[Tex/LaTex] Piecewise-defined functions

casesequationsmath-mode

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?

Best Answer

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

Related Solutions

[Tex/LaTex] Clean-Looking Piecewise-Defined Functions

A simpler solution for aligning fractions is to let TeX decide what space to add:

\[
 f(n) =
  \begin{cases} 
      \hfill \frac{n}{2}    \hfill & \text{ if $n$ is even} \\
      \hfill -\frac{n-1}{2} \hfill & \text{ if $n$ is odd} \\
  \end{cases}
\]

As explained in the comments, \hfill takes up as much space as possible, so putting one on both sides will have the effect of centering the text. If you do this in both lines, you don't have to figure out which one is longer. This is more resistant to changes in your code than using \phantom. I have also gone ahead and changed \textrm to \text, since this what \text is intended for.

[Tex/LaTex] Typesetting a pattern matching equation

Without an image of exactly how you want this typeset it is difficult to know for sure, but perhaps one of these is what you are looking for:

enter image description here

or perhaps:

enter image description here

\documentclass{book}
\usepackage{amsmath}
\newcommand{\fib}{\mathrm{fib}}

\begin{document}
\begin{align*}
    &\text{if }  x < 2 & \fib X &= 1 \\
    &\text{otherwise } & \fib X &= (\fib (X - 1)) + (\fib (X - 2))
\end{align*}
Another option is:
\begin{align*}
\fib X = \begin{cases}
    \text{if }  x < 2 & = 1 \\
    \text{otherwise } & = (\fib (X - 1)) + (\fib (X - 2))
\end{cases}
\end{align*}
\end{document}

Here is how you can modify the given MWE to obtain better spacing:

enter image description here

Notes:

@{} is used to eliminate the inter column spacing
I added {} before the = to get proper math spacing.
I replaced the $$ ... $$ with \[ ... \]. See Why is \[ ... \] preferable to $$ ... $$? for more details.
Changes as per egreg's suggestions:
1. \mathit{foreign}, \mathit{time\_of\_call} and \mathrm{head} for better appearance of the formulas.
2. Removed \, after \prodtime, and the other uses of \operatorname.

Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\prodtime}{\operatorname{prodtime}}

\begin{document}
\[
\begin{array}{l l @{}l}
\prodtime V & X = Y                        &{}= 0 \\
\prodtime V & X = f(\ldots)                &{}= 0 \\
\prodtime V & p(X_1,\,\ldots,\,X_n)        &{}= \prodtime V\,(\operatorname{body} p) \\
\prodtime V & V = \,f(X_1,\,\ldots,\,X_n)  &{}= \prodtime V\,(\operatorname{body} f) \\
\prodtime V & X_0(X_1,\,\ldots,\,X_n)      &{}= \mathit{time\_of\_call} \\
\prodtime V & m(X_1,\,\ldots,\,X_n)        &{}= \mathit{time\_of\_call} \\
\prodtime V & \mathit{foreign}(\ldots)     &{}= 0 \\
\prodtime V & G_\mathrm{head},\,G_\mathrm{tail}
\end{array}
\]
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Clean-Looking Piecewise-Defined Functions

[Tex/LaTex] Typesetting a pattern matching equation

Notes:

Code:

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