# Splitting a formula

What is the best way to split an overlong formula such as the following one to multiple lines:

\documentclass{scrartcl}
\usepackage{amsmath}

\begin{document}

\begin{eqnarray}
P2‘‘ &=&
\begin{pmatrix}
(1-\cos \alpha) \times x\times x + \cos \alpha (1-\cos \alpha) \times  x\times  y -\sin \alpha \times  z  (1-\cos \alpha) \times x\times z +\sin \alpha \times  y \\
(1-\cos \alpha) \times  x\times y + \sin \alpha \times  z (1-\cos \alpha) \times y\times y + \cos \alpha  (1-\cos \alpha) \times y\times z - \sin \alpha \times  x  \\
(1-\cos \alpha) \times  x\times z - \sin \alpha \times  y (1-\cos \alpha) \times y\times z + \sin \alpha \times  x  (1-\cos \alpha) \times z\times z + \cos \alpha
\end{pmatrix} \\
&\times &
\begin{pmatrix}
p2‘_X \\
p2‘_Y \\
p2‘_Z
\end{pmatrix}
\end{eqnarray}

\end{document}

-
I recommend using \cdot instead of \times. – azetina Dec 15 '12 at 16:32
Is it a cross product with everything else being vectors? Otherwise the expression is not a valid multiplication. And if it is so, can you split them up into individual steps? – percusse Dec 15 '12 at 16:44
The align environment is the preferred replacement for eqnarray. (Note when you switch that it requires fewer & symbols for alignment.) See tex.stackexchange.com/questions/196/eqnarray-vs-align – Ethan Bolker Dec 15 '12 at 16:49
get rid of the X for times, use . (or nothing) which will reduce the width of your formula by about 25-50% – Nicholas Hamilton Dec 15 '12 at 16:52

A variation of barbara's idea, but without the added complications. Just use \hfill in suitable places in order to shove left or right the entry. To one of them I add a fixed space, to give more room. Also some vertical spacings are used to separate each "cell" from the next.

\documentclass{scrartcl}
\usepackage{amsmath}

\begin{document}
$$P2 = \begin{pmatrix} (1-\cos\alpha) \cdot x\cdot x + \cos\alpha (1-\cos\alpha) \cdot x\cdot y \hfill \hspace{2.5pc} %%% space added to a wide half line, adjust visually \\ \hfill{}-\sin\alpha \cdot z (1-\cos\alpha) \cdot x\cdot z +\sin\alpha \cdot y \1ex] (1-\cos\alpha) \cdot x\cdot y + \sin\alpha \cdot z (1-\cos\alpha) \cdot y\cdot y \hfill\\ \hfill{}+ \cos\alpha (1-\cos\alpha) \cdot y\cdot z - \sin\alpha \cdot x \\[1ex] (1-\cos\alpha) \cdot x\cdot z - \sin\alpha \cdot y (1-\cos\alpha) \cdot y\cdot z \hfill\\ \hfill{}+ \sin\alpha \cdot x (1-\cos\alpha) \cdot z\cdot z + \cos\alpha \end{pmatrix} \cdot \begin{pmatrix} p2_X \\[1ex] p2_Y \\[1ex] p2_Z \end{pmatrix}$$ \end{document} - this is really much better than mine. i was trying too hard. – barbara beeton Dec 15 '12 at 18:33 I think this is one of those problems where some local redefinitions could be very useful. I've defined matrices A and p in the below, and used \cdot instead of \times (assuming that this doesn't change the meaning drastically- if it does, let me know) I've also used align instead of eqnarray as detailed in \eqnarray vs \align \documentclass{scrartcl} \usepackage{amsmath} \begin{document} We have the matrix equation \begin{align} P2'' &= A \cdot p \end{align} where \[ A=\begin{pmatrix} (1-\cos \alpha) \cdot x\cdot x + \cos \alpha (1-\cos \alpha) \cdot x\cdot y -\sin \alpha \cdot z (1-\cos \alpha) \cdot x\cdot z +\sin \alpha \cdot y \\ (1-\cos \alpha) \cdot x\cdot y + \sin \alpha \cdot z (1-\cos \alpha) \cdot y\cdot y + \cos \alpha (1-\cos \alpha) \cdot y\cdot z - \sin \alpha \cdot x \\ (1-\cos \alpha) \cdot x\cdot z - \sin \alpha \cdot y (1-\cos \alpha) \cdot y\cdot z + \sin \alpha \cdot x (1-\cos \alpha) \cdot z\cdot z + \cos \alpha \end{pmatrix}
and
$p=\begin{pmatrix} p2‘_X \\ p2‘_Y \\ p2‘_Z \end{pmatrix}$

\end{document}
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+1 Too complicated formulas are simply too complicated. As my fav teacher says: simplify, simplify, simplify. It is much easier to understand couple simple equations than one very complex one. – yo' Dec 16 '12 at 0:05

here's a different approach.

major changes:

• eqnarray is replaced by align;
• i've replaced \times by \cdot as suggested by azetina;
• the multiple lines of the first pmatrix have been packed into a minipage and within the box, multlined from mathtools has been used, with alternate "middle" lines shoved left or right as appropriate;
• math has to be specified explicitly within the minipage;
• multlined doesn't seem to want to use the entire specified width of the minipage so some extra space had to be added to the right-adjusted lines; pmatrix doesn't like just a single line (the minipage), so it was replaced with \left( ... \right); minipage width was adjusted by experiment, and a small \vspace added at the top for better appearance.

\documentclass{scrartcl}
\usepackage{mathtools}

\begin{document}
\begin{align}
P2 &=
\left(
{\begin{minipage}{.72\textwidth}
\vspace{2pt}
\abovedisplayskip=2pt \abovedisplayshortskip=2pt
$\begin{multlined} (1-\cos \alpha) \cdot x\cdot x + \cos \alpha (1-\cos \alpha)\\ \shoveright{\kern8em \cdot x\cdot y -\sin \alpha \cdot z (1-\cos \alpha) \cdot x\cdot z +\sin \alpha \cdot y } \\ \shoveleft{ (1-\cos \alpha) \cdot x\cdot y + \sin \alpha \cdot z (1-\cos \alpha) } \\ \shoveright{\kern8em \cdot y\cdot y + \cos \alpha (1-\cos \alpha) \cdot y\cdot z - \sin \alpha \cdot x } \\ \shoveleft{ (1-\cos \alpha) \cdot x\cdot z - \sin \alpha \cdot y (1-\cos \alpha) } \\ \kern8em \cdot y\cdot z + \sin \alpha \cdot x (1-\cos \alpha) \cdot z\cdot z + \cos \alpha \end{multlined}$
\end{minipage}}
\right) \\
\begin{pmatrix}
p2_X \\
p2_Y \\
p2_Z
\end{pmatrix}
\end{align}

\end{document}
-
If you switch the last two terms in each row of the wide matrix then the long term is on a line by itself (rather than split), which makes the algebra much more readable. – Ethan Bolker Dec 15 '12 at 20:31
@EthanBolker -- you're right. that's what egreg has done, and his answer is better in other ways too. – barbara beeton Dec 15 '12 at 20:34
1. \begin{small}\begin{eqnarray}...\end{eqnarray}\end{small}