[OS X TeX] A little help needed (math formula problem)

[Claus Gerhardt]

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
> ------------------------------------------------------------------------
> 
> 
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