Math & Science ⇒ Question regarding integrals and differential d's

[Sleort]

As a physicist I often use both the

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$\int f(x) \mathrm{d}x$
 
 
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and the

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$\int \mathrm{d}x f(x)$
 
 
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convention when writing integrals, i.e. I sometimes write the differential after the function I want to integrate, and sometimes in front of it (right after the integral symbol).

The code written above is of course not very pretty; I want some extra space between the function and the differential in order to separate what's what. In addition I would like to adjust the whitespace between the integral sign and what follows (the space is often too big in my opinion). In code I want something like

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$\int \! f(x) \, \mathrm{d}x \,$
 
 
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and

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$\int \!\mathrm{d}x \, f(x)$
 
 
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And, by the way, when there are more differentials I want there to be less space between them than if one of the differentials had been a function. I want something like

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\mathrm{d}x \mathrm{d}y
 
 
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not

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\mathrm{d}x \,\mathrm{d}y
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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So my question boils down to: Is there some way to make a macro/new symbol that follow these rules automatically, i.e. it is possible to make the differential's behavior neighbor symbol dependent? (I guess there is if you are into low level Tex programming, but unfortunately I'm not ) Alternatively: Do any of you know if there exists a package where this is implemented? (I haven't found any despite extensive searches)

Thanks!

[php1ic]

Hi Sleort,

This may not be exactly what you want, but can edit it.

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\documentclass[a4paper,11pt]{article}
\newcommand{\myint}[2]{$\int \; #1 \, \mathrm{d}#2\,$}
\begin{document}
\myint{f(x)}{x}
\end{document}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Run LaTeX here

There is a good explanation here
http://en.wikibooks.org/wiki/LaTeX/Customizing_LaTeX

[Sleort]

Hi Sleort,

This may not be exactly what you want, but can edit it.

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Code, edit and compile here:

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\documentclass[a4paper,11pt]{article}
\newcommand{\myint}[2]{$\int \; #1 \, \mathrm{d}#2\,$}
\begin{document}
\myint{f(x)}{x}
\end{document}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Run LaTeX here

There is a good explanation here
http://en.wikibooks.org/wiki/LaTeX/Customizing_LaTeX

Thanks for the reply! I am aware of that possibility, but no, that wasn't what I wanted. First of all this macro/newcommand does not open up for the other way (the "\int dx f(x)" way --where the differential is before the integrand) of writing the integrals. Then I could of course define another macro (e.g. "\myint2") where this is the case, like

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\newcommand{\myint2}[2]{\int \mathrm{d}#2 \, #1 \,}
 
 
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, but I don't think that is a very elegant (or smart) solution. And what if I would like to write a multidimensional integral? Or include explicit limits of integration? No, this simple \newcommand way of doing it isn't, unfortunately, good enough.

As I said: I think one has to focus on the differential d (the differential operator) and somehow make it dependent on the neighbor character. I don't know if it is possible, but the (pseudo)code should be something like:

if(character (excluding _{} and ^{}) to the right = integral) then (\! \mathrm{d}{#1} \,)
else if(character to the right = differential) then (\mathrm{d}{#1} \,)
else (\, \mathrm{d}{#1} \,)

Is this possible in Latex? (Or Tex...) If yes: how do I do it?

[Montag]

Hi Sleort,

This may not be exactly what you want, but can edit it.

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Code, edit and compile here:

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\documentclass[a4paper,11pt]{article}
\newcommand{\myint}[2]{$\int \; #1 \, \mathrm{d}#2\,$}
\begin{document}
\myint{f(x)}{x}
\end{document}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Run LaTeX here

There is a good explanation here
http://en.wikibooks.org/wiki/LaTeX/Customizing_LaTeX

Sorry for hijacking, but what exactly is the

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\,
 
 
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good for in

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\mathrm{d}#2\,$}
 
 
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of your new command definition? AFAIK, there is always a normal space after math mode ends, isn't there?

[pizzocaro]

Hi,
try to have a look at C. Beccari. TUGBoat 18 (1997) No. 1.

In this article, the author also addresses how to typeset differential d's. He came up with a quite complicated, definition (that, btw, I do not understand).
I report it here for convenience (hoping there will be no typos)

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\makeatletter
\providecommand*{\diff}%
    {\@ifnextchar^{\DIfF}{\DIfF^{}}}
\def\DIfF^#1{%
    \mathop{\mathrm{\mathstrut d}}%
        \nolimits^{#1}\gobblespace
}
\def\gobblespace{%
    \futurelet\diffarg\opspace}
\def\opspace{%
    \let\DiffSpace\!%
    \ifx\diffarg(%
        \let\DiffSpace\relax
    \else
        \ifx\diffarg\[%
            \let\DiffSpace\relax
        \else
            \ifx\diffarg\{%
                \let\DiffSpace\relax
            \fi\fi\fi\DiffSpace}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Run LaTeX here

It defines the d as an operator (I believe it require the amsmath package) so that spaces are handled correctly. Moreover it handles the right space with special care.

Use it as in

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\int f(x)\diff x
 
 
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Can this help?
Regards,
Marco

[Sleort]

Now we're talking! Thanks!

BUT: Although

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\iint f(x,y) \diff x \diff y
 
 
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looks (very) nice,

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\int \diff x \int \diff y f(x,y)
 
 
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doesn't. There is too much space between the integral signs and the differentials and there should be some space between the differential and the function,

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\diff y f(x,y)
 
 
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Maybe it is possible to extend Beccari's code with an extra if-then statement? Unfortunately I do not know how to do this, but maybe there are someone out there who does (and would like to help )?

[pizzocaro]

Regarding the space between the differentials and the function, it needs probably to be put at hand: how does LaTeX knows that the function is indeed the integral argument?

Regarding the space between the integral sign and the differential... I did not find any difference between \diff and \mathrm{d}...

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\[\int \diff x \diff y \, f(x,y) = \int \mathrm{d} x \mathrm{d} y f(x,y)\]
 
 
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and I do not think it looks bad.

Regards,
Marco

[Sleort]

Regarding the space between the differentials and the function, it needs probably to be put at hand: how does LaTeX knows that the function is indeed the integral argument?

You mean the space between the differentials and the function like in this case:

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\diff x f(x)
 
 
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? Well, that's easily solved. The "\diff" operator should just pick the first character following it as the integral variable (the "x" in this case), and then consider what is following (here "f(x)") as the integrand. If the variable should contain more characters one could just use some brackets, like

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\diff{cos(x)}f(x)
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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... Or wasn't that what you meant?

Regarding the space between the integral sign and the differential... I did not find any difference between \diff and \mathrm{d}...

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\[\int \diff x \diff y \, f(x,y) = \int \mathrm{d} x \mathrm{d} y f(x,y)\]
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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and I do not think it looks bad.

I don't see any difference either (strange) but I do think it looks bad ... The space is too wide. I'd like to think of

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\int \diff x
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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(as a whole) as an operator, and then there is too much space... It should rather be something like

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\int \! \diff x
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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...and this is what I would like to see be done automatically - but (of course) only when there is an integral sign in front of the differential.

Summarized:

• Need more space between "\diff x" and "f(x)"
  Need less space between "\int" and "\diff x"
  ... All this while the old/alternative "\int f(x) \diff x" functionality is preserved/unchanged.

It shouldn't be impossible...

[pizzocaro]

In my humble opinion, it is worth to define something like

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\newcommand{\idiff}{\int \! \diff}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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You have already argued that in this way you can not put limits to the integral. However, where there are limits you do not want the space changed, as in

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\[ \int_V \diff^3 r f(r) \]
 
 
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[Sleort]

You have already argued that in this way you can not put limits to the integral. However, where there are limits you do not want the space changed, as in

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\[ \int_V \diff^3 r f(r) \]
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Yes, but in this example there should be some space between \diff^3 r and f(r), like

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\[ \int_V \diff^3 r \, f(r) \]
 
 
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and then it starts getting complicated... Maybe I'm too demanding, but it would be really cool if everything could be included in just one symbol/command ("\diff") instead several (\idiff, \diff etc.). And I'm pretty shure it is possible if one uses some lover level Tex programming. (My problem is just that I don't know how... I cross my fingers that some of the forum members do! )