Piecewise-defined functions

Question

I'm trying to write these four piecewise-defined functions.

enter image description here

I wrote this code:

\begin{equation}
 \theta = \begin{cases}
  \theta r + Se \left( \theta s - \theta r \right)  & Hp < 0 \\
  \theta s                                                        & Hp \geq 0
  \end{cases} \\
\end{equation}

\begin{equation}
 Se =  \begin{cases}
  \frac{1}{[1 + |\alpha Hp|^n]^m}  & Hp < 0 \\
  1                                               & Hp \geq 0
  \end{cases} \\
\end{equation}

\begin{equation}
 C_m = \begin{cases}
  \frac{\alpha m}{1 - m} \left( \theta s - \theta r \right) Se^{\frac{1}{m}} [1 - Se^{\frac{1}{m}} ]^m & Hp < 0 \\
  0                                                                                                                                                & Hp \geq 0
  \end{cases} \\
\end{equation}

\begin{equation}
 K_r = \begin{cases}
  Se^ l [1-[1- Se^{\frac{1}{m}}]^m] ^2 & Hp < 0 \\
  1                                                       & Hp \geq 0
  \end{cases}\\
\end{equation}

And I got this result: enter image description here

How is it possible to separate these four piecewise-defined functions?

possible duplicate of How to write a function (piecewise) with bracket outside? — ChrisS, Feb 17 '15 at 08:50
Welcome to TeX.SE. Thanks for including most of the required code. But, while code snippets are useful in explanations, it is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. — Peter Grill, Feb 17 '15 at 14:57

score 8 · Answer 1 · answered Feb 17 '15 at 08:55

8

Only use one ampersand, &.

See page 68 in lshort: https://tobi.oetiker.ch/lshort/lshort.pdf

Example:

\begin{equation*}
    |x| = \begin{cases}
              -x & \text{if } x < 0,\\
               0 & \text{if } x = 0,\\
               x & \text{if } x > 0.
          \end{cases}
\end{equation*}

Produces:

enter image description here

answered Feb 17 '15 at 08:55

Tommy L

181

1

I tend to prefer cases* which gives you the second cell in text mode so this line would be -x & if $x < 0$,\\. BTW, what font is that? – Manuel Feb 17 '15 at 09:33
Yes, the starred version is useful. It's the Arev font: http://www.tug.dk/FontCatalogue/arev/ – Tommy L Feb 17 '15 at 10:31

score 4 · Answer 2 · edited Jun 10 '20 at 12:32

Besides the use of cases as per Tommy L's answer, you could also:

Use an align environment since you have multiple consecutive equations,
Use a \makebox to obtain an alignment of the conditions.

enter image description here

Notes:

It is only necessary to apply the \MakeBox macro on one of the cases.
I used the mathtools package as that incorporates some fixes on amsmath even though it doesn't make a difference in this particular case.

Code:

\documentclass{article}
\usepackage{mathtools}
\usepackage{calc}
\newcommand{\WidestExpression}{\frac{\alpha m}{1 - m} \left( \theta s - \theta r \right) Se^{\frac{1}{m}} [1 - Se^{\frac{1}{m}} ]^m}
\newcommand{\MakeBox}[1]{\makebox[\widthof{$\WidestExpression$}][l]{$#1$}}
\begin{document}
\begin{align}
 \theta &= \begin{cases}
  \theta r + Se \left( \theta s - \theta r \right)  & Hp < 0 \
   \MakeBox{\theta s}                               & Hp \geq 0
  \end{cases} \
 Se &=  \begin{cases}
  \frac{1}{[1 + |\alpha Hp|^n]^m}                   & Hp < 0 \
  \MakeBox{1}                                       & Hp \geq 0
  \end{cases} \
 C_m &= \begin{cases}
  \WidestExpression                                 & Hp < 0 \
  0                                                 & Hp \geq 0
  \end{cases} \
 K_r &= \begin{cases}
  Se^ l [1-[1- Se^{\frac{1}{m}}]^m] ^2              & Hp < 0 \
  \MakeBox{1}                                       & Hp \geq 0
  \end{cases}\
\end{align}
\end{document}

Piecewise-defined functions

2 Answers2

Notes:

Code: