[Tex/LaTex] Error with cases enviroment: missing $ inserted

Question

Hey there I have a problem with the cases enviroment inside an equation i'm getting the error missing $ inserted but i don't know why.
I already searched and found that there are now blank lines inside a equation allowed but i'm not sure where they should be in my case.
Here is my code.

\documentclass[11pt,a4paper,oneside]{amsbook}
%Sprache
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
%Zeichensatz
\usepackage[utf8]{inputenc}
%PDF Integrierung
\usepackage{pdflscape}
\usepackage{rotating}
\usepackage{pdfpages}
\renewcommand{\familydefault}{\sfdefault}
%Formatierung
\usepackage[left=2.5cm,right=2.5cm,top=2cm,bottom=2cm]{geometry}
\usepackage[onehalfspacing]{setspace}
%Schriftart
\usepackage{helvet}
%Mathepackages
\usepackage{amsfonts,amstext,amsmath,amssymb,mathrsfs}
%Algorithmen
\usepackage{algorithm,algorithmic,program}
%diverses
\usepackage{enumerate}
%Theoreme und Gleichungen
\numberwithin{equation}{section}
\newtheorem{prop}{Satz}
\newtheorem{lemma}{Lemma}
\floatname{algorithm}{Algorithmus}
%Titelseite festlegen
\author{name\\
}
\title{Bachelorarbeit}
%Beginn der Seminarbeit
\begin{document}
\newtheorem{lemma}{Lemma}
\begin{lemma}
Die Supremumsnorm den k-ten Potenz von M ist gegeben durch
\begin{equation*}
\|M^k\| = \begin{cases}
\binom{N-1}{k} &  | \beta | = 1,\\
\frac{1}{(k-1)!} \frac{d^{k-1}}{dz^{k-1}} \frac{z^{N-1}-1}{z-1} z =|\beta| & 7 | \beta | \neq 1
\end{cases}
\end{equation*}
\end{lemma}
\end{document}

I would be very glad if you could help me, i have another equation where it works just fine.
Naro

Answer 1

The program package defines | as an active character for its usage in the program environment and this causes the problem you have. However, the package provides an adjustment in case you want to use | in math mode.

\documentclass[11pt,a4paper,oneside]{amsbook}

\usepackage{program}

\normalbaroutside % <----- ADDED

\begin{document}

\begin{equation*}
\|M^k\| = \begin{cases}
\binom{N-1}{k} &  | \beta | = 1,\\
\frac{1}{(k-1)!} \frac{d^{k-1}}{dz^{k-1}} \frac{z^{N-1}-1}{z-1} z =|\beta| & | \beta | \neq 1
\end{cases}
\end{equation*}

\end{document}

However, it would be much better with

\lVert M^k\rVert

and

\lvert\beta\rvert

avoiding the unadorned | that is overloaded.

---

A good alternative to using \lVert–\rVert and \lvert–\rvert is with mathtools that also provides a dcases environment. Here's an example with both input and output. Note that in your text you don't have k and M in math mode, which is wrong.

\documentclass[11pt,a4paper,oneside]{amsbook}
\usepackage{mathtools}
\usepackage{program}

\normalbaroutside % it should be standard

\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\begin{document}

Die Supremumsnorm den $k$-ten Potenz von $M$ ist gegeben durch
\begin{equation*}
\norm{M^k} = \begin{dcases}
\binom{N-1}{k} &  \abs{\beta} = 1,\\
\frac{1}{(k-1)!} \frac{d^{k-1}}{dz^{k-1}} \frac{z^{N-1}-1}{z-1} z =\abs{\beta} &
   \abs{\beta} \neq 1
\end{dcases}
\end{equation*}

\end{document}