\begin{frame} \frametitle{Determinants} \begin{block}{Determinants (Non-trivial, minimal FDs)} \raggedright $\{\, A_1, \dots, A_n \,\}$ is a \emph{determinant} for $\{\, B_1, \dots, B_m \,\}$ if \begin{itemize} \item the FD $A_1, \dots, A_n \to B_1, \dots B_m$ holds, and \item the \emph{left-hand side is minimal}, that is, if any $A_i$ is removed then $A_1, \dots, A_{i-1}, A_{i+1}, A_n \to B_1, \dots B_m$ does \textit{not} hold, and \item it is \emph{not trivial}, that is, $\{B_1, \dots, B_m\} \not\subseteq \{A_1, \dots, A_n\}$. \end{itemize} \end{block} (In a canonical set of FDs, all FDs are determinants.) \pause \begin{exampleblock}{} \begin{center} $ \mathcal{F} = \left\{ \begin{array}{rcl} \sql{sid}, \sql{exercise} & \to & \sql{points} \\ \sql{exercise} & \to & \sql{maxPoints} \end{array} \right\} $\vspace{-.5ex} \end{center} Are the following determinants? \begin{itemize} \pause \item $\sql{points},\; \sql{maxPoints}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause No \pause \item $\sql{exercise}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause No \pause \item $\sql{sid},\; \sql{exercise}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause Yes \pause \item $\sql{exercise},\; \sql{points}$ \;for\; $\sql{points},\; \sql{maxPoints}$ \;? \pause Yes \end{itemize} \end{exampleblock} \end{frame}