uk/faq
> List Reminders and Etiquette: http://email.esm.psu.edu/mac-tex/
> List Archive: http://tug.org/pipermail/macostex-archives/
> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
> List Info: http://email.esm.psu.edu/mailman/listinfo/macosx-tex
>
More information about the MacOSX-TeX
mailing list