A section of a database systems homework that uses handy relational algebra commands.

relational_algebra.tex

\documentclass[letterpaper]{article}

\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{inconsolata}
%\pagestyle{empty}

%% About the assignment...
\newcommand{\name}{Adam Lloyd}
\newcommand{\class}{CSCI 4380}
\newcommand{\subdate}{14 Sep 2010}
\newcommand{\assignment}{Relational Algebra Examples}

%% The header:
\newcommand{\betterheader}{\begin{center}\Large\textbf{\class:
\assignment}\normalsize\\\vspace{1mm}\name\\\vspace{0.5mm}\subdate\end{center}\vspace{0.1mm}}

%% Question/answer headers:
\newcommand{\question}[1]{\vspace{0.6mm}\begin{flushleft}\large{\textbf{Question #1}}\end{flushleft}}
\newcommand{\answer}{\textbf{Answer: }}

%% Relational algebra helpers:
\newcommand{\select}[2]{\ensuremath{\sigma_{\mathrm{#1}}\left(#2\right)}}
\newcommand{\project}[2]{\ensuremath{\Pi_{\mathrm{#1}}\left(#2\right)}}
\newcommand{\join}[3]{\ensuremath{(#1)\bowtie_{\mathrm{#3}}(#2)}}
\newcommand{\naturaljoin}[2]{\ensuremath{(#1)\bowtie(#2)}}
\newcommand{\union}[2]{\ensuremath{(#1)\cup(#2)}}
\newcommand{\rename}[2]{\ensuremath{\rho_{#1}(#2)}}
\newcommand{\difference}[2]{\ensuremath{(#2)-(#1)}}


\begin{document}
\betterheader

%% Make item labels in enumerate look like (a), (b), etc.
\renewcommand{\labelenumi}{(\alph{enumi})}


\question{X}

\begin{enumerate}
  \item \select{classroom='Low\;3051'}{class}
  \item
    \project{facultyRIN}{\select{positionName='Center\;Director'}{appointment}}
  \item
    \project{name}{\join{faculty}{\select{name='Computer\;Science'}{department}}{departmentCode=code}}
  \item There is no clearly defined relationship between a class and a
    department.  If we choose say that a class is offered by a
    department if the department code matches the subject code, then
    the query is simply
    $\project{name}{\join{department}{\select{subjectCode='CSCI'}{class}}{code=subjectCode}}$,
    and it is rather silly.  (This is explanation is consistent with my
    understanding, but it is not suggested by the database schema.)
    
    Alternatively, if we decide that a course is offered by a
    department if one of that department's faculty teaches it, we get
    \begin{align*}
      C &:= \select{subjectCode='CSCI'}{class} \\
      F &:= \join{faculty}{C}{rin=instructorRIN} \\
      D &:= \join{department}{D}{code=departmentCode} \\
      result  &:= \project{name}{F}
    \end{align*}
    but risk not considering cross-listed courses properly.

  \item \begin{align*}
    D &:= \select{departmentCode='ABCD'}{faculty} \\
    D\_RIN &:= \project{rin}{D} \\
    VP &:= \select{positionName='Vice\;President'}{appointment} \\
    VP\_RIN &:= \rename{S(rin)}{\project{facultyRIN}{VP}} \\
    result &:= \union{D\_RIN}{VP\_RIN}
  \end{align*}

  \item \begin{align*}
    C &:= \select{semester='spring'\;AND\;year=2010}{class} \\
    FT\_RIN &:= \rename{S(rin)}{\project{instructorRIN}{C}} \\
    FNT\_RIN &:= \project{rin}{faculty} \\
    result &:= \difference{FT\_RIN}{FNT\_RIN}
  \end{align*}
    
\end{enumerate}
\end{document}