--- /dev/null
+\documentclass{report}
+
+\usepackage{mjotex}
+\usepackage{mathtools}
+
+\begin{document}
+
+ \begin{section}{Algorithm}
+ An example of an algorithm (bogosort) environment.
+
+ \begin{algorithm}[H]
+ \caption{Sort a list of numbers}
+ \begin{algorithmic}
+ \Require{A list of numbers $L$}
+ \Ensure{A new, sorted copy $M$ of the list $L$}
+
+ \State{$M \gets L$}
+
+ \While{$M$ is not sorted}
+ \State{Rearrange $M$ randomly}
+ \EndWhile
+
+ \Return{$M$}
+ \end{algorithmic}
+ \end{algorithm}
+ \end{section}
+
+ \begin{section}{Arrow}
+ The identity operator on $V$ is $\identity{V}$. The composition of
+ $f$ and $g$ is $\compose{f}{g}$. The inverse of $f$ is
+ $\inverse{f}$.
+ \end{section}
+
+ \begin{section}{Common}
+ The function $f$ applied to $x$ is $f\of{x}$. We can group terms
+ like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. Here's a
+ set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. Here's a pair
+ of things $\pair{1}{2}$ or a triple of them
+ $\triple{1}{2}{3}$. The Cartesian product of two sets $A$ and $B$
+ is $\cartprod{A}{B}$; if we take the product with $C$ as well,
+ then we obtain $\cartprodthree{A}{B}{C}$. The direct sum of $V$
+ and $W$ is $\directsum{V}{W}$ and the factorial of the number $10$
+ is $\factorial{10}$.
+
+ Here are a few common tuple spaces that should not have a
+ superscript when that superscript would be one: $\Nn[1]$,
+ $\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
+ superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
+ $\Qn[2]$, $\Rn[2]$, $\Cn[2]$.
+
+ We also have a few basic set operations, for example the union of
+ two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
+ course with union comes intersection: $\intersect{A}{B}$,
+ $\intersectthree{A}{B}{C}$.
+ \end{section}
+
+ \begin{section}{Cone}
+ The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
+ are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$. If cones
+ $K_{1}$ and $K_{2}$ are given, we can define $\posops{K_{1}}$,
+ $\posops[K_{2}]{K_{1}}$, $\Sof{K_{1}}$, $\Zof{K_{1}}$,
+ $\LL{K_{1}}$, and $\lyapunovrank{K_{1}}$. We can also define $x
+ \gecone_{K} y$, $x \gtcone_{K} y$, $x \lecone_{K} y$, and $x
+ \ltcone_{K} y$ with respect to a cone $K$.
+ \end{section}
+
+ \begin{section}{Convex}
+ The conic hull of a set $X$ is $\cone{X}$; its affine hull is
+ $\aff{X}$, and its convex hull is $\conv{X}$. If $K$ is a cone,
+ then its lineality space is $\linspace{K}$, its lineality is
+ $\lin{K}$, and its extreme directions are $\Ext{K}$.
+ \end{section}
+
+ \begin{section}{Font}
+ We can write things like Carathéodory and Güler and $\mathbb{R}$.
+ \end{section}
+
+ \begin{section}{Linear algebra}
+ The absolute value of $x$ is $\abs{x}$, or its norm is
+ $\norm{x}$. The inner product of $x$ and $y$ is $\ip{x}{y}$ and
+ their tensor product is $\tp{x}{y}$. The Kronecker product of
+ matrices $A$ and $B$ is $\kp{A}{B}$. The adjoint of the operator
+ $L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
+ $\transpose{L}$. Its trace is $\trace{L}$.
+
+ 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
+ automorphism group of $X$ is $\Aut{X}$, and its Lie algebra is
+ $\Lie{X}$. We can write a column vector $x \coloneqq
+ \colvec{x_{1},x_{2},x_{3},x_{4}}$ and turn it into a $2 \times 2$
+ matrix with $\matricize{x}$. To recover the vector, we use
+ $\vectorize{\matricize{x}}$.
+
+ The set of all bounded linear operators from $V$ to $W$ is
+ $\boundedops[W]{V}$. If $W = V$, then we write $\boundedops{V}$
+ instead.
+ \end{section}
+
+ \begin{section}{Listing}
+ Here's an interactive sage prompt:
+
+ \begin{tcblisting}{listing only,
+ colback=codebg,
+ coltext=codefg,
+ listing options={language=sage,style=sage}}
+ sage: K = Cone([ (1,0), (0,1) ])
+ sage: K.positive_operator_gens()
+ [
+ [1 0] [0 1] [0 0] [0 0]
+ [0 0], [0 0], [1 0], [0 1]
+ ]
+ \end{tcblisting}
+ \end{section}
+
+ \begin{section}{Miscellaneous}
+ The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
+ = 3$.
+ \end{section}
+
+ \begin{section}{Proof by cases}
+
+ \begin{proposition}
+ There are two cases in the following proof.
+
+ \begin{proof}
+ The result should be self-evident once we have considered the
+ following two cases.
+ \begin{pcases}
+ \begin{case}[first case]
+ Nothing happens in the first case.
+ \end{case}
+ \begin{case}[second case]
+ The same thing happens in the second case.
+ \end{case}
+ \end{pcases}
+
+ You see?
+ \end{proof}
+ \end{proposition}
+
+ Here's another one.
+
+ \renewcommand{\baselinestretch}{2}
+ \begin{proposition}
+ Cases should display intelligently even when the document is
+ double-spaced.
+
+ \begin{proof}
+ Here we go again.
+
+ \begin{pcases}
+ \begin{case}[first case]
+ Nothing happens in the first case.
+ \end{case}
+ \begin{case}[second case]
+ The same thing happens in the second case.
+ \end{case}
+ \end{pcases}
+
+ Now it's over.
+ \end{proof}
+ \end{proposition}
+ \renewcommand{\baselinestretch}{1}
+ \end{section}
+
+ \begin{section}{Theorems}
+ \begin{corollary}
+ The
+ \end{corollary}
+
+ \begin{lemma}
+ quick
+ \end{lemma}
+
+ \begin{proposition}
+ brown
+ \end{proposition}
+
+ \begin{theorem}
+ fox
+ \end{theorem}
+
+ \begin{definition}
+ quod
+ \end{definition}
+
+ \begin{example}
+ erat
+ \end{example}
+
+ \begin{remark}
+ demonstradum.
+ \end{remark}
+ \end{section}
+
+ \begin{section}{Theorems (starred)}
+ \begin{corollary*}
+ The
+ \end{corollary*}
+
+ \begin{lemma*}
+ quick
+ \end{lemma*}
+
+ \begin{proposition*}
+ brown
+ \end{proposition*}
+
+ \begin{theorem*}
+ fox
+ \end{theorem*}
+
+ \begin{definition*}
+ quod
+ \end{definition*}
+
+ \begin{example*}
+ erat
+ \end{example*}
+
+ \begin{remark*}
+ demonstradum.
+ \end{remark*}
+ \end{section}
+
+ \begin{section}{Topology}
+ The interior of a set $X$ is $\interior{X}$. Its closure is
+ $\closure{X}$ and its boundary is $\boundary{X}$.
+ \end{section}
+
+\end{document}
LATEX = pdflatex -file-line-error -halt-on-error
# The name of this document.
-PN = paper
+PN = examples
# A space-separated list of bib files. These must all belong to paths
# contained in your $BIBINPUTS environment variable.
-BIBS = references.bib
+#
+# Leave commented if you don't use a bibliography file.
+#
+#BIBS = references.bib
# A space-separated list of the mjotex files that you use. The path to
# mjotex must be contain in your $TEXINPUTS environment variable.
# As a side effect, we now need to depend on $(SRCS) here, since we
# won't pick it up transitively from $(PN).aux.
#
+# If the $BIBS variable is undefined, we presume that there are no
+# references and create an empty bbl file. Otherwise, we risk trying
+# to run biblatex on an aux file containing no citations.
+#
$(PN).bbl: $(SRCS) | $(PN).aux
+ifdef BIBS
bibtex $(PN).aux
-
+else
+ echo -n '' > $@
+endif
# Run chktex to find silly mistakes. There is some exit code weirdness
# (Savannah bug 45979), so we just look for empty output.
# Clean up leftover junk.
.PHONY: clean
clean:
- rm -f *.{aux,bbl,bcf,bib,blg,lof,log,nav,out,pdf,snm,toc,xml}
+ rm -f *.{aux,bbl,bcf,bib,blg,listing,lof,log,nav,out,pdf,snm,toc,xml}
rm -rf dist/
# If this document will be published, the publisher isn't going to
projects / mjotex.git / commitdiff