General ⇒ Displaying/formatting very long formulae

[alphanumeric]

I have some very long formulae from MATLAB I have exported into Latex to view properly. Because they are so long they just run straight off the page. I have tried to line break it where appropriate using \\ and then && on the start of the next line to align it properly but I get several errors and it's a very ineffiecient process. What would be the best way to format very long formulae to display properly in Latex?

This code will work for the first 2 terms, but gives around 18 errors. Mostly about unclosed brackets (I think).

Code: Select all

\documentclass[a4paper,10pt]{article}
\usepackage[landscape]{geometry}
\begin{document}
\begin{eqnarray}
&&\left(  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}\\
&&-\sin \left( t \left( r \right)  \right)  \left( {\frac {d^{2}}{d{r}^{2}}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}\\
&&-1/2\,{\frac {\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right)  \left( -2\, \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) -2\, \left( {\frac {d}{dr}}v \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) }{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}}}+\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right) -\cos \left( t \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}+{\frac { \left( -\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}-\cos \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) }{ \left( 1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2} \right) ^{3/2}}} \right)  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}+\sin \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}
\end{eqnarray}
\end{document}

As I increase the number of line breaks after each term Latex eventually records over 100 errors and will not create a pdf at all. Any help would be greatly appreciated.

[localghost]

In another topic there are given the reasons why not to use the eqnarray environment [1]. Moreover there are shown some alternatives how to get along with such big equations that occupy more than one line.

[1] View topic - Issue with page margins


Best regards and welcome to the board
Thorsten¹

[alphanumeric]

Thanks, I actually already read the link you posted. While that paper explained why not to use eqnarray, it didn't have much to say about formatting long formulae. Tried using amsmath and multline, but that actually gave me more errors than using eqnarray.

[phi]

The problem is that you cannot insert line breaks in formulae without closing all open \left...\right groups first. When you delete the line breaks, the errors vanish. With the breqn package, it works better, while not perfect:

Code: Select all

\documentclass[a4paper,10pt]{article}
\usepackage[landscape]{geometry}
\usepackage{breqn}
\begin{document}
\begin{dmath}
\left(  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}} -\sin \left( t \left( r \right)  \right)  \left( {\frac {d^{2}}{d{r}^{2}}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}} -1/2\,{\frac {\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right)  \left( -2\, \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) -2\, \left( {\frac {d}{dr}}v \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) }{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}}}+\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right) -\cos \left( t \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}+{\frac { \left( -\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}-\cos \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) }{ \left( 1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2} \right) ^{3/2}}} \right)  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}+\sin \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}
\end{dmath}
\end{document}

To avoid problems like this, you should try to simplify your formula by introducing intermediate variables and functions and by making some constructions shorter. For example, if w is a function of one variable, \left( {\frac {d}{dr}}w \left( r \right) \right) can be replaced by the much shorter w'(r). Using some simple text replacements, I could reduce your formula to the following, which is still too long, but already much easier:

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\documentclass[a4paper,10pt]{article}

\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{breqn}


\begin{document}

\begin{align*}
  a(r) &\coloneqq \sqrt {1- (w'(r)) ^{2}- (v'(r)) ^{2}} \\
  b(r) &\coloneqq \frac {1}{\sqrt {1- (w'(r)) ^{2}}}
\end{align*}

\begin{dmath}
\left(  \left( -\cos(t(r)) (t'(r))  (w'(r)) a(r) -\sin(t(r))  \left( w''(r)  \right) a(r) -1/2\,{\frac {\sin(t(r))  (w'(r))  \left( -2\, (w'(r)) w''(r) -2\, (v'(r)) v''(r)  \right) }{a(r)}}+\sin(t(r)) (t'(r)) v'(r)-\cos(t(r)) v''(r)  \right) b(r)+{\frac { \left( -\sin(t(r))  (w'(r)) a(r)-\cos(t(r)) v'(r) \right)  (w'(r)) w''(r) }{ b(r)^{-3}}} \right)  \left( -\cos(t(r))  (w'(r)) a(r)+\sin(t(r)) v'(r) \right) b(r)
\end{dmath}

\end{document}

[Juanjo]

Edited: I haven't read the second part of phi's post when sending mine. I subscribe the approach he proposes.

Which is really your goal? Just visualize the formulas on the screen? Include them in a document? In the first case, use the geometry package to set up a custom paper size big enough to contain the formula. For example:

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\documentclass[10pt]{article}
\usepackage[paperwidth=100cm,paperheight=5cm]{geometry}
\begin{document}
\begin{displaymath}
\left(  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}
-\sin \left( t \left( r \right)  \right)  \left( {\frac {d^{2}}{d{r}^{2}}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}
-1/2\,{\frac {\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right)  \left( -2\, \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) -2\, \left( {\frac {d}{dr}}v \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) }{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}}}+\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right) -\cos \left( t \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}+{\frac { \left( -\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}-\cos \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) }{ \left( 1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2} \right) ^{3/2}}} \right)  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}+\sin \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}
\end{displaymath}
\end{document}

or, as suggested by phi, using breqn

Code: Select all

\documentclass[10pt]{article}
\usepackage[paperwidth=35cm,paperheight=20cm]{geometry}
\usepackage{breqn}
\begin{document}
\begin{dmath*}
\left(  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}
-\sin \left( t \left( r \right)  \right)  \left( {\frac {d^{2}}{d{r}^{2}}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}
-1/2\,{\frac {\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right)  \left( -2\, \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) -2\, \left( {\frac {d}{dr}}v \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) }{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}}}+\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right) -\cos \left( t \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}+{\frac { \left( -\sin \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}-\cos \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) {\frac {d^{2}}{d{r}^{2}}}w \left( r \right) }{ \left( 1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2} \right) ^{3/2}}} \right)  \left( -\cos \left( t \left( r \right)  \right)  \left( {\frac {d}{dr}}w \left( r \right)  \right) \sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}- \left( {\frac {d}{dr}}v \left( r \right)  \right) ^{2}}+\sin \left( t \left( r \right)  \right) {\frac {d}{dr}}v \left( r \right)  \right) {\frac {1}{\sqrt {1- \left( {\frac {d}{dr}}w \left( r \right)  \right) ^{2}}}}
\end{dmath*}
\end{document}

If you want to include the formula in a document, things are different. Then you should use an amsmath environment. Of course, from a mathematical point of view, you should introduce simplifications and auxiliary notations to transform the formula into a more readable expression.

[alphanumeric]

@phi
I think I used \right. to close some of them, but was still getting other errors when using multline that are probably due to my lack of knowledge using Latex in general. I will try and experiment using breqn.

@Juanjo & phi
I'm trying to verify my hand calculations by using MATLAB, but even using pretty() MATLAB is awkward to read at best. So I just wanted to import into Latex to view the formulae, without having to preform many manipulations.

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\usepackage[paperwidth=100cm,paperheight=5cm]{geometry}

Worked perfectly for what I needed. (When I tried changing paper size from A4 to A1 it didn't work.)

When it comes time to do a proper write up I will definitely look at simplification as you have both suggested. Thank you very much for your input.