If $R$ is a \index{commutative ring}, then $\polyring{R}{X,Y,Z}$
is a multivariate polynomial ring with indeterminates $X$, $Y$,
and $Z$, and coefficients in $R$. If $R$ is a moreover an integral
- domain, then its fraction field is $\Frac{R}$.
+ domain, then its fraction field is $\Frac{R}$. If $x,y,z \in R$,
+ then $\ideal{\set{x,y,z}}$ is the ideal generated by
+ $\set{x,y,z}$, which is defined to be the smallest ideal in $R$
+ containing that set. Likewise, if we are in an algebra
+ $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
+ $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
+ containing the set $\set{x,y,z}$.
\end{section}
\begin{section}{Algorithm}
\end{section}
\begin{section}{Font}
- We can write things like Carathéodory and Güler and $\mathbb{R}$.
+ We can write things like Carathéodory and Güler and
+ $\mathbb{R}$. The PostScript Zapf Chancery font is also available
+ in both upper- and lower-case:
+ %
+ \begin{itemize}
+ \begin{item}$\mathpzc{abcdefghijklmnopqrstuvwxyz}$\end{item}
+ \begin{item}$\mathpzc{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\end{item}
+ \end{itemize}
\end{section}
\begin{section}{Linear algebra}
$L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
$\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
concept is the Moore-Penrose pseudoinverse of $L$, denoted by
- $\pseudoinverse{L}$.
+ $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
+ $\rank{L}$.
The span of a set $X$ is $\spanof{X}$, and its codimension is
$\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The
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