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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /info/examples/FirstSteps
Initial commit
Diffstat (limited to 'info/examples/FirstSteps')
-rw-r--r--info/examples/FirstSteps/Contents23
-rw-r--r--info/examples/FirstSteps/article.tpl94
-rw-r--r--info/examples/FirstSteps/article2.tpl100
-rw-r--r--info/examples/FirstSteps/bibl.tpl135
-rw-r--r--info/examples/FirstSteps/gallery.tex254
-rw-r--r--info/examples/FirstSteps/ggamsart.tpl112
-rw-r--r--info/examples/FirstSteps/ggart.tpl97
-rw-r--r--info/examples/FirstSteps/ggart2.tpl101
-rw-r--r--info/examples/FirstSteps/intrart.tex127
-rw-r--r--info/examples/FirstSteps/lattice.sty122
-rw-r--r--info/examples/FirstSteps/math.tex21
-rw-r--r--info/examples/FirstSteps/mathb.tex24
-rw-r--r--info/examples/FirstSteps/note1.tex22
-rw-r--r--info/examples/FirstSteps/note1b.tex22
-rw-r--r--info/examples/FirstSteps/note2.tex14
-rw-r--r--info/examples/FirstSteps/noteslug.tex22
-rw-r--r--info/examples/FirstSteps/sampart.tex258
-rw-r--r--info/examples/FirstSteps/sampart2.tex252
18 files changed, 1800 insertions, 0 deletions
diff --git a/info/examples/FirstSteps/Contents b/info/examples/FirstSteps/Contents
new file mode 100644
index 0000000000..ccfa66eefb
--- /dev/null
+++ b/info/examples/FirstSteps/Contents
@@ -0,0 +1,23 @@
+Sample articles and notes:
+
+gallery.tex the formulas from Chapter 3
+intrart.tex introductory sample article, Chapter 4
+lattice.sty personalized file for user defined commands, Section 5.6
+note1.tex first note, Section 1.3
+note1b.tex note1.tex with lines too long, Section 1.4
+noteslug.tex note1b.tex with slug, Section 1.4
+note2.tex second note, Section 1.5
+math.tex first note with math, Section 2.1
+mathb.tex first note with math with mistakes, Section 2.2
+sampart.tex sample article with AMS, Chapter 5
+sampart2.tex sample article with AMS and user defined commands, Section 5.6
+
+
+Templates:
+
+article.tpl article template for one author, Section 4.3
+article2.tpl article template for two authors, Section 4.3
+bibl.tpl templates for bibliographic entries, Section 4.4.4
+ggart.tpl article.tpl personalized, Section 4.3
+ggart2.tpl article2.tpl personalized, Section 4.3
+ggamsart.tpl personalized template for amsart document class, Section 5.4
diff --git a/info/examples/FirstSteps/article.tpl b/info/examples/FirstSteps/article.tpl
new file mode 100644
index 0000000000..110b108671
--- /dev/null
+++ b/info/examples/FirstSteps/article.tpl
@@ -0,0 +1,94 @@
+% Sample file: article.tpl
+% Typeset with LaTeX format
+
+\documentclass{article}
+\usepackage{amssymb,latexsym,amsmath}
+
+\newtheorem{theorem}{Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+\newtheorem{definition}{Definition}
+\newtheorem{corollary}{Corollary}
+\newtheorem{notation}{Notation}
+
+\begin{document}
+\title{titleline1\\
+ titleline2}
+\author{name\thanks{support}\\
+ addressline1\\
+ addressline2\\
+ addressline3}
+\date{date}
+\maketitle
+
+\begin{abstract}
+ abstract text
+\end{abstract}
+
+\begin{thebibliography}{99}
+ bibliographic entries
+\end{thebibliography}
+\end{document}
+
+Papers:
+
+\bibitem{xxx}
+ author, \emph{title,} journal \textbf{volume}
+ (year), pages.
+
+Books:
+
+\bibitem{xxx}
+ author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+ author, \emph{title,} series, vol.~volume,
+ publisher, address, edition, date.
+
+\bibitem{xxx}
+ editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+ author, \emph{title,} book title, publisher,
+ year, pp~pages.
+
+\bibitem{xxx}
+ author, \emph{title,} book title (editor, ed.),
+ vol.~volume, publisher, publisher address, date,
+ pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+ author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+ author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+ author, \emph{title,} Research Note number,
+ university, location, date, research paper in
+ preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+ author, \emph{title,} conference title (location,
+ year).
+
+\bibitem{xxx}
+ author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+ author, \emph{title,} Abstract: journal, volume,
+ year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/article2.tpl b/info/examples/FirstSteps/article2.tpl
new file mode 100644
index 0000000000..3075530cd2
--- /dev/null
+++ b/info/examples/FirstSteps/article2.tpl
@@ -0,0 +1,100 @@
+% Sample file: article2.tpl for two authors
+% Typeset with LaTeX format
+
+\documentclass{article}
+\usepackage{amssymb,latexsym,amsmath}
+
+\newtheorem{theorem}{Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+\newtheorem{definition}{Definition}
+\newtheorem{corollary}{Corollary}
+\newtheorem{notation}{Notation}
+
+\begin{document}
+
+\title{titleline1\\
+ titleline2}
+\author{name1\thanks{support1}\\
+ address1line1\\
+ address1line2\\
+ address1line3
+ \and
+ name2\thanks{support2}\\
+ address2line1\\
+ address2line2\\
+ address2line3}
+\date{date}
+\maketitle
+
+\begin{abstract}
+ abstract text
+\end{abstract}
+
+\begin{thebibliography}{99}
+ bibliographic entries
+\end{thebibliography}
+\end{document}
+
+Papers:
+
+\bibitem{xxx}
+ author, \emph{title,} journal \textbf{volume}
+ (year), pages.
+
+Books:
+
+\bibitem{xxx}
+ author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+ author, \emph{title,} series, vol.~volume,
+ publisher, address, edition, date.
+
+\bibitem{xxx}
+ editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+ author, \emph{title,} book title, publisher,
+ year, pp~pages.
+
+\bibitem{xxx}
+ author, \emph{title,} book title (editor, ed.),
+ vol.~volume, publisher, publisher address, date,
+ pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+ author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+ author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+ author, \emph{title,} Research Note number,
+ university, location, date, research paper in
+ preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+ author, \emph{title,} conference title (location,
+ year).
+
+\bibitem{xxx}
+ author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+ author, \emph{title,} Abstract: journal, volume,
+ year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/bibl.tpl b/info/examples/FirstSteps/bibl.tpl
new file mode 100644
index 0000000000..d7c40bb1e6
--- /dev/null
+++ b/info/examples/FirstSteps/bibl.tpl
@@ -0,0 +1,135 @@
+% Sample file: bibl.tpl
+% bibliography template file
+
+\begin{thebibliography}{99}
+\bibitem{hA70}
+ Henry~H. Albert,
+ \emph{Free torsoids,}
+ Current Trends in Lattice Theory, D.~Van Nostrand, 1970.
+\bibitem{hA70a}
+ Henry~H. Albert,
+ \emph{Free torsoids,}
+ Current Trends in Lattice Theory (G.H. Birnbaum, ed.), vol.~7,
+ D.~Van Nostrand, Princeton-Toronto-London-Melbourne,
+ January 1970,
+ no translation available, pp.~173--215 (Hungarian).
+\bibitem{sF90}
+ Soo-Key Foo,
+ \emph{Lattice Constructions,}
+ Ph.D. thesis,
+ University of Winnebago, 1990.
+\bibitem{sF90a}
+ Soo-Key Foo,
+ \emph{Lattice Constructions,}
+ Ph.D. thesis,
+ University of Winnebago, Winnebago, MN, December, 1990,
+ final revision not yet available (Chinese).
+\bibitem{gF86}
+ Grant~H. Foster,
+ \emph{Computational complexity in lattice theory,}
+ tech. report, Carnegie Mellon University, 1986.
+\bibitem{gF86a}
+ Grant~H. Foster,
+ \emph{Computational complexity in lattice theory,}
+ Research Note 128A, Carnegie Mellon University,
+ Pittsburgh PA, December 1986,
+ research article in preparation (English).
+\bibitem{pK69}
+ Peter~A. Konig,
+ \emph{Composition of functions,}
+ Proceedings of the Conference on Universal Algebra
+ (Kingston, 1969).
+\bibitem{pK69a}
+ Peter~A. Konig,
+ \emph{Composition of functions,}
+ Proceedings of the Conference on Universal Algebra, 1969
+ (G.H. Birnbaum, ed.), vol.~7, Canadian Mathematical
+ Society, Queen's Univ., available from the Montreal office,
+ pp.~1--106 (English).
+\bibitem{wL75}
+ William~A. Landau,
+ \emph{Representations of complete lattices,}
+ Abstract: Notices Amer. Math. Soc., \textbf{18}, 937.
+\bibitem{wL75a}
+ William~A. Landau,
+ \emph{Representations of complete lattices,}
+ Abstract: Notices Amer. Math. Soc. \textbf{18}, 937,
+ December 1975 (English).
+\bibitem{gM68}
+ George~A. Menuhin,
+ \emph{Universal Algebra,}
+ D.~van Nostrand, Princeton-Toronto-London-Melbourne, 1968.
+\bibitem{gM68a}
+ George~A. Menuhin,
+ \emph{Universal Algebra,}
+ University Series in Higher Mathematics, vol.~58,
+ D.~van Nostrand, Princeton-Toronto-London-Melbourne,
+ second ed., March 1968, no Russian translation (English).
+\bibitem{eM57}
+ Ernest~T. Moynahan,
+ \emph{On a problem of M.H. Stone,}
+ Acta Math. Acad. Sci. Hungar. \textbf{8} (1957), 455--460.
+\bibitem{eM57a}
+ Ernest~T. Moynahan,
+ \emph{On a problem of M.H. Stone,}
+ Acta Math. Acad. Sci. Hungar. \textbf{8} (1957), 455--460,
+ Russian translation available (English).
+\end{thebibliography}
+
+Papers:
+
+\bibitem{xxx}
+author, \emph{title,} journal \textbf{volume} (year),
+pp.~pages.
+
+Books:
+
+\bibitem{xxx}
+author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+author, \emph{title,} series, vol.~volume, publisher,
+ address, edition, date.
+
+\bibitem{xxx}
+editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+author, \emph{title,} book title, publisher, year, pp~pages.
+
+\bibitem{xxx}
+author, \emph{title,} book title (editor, ed.), vol.~volume,
+publisher, publisher address, date, pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+author, \emph{title,} Research Note number, university,
+location, date, research paper in preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+author, \emph{title,} conference title (location, year).
+
+\bibitem{xxx}
+author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+author, \emph{title,} Abstract: journal, volume, year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/gallery.tex b/info/examples/FirstSteps/gallery.tex
new file mode 100644
index 0000000000..2dee9d3ff0
--- /dev/null
+++ b/info/examples/FirstSteps/gallery.tex
@@ -0,0 +1,254 @@
+% Sample file: gallery.tex formula template file
+% Typeset with LaTeX format
+
+\documentclass{article}
+
+\usepackage{amssymb,latexsym,amsmath}
+
+\begin{document}
+
+Section 3.1 Formula gallery
+
+Formula 1
+\[
+ x \mapsto \{\, c \in C \mid c \leq x \,\}
+\]
+
+Formula 2
+\[
+ \left| \bigcup (\, I_{j} \mid j \in J \,) \right|
+ < \mathfrak{m}
+\]
+
+Formula 3
+\[
+ A = \{\, x \in X \mid x \in X_{i},
+ \mbox{ for some } i \in I \,\}
+\]
+
+Formula 4
+\[
+ \langle a_{1}, a_{2} \rangle \leq \langle a'_{1}, a'_{2}\rangle
+ \qquad \mbox{if{f}} \qquad a_{1} < a'_{1} \quad \mbox{or}
+ \quad a_{1} = a'_{1} \mbox{ and } a_{2} \leq a'_{2}
+\]
+
+Formula 5
+\[
+ \Gamma_{u'} = \{\, \gamma \mid \gamma < 2\chi,
+ \ B_{\alpha} \nsubseteq u', \ B_{\gamma} \subseteq u' \,\}
+\]
+
+Formula 6
+\[
+ A = B^{2} \times \mathbb{Z}
+\]
+
+Formula 7
+\[
+ \left( \bigvee (\, s_{i} \mid i \in I \,) \right)^{c} =
+ \bigwedge (\, s_{i}^{c} \mid i \in I \,)
+\]
+
+Formula 8
+\[
+ y \vee \bigvee (\, [B_{\gamma}] \mid \gamma
+ \in \Gamma \,) \equiv z \vee \bigvee (\, [B_{\gamma}]
+ \mid \gamma \in \Gamma \,) \pmod{ \Phi^{x} }
+\]
+
+Formula 9
+\[
+ f(\mathbf{x}) = \bigvee\nolimits_{\!\mathfrak{m}}
+ \left(\,
+ \bigwedge\nolimits_{\mathfrak{m}}
+ (\, x_{j} \mid j \in I_{i} \,) \mid i < \aleph_{\alpha}
+ \,\right)
+\]
+
+Formula 10
+\[
+ \left. \widehat{F}(x) \right|_{a}^{b} =
+ \widehat{F}(b) - \widehat{F}(a)
+\]
+
+Formula 11
+\[
+ u \underset{\alpha}{+} v \overset{1}{\thicksim} w
+ \overset{2}{\thicksim} z
+\]
+
+Formula 12
+\[
+ f(x) \overset{ \text{def} }{=} x^{2} - 1
+\]
+
+Formula 13
+\[
+ \overbrace{a + b + \cdots + z}^{n}
+\]
+
+Formula 14
+\[
+ \begin{vmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{vmatrix}
+ = 7
+\]
+
+\[
+ \begin{Vmatrix}
+ a + b + c & uv\\
+ a + b & c + d
+ \end{Vmatrix}
+ = 7
+\]
+
+Formula 15
+\[
+ \sum_{j \in \mathbf{N}} b_{ij} \hat{y}_{j} =
+ \sum_{j \in \mathbf{N}} b^{(\lambda)}_{ij} \hat{y}_{j} +
+ (b_{ii} - \lambda_{i}) \hat{y}_{i} \hat{y}
+\]
+
+Formula 16
+\[
+ \left( \prod^n_{\, j = 1} \hat x_{j} \right) H_{c} =
+ \frac{1}{2} \hat k_{ij} \det \hat{ \mathbf{K} }(i|i)
+\]
+
+\[
+ \biggl( \prod^n_{\, j = 1} \hat x_{j} \biggr) H_{c} =
+ \frac{1}{2} \hat{k}_{ij} \det \widehat{ \mathbf{K} }(i|i)
+\]
+
+Formula 17
+\[
+ \det \mathbf{K} (t = 1, t_{1}, \ldots, t_{n}) =
+ \sum_{I \in \mathbf{n} }(-1)^{|I|}
+ \prod_{i \in I} t_{i}
+ \prod_{j \in I} (D_{j} + \lambda_{j} t_{j})
+ \det \mathbf{A}^{(\lambda)} (\,\overline{I} | \overline{I}\,) = 0
+\]
+
+Formula 18
+\[
+ \lim_{(v, v') \to (0, 0)}
+ \frac{H(z + v) - H(z + v') - BH(z)(v - v')}
+ {\| v - v' \|} = 0
+\]
+
+Formula 19
+\[
+ \int_{\mathcal{D}} | \overline{\partial u} |^{2}
+ \Phi_{0}(z) e^{\alpha |z|^2} \geq
+ c_{4} \alpha \int_{\mathcal{D}} |u|^{2} \Phi_{0}
+ e^{\alpha |z|^{2}} + c_{5} \delta^{-2} \int_{A}
+ |u|^{2} \Phi_{0} e^{\alpha |z|^{2}}
+\]
+
+Formula 20
+\[
+ \mathbf{A} =
+ \begin{pmatrix}
+ \dfrac{\varphi \cdot X_{n, 1}}
+ {\varphi_{1} \times \varepsilon_{1}}
+ & (x + \varepsilon_{2})^{2} & \cdots
+ & (x + \varepsilon_{n - 1})^{n - 1}
+ & (x + \varepsilon_{n})^{n}\\[10pt]
+ \dfrac{\varphi \cdot X_{n, 1}}
+ {\varphi_{2} \times \varepsilon_{1}}
+ & \dfrac{\varphi \cdot X_{n, 2}}
+ {\varphi_{2} \times \varepsilon_{2}}
+ & \cdots & (x + \varepsilon_{n - 1})^{n - 1}
+ & (x + \varepsilon_{n})^{n}\\
+ \hdotsfor{5}\\
+ \dfrac{\varphi \cdot X_{n, 1}}
+ {\varphi_{n} \times \varepsilon_{1}}
+ & \dfrac{\varphi \cdot X_{n, 2}}
+ {\varphi_{n} \times \varepsilon_{2}}
+ & \cdots & \dfrac{\varphi \cdot X_{n, n - 1}}
+ {\varphi_{n} \times \varepsilon_{n - 1}}
+ & \dfrac{\varphi\cdot X_{n, n}}
+ {\varphi_{n} \times \varepsilon_{n}}
+ \end{pmatrix}
+ + \mathbf{I}_{n}
+\]
+
+
+Section 3.2. User-defined commands
+
+Formula 20 with user-defined commands:
+
+\newcommand{\quot}[2]{%
+\dfrac{\varphi \cdot X_{n, #1}}%
+{\varphi_{#2} \times \varepsilon_{#1}}}
+\newcommand{\exn}[1]{(x+\varepsilon_{#1})^{#1}}
+
+\[
+ \mathbf{A} =
+ \begin{pmatrix}
+ \quot{1}{1} & \exn{2} & \cdots & \exn{n - 1}&\exn{n}\\[10pt]
+ \quot{1}{2} & \quot{2}{2} & \cdots & \exn{n - 1} &\exn{n}\\
+ \hdotsfor{5}\\
+ \quot{1}{n} & \quot{2}{n} & \cdots &
+ \quot{n - 1}{n} & \quot{n}{n}
+ \end{pmatrix}
+ + \mathbf{I}_{n}
+\]
+
+Section 3.3. Building a formula step-by-step
+
+Step 1
+$\left[ \frac{n}{2} \right]$
+
+Step 2
+\[
+ \sum_{i = 1}^{ \left[ \frac{n}{2} \right] }
+\]
+
+Step 3
+\[
+ x_{i, i + 1}^{i^{2}} \qquad \left[ \frac{i + 3}{3} \right]
+\]
+
+Step 4
+\[
+ \binom{ x_{i,i + 1}^{i^{2}} }{ \left[ \frac{i + 3}{3} \right] }
+\]
+
+Step 5
+$\sqrt{ \mu(i)^{ \frac{3}{2} } (i^{2} - 1) }$
+
+$\sqrt{ \mu(i)^{ \frac{3}{2} } (i^{2} - 1) }$
+
+Step 6
+$\sqrt[3]{ \rho(i) - 2 }$ $\sqrt[3]{ \rho(i) - 1 }$
+
+Step 7
+\[
+ \frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} -1) } }
+ { \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} }
+\]
+
+Step 8
+\[
+ \sum_{i = 1}^{ \left[ \frac{n}{2} \right] }
+ \binom{ x_{i, i + 1}^{i^{2}} }
+ { \left[ \frac{i + 3}{3} \right] }
+ \frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} - 1) } }
+ { \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} }
+\]
+
+\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}}
+{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3}
+{2}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\]
+
+%\[\sum_{i=1}^{\left[\frac{n}{2}\right]}\binom{x_{i,i+1}^{i^{2}}}
+%{\left[\frac{i+3}{3}\right]}\frac{\sqrt{\mu(i)^{\frac{3}
+%{2}}}(i^{2}-1)}}{\sqrt[3]{\rho(i)-2}+\sqrt[3]{\rho(i)-1}}\]
+
+
+\end{document}
+
diff --git a/info/examples/FirstSteps/ggamsart.tpl b/info/examples/FirstSteps/ggamsart.tpl
new file mode 100644
index 0000000000..1f4a045881
--- /dev/null
+++ b/info/examples/FirstSteps/ggamsart.tpl
@@ -0,0 +1,112 @@
+% Sample file: ggams.tpl
+% Typeset with LaTeX format
+
+\documentclass{amsart}
+\usepackage{amssymb,latexsym}
+
+% theorems, corollaries, lemmas, and propositions,
+% in the most emphatic (plain) style;
+% all are numbered separately
+% There is a Main Theorem in the most emphatic (plain)
+% style, unnumbered
+% There are definitions, in the less emphatic (definition) style
+% There are notations, in the least emphatic (remark) style,
+% unnumbered
+
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}
+\newtheorem{corollary}{Corollary}
+\newtheorem*{main}{Main Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{definition}{Definition}
+
+\theoremstyle{remark}
+\newtheorem*{notation}{Notation}
+
+\begin{document}
+\title[short title]{titleline1\\
+ titleline2}
+\author{George Gr\"{a}tzer}
+\address{University of Manitoba\\
+ Department of Mathematics\\
+ Winnipeg, MN, R3T 2N2\\
+ Canada}
+\email{gratzer@cc.umanitoba.ca}
+\urladdr{http://server.maths.umanitoba.ca/homepages/gratzer/}
+\thanks{Research supported by the NSERC of Canada}
+
+\keywords{keywords}
+\subjclass{Primary: subject; Secondary: subject}
+\date{date}
+
+\begin{abstract}
+ abstract text
+\end{abstract}
+\maketitle
+
+% Bibliography
+\begin{thebibliography}{99}
+ bibliographic entries
+\end{thebibliography}
+\end{document}
+
+Papers:
+
+\bibitem{xxx}
+author, \emph{title,} journal \textbf{volume} (year),
+pp.~pages.
+
+Books:
+
+\bibitem{xxx}
+author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+author, \emph{title,} series, vol.~volume, publisher,
+ address, edition, date.
+
+\bibitem{xxx}
+editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+author, \emph{title,} book title, publisher, year, pp~pages.
+
+\bibitem{xxx}
+author, \emph{title,} book title (editor, ed.), vol.~volume,
+publisher, publisher address, date, pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+author,\emph{title,} Research Note number, university,
+location, date, research paper in preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+author, \emph{title,} conference title (location, year).
+
+\bibitem{xxx}
+author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+author, \emph{title,} Abstract: journal, volume, year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/ggart.tpl b/info/examples/FirstSteps/ggart.tpl
new file mode 100644
index 0000000000..15bd6718ed
--- /dev/null
+++ b/info/examples/FirstSteps/ggart.tpl
@@ -0,0 +1,97 @@
+% Sample file: ggart.tpl
+% Typeset with LaTeX format
+
+\documentclass{article}
+\usepackage{amssymb,latexsym,amsmath}
+
+\newtheorem{theorem}{Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+\newtheorem{definition}{Definition}
+\newtheorem{corollary}{Corollary}
+\newtheorem{notation}{Notation}
+
+\begin{document}
+\title{titleline1\\
+ titleline2}
+\author{George Gr\"{a}tzer\thanks{Research supported by the
+ NSERC of Canada.}\\
+ University of Manitoba\\
+ Department of Mathematics\\
+ Winnipeg, MN, R3T 2N2\\
+ Canada}
+\date{date}
+\maketitle
+
+\begin{abstract}
+ abstract
+\end{abstract}
+
+\begin{thebibliography}{99}
+
+
+\end{thebibliography}
+\end{document}
+
+Papers:
+
+\bibitem{xxx}
+ author, \emph{title,} journal \textbf{volume}
+ (year), pages.
+
+Books:
+
+\bibitem{xxx}
+ author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+ author, \emph{title,} series, vol.~volume,
+ publisher, address, edition, date.
+
+\bibitem{xxx}
+ editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+ author, \emph{title,} book title, publisher,
+ year, pp~pages.
+
+\bibitem{xxx}
+ author, \emph{title,} book title (editor, ed.),
+ vol.~volume, publisher, publisher address, date,
+ pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+ author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+ author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+ author, \emph{title,} Research Note number,
+ university, location, date, research paper in
+ preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+ author, \emph{title,} conference title (location,
+ year).
+
+\bibitem{xxx}
+ author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+ author, \emph{title,} Abstract: journal, volume,
+ year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/ggart2.tpl b/info/examples/FirstSteps/ggart2.tpl
new file mode 100644
index 0000000000..f56c2f781c
--- /dev/null
+++ b/info/examples/FirstSteps/ggart2.tpl
@@ -0,0 +1,101 @@
+% Sample file: ggart2.tpl for two authors
+% Typeset with LaTeX format
+
+\documentclass{article}
+\usepackage{amssymb,latexsym,amsmath}
+
+\newtheorem{theorem}{Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+\newtheorem{definition}{Definition}
+\newtheorem{corollary}{Corollary}
+\newtheorem{notation}{Notation}
+
+\begin{document}
+\title{titleline1\\
+ titleline2}
+\author{George Gr\"{a}tzer\thanks{Research supported by the
+ NSERC of Canada.}\\
+ University of Manitoba\\
+ Department of Mathematics\\
+ Winnipeg, MN, R3T 2N2\\
+ Canada
+ \and
+ name2\thanks{support2}\\
+ address2line1\\
+ address2line2\\
+ address2line3}
+\date{date}
+\maketitle
+
+\begin{abstract}
+ abstract
+\end{abstract}
+
+\begin{thebibliography}{99}
+ bibliographic entries
+\end{thebibliography}
+\end{document}
+
+Papers:
+
+\bibitem{xxx}
+ author, \emph{title,} journal \textbf{volume}
+ (year), pages.
+
+Books:
+
+\bibitem{xxx}
+ author, \emph{title,} publisher, address, year.
+
+\bibitem{xxx}
+ author, \emph{title,} series, vol.~volume,
+ publisher, address, edition, date.
+
+\bibitem{xxx}
+ editor, ed., \emph{title,} publisher, address, year.
+
+Papers in books:
+
+\bibitem{xxx}
+ author, \emph{title,} book title, publisher,
+ year, pp~pages.
+
+\bibitem{xxx}
+ author, \emph{title,} book title (editor, ed.),
+ vol.~volume, publisher, publisher address, date,
+ pp.~pages.
+
+Theses:
+
+\bibitem{xxx}
+ author, \emph{title,} Ph.D. thesis, university, year.
+
+Tech reports:
+
+\bibitem{xxx}
+ author, \emph{title,} tech. report, university, year.
+
+Research notes:
+
+\bibitem{xxx}
+ author, \emph{title,} Research Note number,
+ university, location, date, research paper in
+ preparation.
+
+Conference proceedings:
+
+\bibitem{xxx}
+ author, \emph{title,} conference title (location,
+ year).
+
+\bibitem{xxx}
+ author, \emph{title,} conference title, year
+ (editor, ed.), vol.~volume, publisher, address,
+ pp.~pages.
+
+Abstracts:
+
+\bibitem{xxx}
+ author, \emph{title,} Abstract: journal, volume,
+ year. \ No newline at end of file
diff --git a/info/examples/FirstSteps/intrart.tex b/info/examples/FirstSteps/intrart.tex
new file mode 100644
index 0000000000..1f35c47723
--- /dev/null
+++ b/info/examples/FirstSteps/intrart.tex
@@ -0,0 +1,127 @@
+% Introductory sample article: intrart.tex
+% Typeset with LaTeX format
+
+\documentclass{article}
+\usepackage{latexsym}
+\newtheorem{theorem}{Theorem}
+\newtheorem{definition}{Definition}
+\newtheorem{notation}{Notation}
+
+\begin{document}
+\title{A construction of complete-simple\\
+ distributive lattices}
+\author{George~A. Menuhin\thanks{Research supported
+ by the NSF under grant number~23466.}\\
+ Computer Science Department\\
+ Winnebago, Minnesota 23714\\
+ menuhin@cc.uwinnebago.edu}
+\date{March 15, 1999}
+\maketitle
+
+\begin{abstract}
+ In this note, we prove that there exist \emph{complete-simple
+ distributive lattices,} that is, complete distributive
+ lattices in which there are only two complete congruences.
+\end{abstract}
+
+\section{Introduction}\label{S:intro}
+In this note, we prove the following result:
+
+\begin{theorem}
+ There exists an infinite complete distributive lattice $K$
+ with only the two trivial complete congruence relations.
+\end{theorem}
+
+\section{The $\Pi^{*}$ construction}\label{S:P*}
+The following construction is crucial in the proof of our Theorem:
+
+\begin{definition}\label{D:P*}
+ Let $D_{i}$, for $i \in I$, be complete distributive
+ lattices satisfying condition~\textup{(J)}. Their
+ $\Pi^{*}$ product is defined as follows:
+ \[
+ \Pi^{*} ( D_{i} \mid i \in I ) =
+ \Pi ( D_{i}^{-} \mid i \in I ) + 1;
+ \]
+ that is, $\Pi^{*} ( D_{i} \mid i \in I )$ is
+ $\Pi ( D_{i}^{-} \mid i \in I )$ with a new unit element.
+\end{definition}
+
+\begin{notation}
+ If $i \in I$ and $d \in D_{i}^{-}$, then
+ \[
+ \langle \ldots, 0, \ldots, d, \ldots, 0, \ldots \rangle
+ \]
+ is the element of $\Pi^{*} ( D_{i} \mid i \in I )$ whose
+ $i$-th component is $d$ and all the other components
+ are $0$.
+\end{notation}
+
+See also Ernest~T. Moynahan~\cite{eM57a}.
+
+Next we verify the following result:
+
+\begin{theorem}\label{T:P*}
+ Let $D_{i}$, $i \in I$, be complete distributive
+ lattices satisfying condition~\textup{(J)}. Let $\Theta$
+ be a complete congruence relation on
+ $\Pi^{*} ( D_{i} \mid i \in I )$.
+ If there exist $i \in I$ and $d \in D_{i}$ with
+ $d < 1_{i}$ such that, for all $d \leq c < 1_{i}$,
+ \begin{equation}\label{E:cong1}
+ \langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
+ \langle \ldots, c, \ldots, 0, \ldots \rangle \pmod{\Theta},
+ \end{equation}
+ then $\Theta = \iota$.
+\end{theorem}
+
+\emph{Proof.} Since
+\begin{equation}\label{E:cong2}
+ \langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
+ \langle \ldots, c, \ldots, 0, \ldots \rangle \pmod{\Theta},
+\end{equation}
+and $\Theta$ is a complete congruence relation, it follows
+from condition~(J) that
+\begin{equation}\label{E:cong}
+ \langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
+ \bigvee ( \langle \ldots, c, \ldots, 0, \ldots \rangle
+ \mid d \leq c < 1 ) \pmod{\Theta}.
+\end{equation}
+
+Let $j \in I$, $j \neq i$, and let $a \in D_{j}^{-}$.
+Meeting both sides of the congruence (\ref{E:cong2}) with
+$\langle \ldots, a, \ldots, 0, \ldots \rangle$, we obtain that
+\begin{equation}\label{E:comp}
+ 0 = \langle \ldots, a, \ldots, 0, \ldots \rangle \pmod{\Theta},
+\end{equation}
+Using the completeness of $\Theta$ and (\ref{E:comp}),
+we get:
+\[
+ 0 \equiv \bigvee ( \langle \ldots, a, \ldots, 0, \ldots \rangle
+ \mid a \in D_{j}^{-} ) = 1 \pmod{\Theta},
+\]
+hence $\Theta = \iota$.
+
+\begin{thebibliography}{9}
+ \bibitem{sF90}
+ Soo-Key Foo,
+ \emph{Lattice Constructions,}
+ Ph.D. thesis,
+ University of Winnebago, Winnebago, MN, December, 1990.
+ \bibitem{gM68}
+ George~A. Menuhin,
+ \emph{Universal Algebra,}
+ D.~van Nostrand, Princeton-Toronto-London-Melbourne, 1968.
+ \bibitem{eM57}
+ Ernest~T. Moynahan,
+ \emph{On a problem of M.H. Stone,}
+ Acta Math. Acad. Sci. Hungar. \textbf{8} (1957), 455--460.
+ \bibitem{eM57a}
+ Ernest~T. Moynahan,
+ \emph{Ideals and congruence relations in lattices.~II,}
+ Magyar Tud. Akad. Mat. Fiz. Oszt. K\"{o}zl. \textbf{9}
+ (1957), 417--434.
+\end{thebibliography}
+
+\end{document}
+
diff --git a/info/examples/FirstSteps/lattice.sty b/info/examples/FirstSteps/lattice.sty
new file mode 100644
index 0000000000..2ebb04e90e
--- /dev/null
+++ b/info/examples/FirstSteps/lattice.sty
@@ -0,0 +1,122 @@
+% lattice.sty
+% Command file for lattice papers
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{lattice}
+ [1999/03/15 Commands for lattices, First Steps]
+\RequirePackage{amsmath}
+\RequirePackage{amssymb}
+\RequirePackage{latexsym}
+\RequirePackage{eucal}
+
+% Lattice operations
+\newcommand{\jj}{\vee}% join
+\newcommand{\mm}{\wedge}% meet
+\newcommand{\JJ}{\bigvee}% big join
+\newcommand{\MM}{\bigwedge}% big meet
+\newcommand{\JJm}[2]{\JJ(\,#1\mid#2\,)}% big join with a middle
+\newcommand{\MMm}[2]{\MM(\,#1\mid#2\,)}% big meet with a middle
+
+% Set operations
+\newcommand{\uu}{\cup}% union
+\newcommand{\ii}{\cap}% intersection
+\newcommand{\UU}{\bigcup}% big union
+\newcommand{\II}{\bigcap}% big intersection
+\newcommand{\UUm}[2]{\UU(\,#1\mid#2\,)}% big union with a middle
+\newcommand{\IIm}[2]{\II(\,#1\mid#2\,)}% big intersection with a middle
+
+% Sets
+\newcommand{\ci}{\subseteq}% contained in with equality
+\newcommand{\nc}{\nsubseteq}% not \ci
+\newcommand{\sci}{\subset}% strictly contained in with equality
+\newcommand{\nci}{\nc}% not \ci
+\newcommand{\ce}{\supseteq}% containing with equality
+\newcommand{\nce}{\nsupseteq}% not \ce
+\newcommand{\nin}{\notin}% not \in
+\newcommand{\es}{\varnothing}% the empty set
+\newcommand{\set}[1]{\{#1\}}% set
+\newcommand{\setm}[2]{\{\,#1\mid#2\,\}}% set with a middle
+\def\vv<#1>{\langle#1\rangle}% vector
+
+% Partial ordering
+\newcommand{\nle}{\nleq}% not \leq
+
+% Greek letters
+\newcommand{\ga}{\alpha}
+\newcommand{\gb}{\beta}
+\newcommand{\gc}{\chi}
+\newcommand{\gd}{\delta}
+\renewcommand{\ge}{\varepsilon}% use \geq for >=
+\newcommand{\gf}{\varphi}
+\renewcommand{\gg}{\gamma}% old use >>
+\newcommand{\gh}{\eta}
+\newcommand{\gi}{\iota}
+\newcommand{\gj}{\theta}
+\newcommand{\gk}{\kappa}
+\newcommand{\gl}{\lambda}
+\newcommand{\gm}{\mu}
+\newcommand{\gn}{\nu}
+\newcommand{\go}{\omega}
+\newcommand{\gp}{\pi}
+\newcommand{\gq}{\theta}
+\newcommand{\gr}{\varrho}
+\newcommand{\gs}{\sigma}
+\newcommand{\gt}{\tau}
+\newcommand{\gu}{\upsilon}
+\newcommand{\gv}{\vartheta}
+\newcommand{\gw}{\omega}
+\newcommand{\gx}{\xi}
+\newcommand{\gy}{\psi}
+\newcommand{\gz}{\zeta}
+
+\newcommand{\gC}{\Xi}
+\newcommand{\gG}{\Gamma}
+\newcommand{\gD}{\Delta}
+\newcommand{\gF}{\Phi}
+\newcommand{\gL}{\Lambda}
+\newcommand{\gO}{\Omega}
+\newcommand{\gP}{\Pi}
+\newcommand{\gQ}{\Theta}
+\newcommand{\gS}{\Sigma}
+\newcommand{\gU}{\Upsilon}
+\newcommand{\gW}{\Omega}
+\newcommand{\gX}{\Xi}
+\newcommand{\gY}{\Psi}
+
+% Font commands
+\newcommand{\tbf}{\textbf}% text bold
+\newcommand{\tit}{\textit}% text italic
+\newcommand{\tsl}{\textsl}% text slanted
+\newcommand{\tsc}{\textsc}% text small cap
+\newcommand{\ttt}{\texttt}% text typewriter
+\newcommand{\trm}{\textrm}% text roman
+\newcommand{\tsf}{\textsf}% text sans serif
+\newcommand{\tup}{\textup}% text upright
+
+\newcommand{\mbf}{\mathbf}% math bold
+\newcommand{\mit}{\mathit}% math italic
+\newcommand{\msf}{\mathsf}% math sans serif
+\newcommand{\mrm}{\mathrm}% math roman
+\newcommand{\mtt}{\mathtt}% math typewriter
+
+\newcommand{\B}{\boldsymbol}
+ % Bold math symbol, use as \B{a}
+\DeclareMathAlphabet{\Bi}{OT1}{cmm}{b}{it}
+ % Bold math italic, use as \Bi{a}
+\newcommand{\C}[1]{\mathcal{#1}}
+ % Euler Script - only caps, use as \C{A}
+\newcommand{\D}[1]{\mathbb{#1}}
+ % Doubled - blackboard bold - only caps, use as \D{A}
+\newcommand{\E}[1]{\mathcal{#1}}% same as \C
+ % Euler Script - only caps, use as \E{A}
+\newcommand{\F}[1]{\mathfrak{#1}}% Fraktur, use as \F{a}
+
+% Miscellaneous
+\newcommand{\nl}{\newline}
+\newcommand{\ol}[1]{\overline{#1}}
+\newcommand{\ul}[1]{\underline{#1}}
+\providecommand{\bysame}{\makebox[3em]{\hrulefill}\thinspace}
+\newcommand{\q}{\quad}% spacing
+\newcommand{\qq}{\qquad}% more spacing
+\newcommand{\iso}{\cong}% isomorphic
+
+\endinput \ No newline at end of file
diff --git a/info/examples/FirstSteps/math.tex b/info/examples/FirstSteps/math.tex
new file mode 100644
index 0000000000..fc96b999eb
--- /dev/null
+++ b/info/examples/FirstSteps/math.tex
@@ -0,0 +1,21 @@
+% Sample file: math.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document}
+In first-year calculus, we define intervals such as
+$(u, v)$ and $(u, \infty)$. Such an interval is a
+\emph{neighborhood} of $a$
+if $a$ is in the interval. Students should
+realize that $\infty$ is only a
+symbol, not a number. This is important since
+we soon introduce concepts
+ such as $\lim_{x \to \infty} f(x)$.
+
+When we introduce the derivative,
+\[
+ \lim_{x \to a} \frac{f(x) - f(a)}{x - a},
+\]
+we assume that the function is defined and continuous
+in a neighborhood of $a$.
+\end{document}
diff --git a/info/examples/FirstSteps/mathb.tex b/info/examples/FirstSteps/mathb.tex
new file mode 100644
index 0000000000..be97c54155
--- /dev/null
+++ b/info/examples/FirstSteps/mathb.tex
@@ -0,0 +1,24 @@
+% Sample file: mathB.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document}
+In first-year calculus, we define intervals such as
+%$(u, v)$ and $(u, \infty)$. Such an interval is a
+ $(u, v)$ and (u, \infty)$. Such an interval is a
+ \emph{neighborhood} of $a$
+if $a$ is in the interval. Students should
+realize that $\infty$ is only a
+symbol, not a number. This is important since
+we soon introduce concepts
+ such as $\lim_{x \to \infty} f(x)$.
+%such as $\lim_{x \to \infty f(x)$.
+
+When we introduce the derivative,
+\[
+ \lim_{x \to a} \frac{f(x) - f(a)}{x - a}
+ %\lim_{x \to a} \frac{f(x) - f(a) x - a}
+\]
+we assume that the function is defined and continuous
+in a neighborhood of $a$.
+\end{document}
diff --git a/info/examples/FirstSteps/note1.tex b/info/examples/FirstSteps/note1.tex
new file mode 100644
index 0000000000..e4425f6779
--- /dev/null
+++ b/info/examples/FirstSteps/note1.tex
@@ -0,0 +1,22 @@
+% Sample file: note1.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document}
+It is of some concern to me that
+the terminology used in multi-section
+ math courses is not uniform.
+
+In several sections of the course on
+matrix theory, the term
+ ``hamiltonian-reduced'' is used.
+ I, personally, would rather call these ``hyper-simple.'' I
+invite others to comment on this problem.
+
+Of special concern to me is the terminology in the course
+by Prof.~Rudi Hochschwabauer.
+ Since his field is new, there is
+ no accepted
+terminology. It is imperative
+that we arrive at a satisfactory solution.
+\end{document}
diff --git a/info/examples/FirstSteps/note1b.tex b/info/examples/FirstSteps/note1b.tex
new file mode 100644
index 0000000000..4de05f5a2b
--- /dev/null
+++ b/info/examples/FirstSteps/note1b.tex
@@ -0,0 +1,22 @@
+% Sample file: note1b.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document}
+It is of some concern to me that
+the terminology used in multi-section
+ math courses is not uniform.
+
+In several sections of the course on
+matrix theory, the strange term
+ ``hamiltonian-reduced'' is used.
+ I, personally, would rather call these ``hyper-simple.'' I
+invite others to comment on this problem.
+
+Of special concern to me is the terminology in the course
+by Prof.~Hochschwabauer.
+ Since his field is new, there is
+ no accepted
+terminology. It is imperative
+that we arrive at a satisfactory solution.
+\end{document} \ No newline at end of file
diff --git a/info/examples/FirstSteps/note2.tex b/info/examples/FirstSteps/note2.tex
new file mode 100644
index 0000000000..7b218f21fa
--- /dev/null
+++ b/info/examples/FirstSteps/note2.tex
@@ -0,0 +1,14 @@
+% Sample file: note2.tex
+% Typeset with LaTeX format
+\documentclass{article}
+
+\begin{document}
+\begin{flushright}
+ \today
+\end{flushright}
+\textbf{From the desk of George Gr\"{a}tzer}\\[22pt]
+April~7--21 \emph{please} use my temporary e-mail address:
+\begin{center}
+ \texttt{George\_Gratzer@umanitoba.ca}
+\end{center}
+\end{document}
diff --git a/info/examples/FirstSteps/noteslug.tex b/info/examples/FirstSteps/noteslug.tex
new file mode 100644
index 0000000000..04d2f46307
--- /dev/null
+++ b/info/examples/FirstSteps/noteslug.tex
@@ -0,0 +1,22 @@
+% Sample file: noteslug.tex
+% Typeset with the LaTeX format
+\documentclass[draft]{article}
+
+\begin{document}
+It is of some concern to me that
+the terminology used in multi-section
+ math courses is not uniform.
+
+In several sections of the course on
+matrix theory, the strange term
+ ``hamiltonian-reduced'' is used.
+ I, personally, would rather call these ``hyper-simple.'' I
+invite others to comment on this problem.
+
+Of special concern to me is the terminology in the course
+by Prof.~Hochschwabauer.
+ Since his field is new, there is
+ no accepted
+terminology. It is imperative
+that we arrive at a satisfactory solution.
+\end{document} \ No newline at end of file
diff --git a/info/examples/FirstSteps/sampart.tex b/info/examples/FirstSteps/sampart.tex
new file mode 100644
index 0000000000..1186358245
--- /dev/null
+++ b/info/examples/FirstSteps/sampart.tex
@@ -0,0 +1,258 @@
+% Sample file: sampart.tex
+% The sample article for the amsart document class
+% Typeset with LaTeX format
+
+\documentclass{amsart}
+\usepackage{amssymb,latexsym}
+
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}
+\newtheorem{corollary}{Corollary}
+\newtheorem*{main}{Main~Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{definition}{Definition}
+
+\theoremstyle{remark}
+\newtheorem*{notation}{Notation}
+
+\numberwithin{equation}{section}
+
+\begin{document}
+\title[Complete-simple distributive lattices]
+ {A construction of complete-simple\\
+ distributive lattices}
+\author{George~A. Menuhin}
+\address{Computer Science Department\\
+ University of Winnebago\\
+ Winnebago, Minnesota 53714}
+\email{menuhin@ccw.uwinnebago.edu}
+\urladdr{http://math.uwinnebago.ca/homepages/menuhin/}
+\thanks{Research supported by the NSF under grant number
+~23466.}
+\keywords{Complete lattice, distributive lattice,
+complete congruence,
+ congruence lattice}
+\subjclass{Primary: 06B10; Secondary: 06D05}
+\date{March 15, 1999}
+\begin{abstract}
+ In this note we prove that there exist \emph{complete-simple distributive
+ lattices,} that is, complete distributive lattices in which there are
+ only two complete congruences.
+\end{abstract}
+
+\maketitle
+
+\section{Introduction}\label{S:intro}
+In this note we prove the following result:
+
+\begin{main}
+ There exists an infinite complete distributive lattice $K$ with only
+ the two trivial complete congruence relations.
+\end{main}
+
+\section{The $D^{\langle 2 \rangle}$ construction}\label{S:Ds}
+For the basic notation in lattice theory and universal algebra, see Ferenc~R.
+Richardson~\cite{fR82} and George~A. Menuhin~\cite{gM68}. We start with some
+definitions:
+
+\begin{definition}\label{D:prime}
+ Let $V$ be a complete lattice, and let $\mathfrak{p} = [u, v]$ be
+ an interval of $V$. Then $\mathfrak{p}$ is called
+ \emph{complete-prime} if the following three conditions are satisfied:
+ \begin{itemize}
+ \item[(1)] $u$ is meet-irreducible but $u$ is \emph{not}
+ completely meet-irreducible;
+ \item[(2)] $v$ is join-irreducible but $v$ is \emph{not}
+ completely join-irreducible;
+ \item[(3)] $[u, v]$ is a complete-simple lattice.
+ \end{itemize}
+\end{definition}
+
+Now we prove the following result:
+
+\begin{lemma}\label{L:ds}
+ Let $D$ be a complete distributive lattice satisfying
+ conditions~\textup{(1)} and~\textup{(2)}. Then
+ $D^{\langle 2 \rangle}$ is a sublattice of $D^{2}$;
+ hence $D^{\langle 2 \rangle}$ is a lattice, and
+ $D^{\langle 2 \rangle}$ is a complete distributive
+ lattice satisfying conditions~\textup{(1)} and \textup{(2)}.
+\end{lemma}
+
+\begin{proof}
+ By conditions~(1) and (2), $D^{\langle 2 \rangle}$ is a sublattice
+ of $D^{2}$. Hence, $D^{\langle 2 \rangle}$ is a lattice.
+
+ Since $D^{\langle 2 \rangle}$ is a sublattice of a distributive
+ lattice, $D^{\langle 2 \rangle}$ is a distributive lattice. Using
+ the characterization of standard ideals in Ernest~T. Moynahan~\cite{eM57},
+ $D^{\langle 2 \rangle}$ has a zero and a unit element,
+ namely, $\langle 0, 0 \rangle$ and $\langle 1, 1 \rangle$.
+ To show that $D^{\langle 2 \rangle}$ is complete, let
+ $\varnothing \ne A \subseteq D^{\langle 2 \rangle}$, and let
+ $a = \bigvee A$ in $D^{2}$. If
+ $a \in D^{\langle 2 \rangle}$, then
+ $a = \bigvee A$ in $D^{\langle 2 \rangle}$; otherwise, $a$
+ is of the form $\langle b, 1 \rangle$ for some
+ $b \in D$ with $b < 1$. Now $\bigvee A = \langle 1, 1\rangle$
+ in $D^{2}$ and the dual argument shows that $\bigwedge A$ also
+ exists in $D^{2}$. Hence $D$ is complete. Conditions~(1) and
+ (2) are obvious for $D^{\langle 2 \rangle}$.
+\end{proof}
+
+\begin{corollary}\label{C:prime}
+ If $D$ is complete-prime, then so is $D^{\langle 2 \rangle}$.
+\end{corollary}
+
+The motivation for the following result comes from Soo-Key Foo~\cite{sF90}.
+
+\begin{lemma}\label{L:ccr}
+ Let $\Theta$ be a complete congruence relation of
+ $D^{\langle 2 \rangle}$ such that
+ \begin{equation}\label{E:rigid}
+ \langle 1, d \rangle \equiv \langle 1, 1 \rangle \pmod{\Theta},
+ \end{equation}
+ for some $d \in D$ with $d < 1$. Then $\Theta = \iota$.
+\end{lemma}
+
+\begin{proof}
+ Let $\Theta$ be a complete congruence relation of
+ $D^{\langle 2 \rangle}$ satisfying \eqref{E:rigid}. Then $\Theta =
+\iota$.
+\end{proof}
+
+\section{The $\Pi^{*}$ construction}\label{S:P*}
+The following construction is crucial to our proof of the Main Theorem:
+
+\begin{definition}\label{D:P*}
+ Let $D_{i}$, for $i \in I$, be complete distributive lattices
+ satisfying condition~\textup{(2)}. Their $\Pi^{*}$ product is defined
+as
+ follows:
+ \[
+ \Pi^{*} ( D_{i} \mid i \in I ) = \Pi ( D_{i}^{-} \mid i \in I ) + 1;
+ \]
+ that is, $\Pi^{*} ( D_{i} \mid i \in I )$ is $\Pi ( D_{i}^{-} \mid
+ i \in I )$ with a new unit element.
+\end{definition}
+
+\begin{notation}
+ If $i \in I$ and $d \in D_{i}^{-}$, then
+ \[
+ \langle \dots, 0, \dots, \overset{i}{d}, \dots, 0, \dots \rangle
+ \]
+ is the element of $\Pi^{*} ( D_{i} \mid i \in I )$ whose $i$-th
+ component is $d$ and all the other components are $0$.
+\end{notation}
+
+See also Ernest~T. Moynahan \cite{eM57a}. Next we verify:
+
+\begin{theorem}\label{T:P*}
+ Let $D_{i}$, for $i \in I$, be complete distributive lattices
+ satisfying condition~\textup{(2)}. Let $\Theta$ be a complete
+congruence
+ relation on $\Pi^{*} ( D_{i} \mid i \in I )$. If there exist
+ $i \in I$ and $d \in D_{i}$ with $d < 1_{i}$ such that for
+ all $d \leq c < 1_{i}$,
+ \begin{equation}\label{E:cong1}
+ \langle \dots, 0, \dots,\overset{i}{d},
+ \dots, 0, \dots \rangle \equiv \langle \dots, 0, \dots,
+ \overset{i}{c}, \dots, 0, \dots \rangle \pmod{\Theta},
+ \end{equation}
+ then $\Theta = \iota$.
+\end{theorem}
+
+\begin{proof}
+ Since
+ \begin{equation}\label{E:cong2}
+ \langle \dots, 0, \dots, \overset{i}{d}, \dots, 0,
+ \dots \rangle \equiv \langle \dots, 0, \dots,
+ \overset{i}{c}, \dots, 0, \dots \rangle \pmod{\Theta},
+ \end{equation}
+ and $\Theta$ is a complete congruence relation, it follows from
+ condition~(3) that
+ \begin{align}\label{E:cong}
+ & \langle \dots, \overset{i}{d}, \dots, 0,
+ \dots \rangle \equiv\\
+ &\qquad \quad \bigvee ( \langle \dots, 0, \dots,
+ \overset{i}{c}, \dots, 0, \dots \rangle \mid d \leq c < 1 )
+ \equiv 1 \pmod{\Theta}. \notag
+ \end{align}
+
+ Let $j \in I$ for $j \neq i$, and let $a \in D_{j}^{-}$.
+ Meeting both sides of the congruence \eqref{E:cong2} with
+ $\langle \dots, 0, \dots, \overset{j}{a}, \dots, 0, \dots \rangle$,
+ we obtain
+ \begin{align}\label{E:comp}
+ 0 &= \langle \dots, 0, \dots, \overset{i}{d}, \dots, 0, \dots
+ \rangle \wedge \langle \dots, 0, \dots, \overset{j}{a}, \dots, 0,
+ \dots \rangle\\
+ &\equiv \langle \dots, 0, \dots, \overset{j}{a}, \dots, 0, \dots
+ \rangle \pmod{\Theta}. \notag
+ \end{align}
+ Using the completeness of $\Theta$ and \eqref{E:comp}, we get:
+ \[
+ 0 \equiv \bigvee ( \langle \dots, 0, \dots, \overset{j}{a},
+ \dots, 0, \dots \rangle \mid a \in D_{j}^{-} ) = 1 \pmod{\Theta},
+ \]
+ hence $\Theta = \iota$.
+\end{proof}
+
+\begin{theorem}\label{T:P*a}
+ Let $D_{i}$ for $i \in I$ be complete distributive lattices
+ satisfying conditions \textup{(2)} and \textup{(3)}. Then
+ $\Pi^{*} ( D_{i} \mid i \in I )$ also satisfies conditions \textup{(2)}
+ and \textup{(3)}.
+\end{theorem}
+
+\begin{proof}
+ Let $\Theta$ be a complete congruence on
+ $\Pi^{*} ( D_{i} \mid i \in I )$. Let $i \in I$. Define
+ \[
+ \widehat{D}_{i} = \{ \langle \dots, 0, \dots, \overset{i}{d},
+ \dots, 0, \dots \rangle \mid d \in D_{i}^{-} \} \cup \{ 1 \}.
+ \]
+ Then $\widehat{D}_{i}$ is a complete sublattice of
+ $\Pi^{*} ( D_{i} \mid i \in I )$, and $\widehat{D}_{i}$ is
+ isomorphic to $D_{i}$. Let $\Theta_{i}$ be the restriction of
+ $\Theta$ to $\widehat{D}_{i}$.
+
+ Since $D_{i}\) is complete-simple, so is $\widehat{D}_{i}$, and
+ hence $\Theta_{i}$ is $\omega$ or $\iota$. If
+ $\Theta_{i} = \rho$ for all $i \in I$, then
+ $\Theta = \omega$. If there is an $i \in I$, such that
+ $\Theta_{i} = \iota$, then $0 \equiv 1 \pmod{\Theta}$, hence
+ $\Theta = \iota$.
+\end{proof}
+
+The Main Theorem follows easily from Theorems~\ref{T:P*} and \ref{T:P*a}.
+
+\begin{thebibliography}{9}
+
+ \bibitem{sF90}
+ Soo-Key Foo, \emph{Lattice Constructions,} Ph.D. thesis, University
+ of Winnebago, Winnebago, MN, December, 1990.
+
+ \bibitem{gM68}
+ George~A. Menuhin, \emph{Universal Algebra,} D.~van Nostrand,
+ Princeton-Toronto-London-Mel\-bourne, 1968.
+
+ \bibitem{eM57}
+ Ernest~T. Moynahan, \emph{On a problem of M.H. Stone,} Acta Math.
+ Acad.Sci. Hungar. \textbf{8} (1957), 455--460.
+
+ \bibitem{eM57a}
+ \bysame, \emph{Ideals and congruence relations in lattices.~II,}
+ Magyar Tud. Akad. Mat. Fiz. Oszt. K\"{o}zl. \textbf{9} (1957),
+ 417--434 (Hungarian).
+
+ \bibitem{fR82}
+ Ferenc~R. Richardson, \emph{General Lattice Theory,} Mir, Moscow,
+ expanded and revised ed., 1982 (Russian).
+
+\end{thebibliography}
+\end{document}
+
diff --git a/info/examples/FirstSteps/sampart2.tex b/info/examples/FirstSteps/sampart2.tex
new file mode 100644
index 0000000000..27a24e3a88
--- /dev/null
+++ b/info/examples/FirstSteps/sampart2.tex
@@ -0,0 +1,252 @@
+% Sample file: sampart2.tex
+% The sample article for the amsart document class
+% with user-defined commands
+% Typeset with LaTeX format
+
+\documentclass{amsart}
+\usepackage{amssymb,latexsym}
+\usepackage{lattice}
+
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}
+\newtheorem{corollary}{Corollary}
+\newtheorem*{main}{Main~Theorem}
+\newtheorem{lemma}{Lemma}
+\newtheorem{proposition}{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{definition}{Definition}
+
+\theoremstyle{remark}
+\newtheorem*{notation}{Notation}
+
+\numberwithin{equation}{section}
+
+\newcommand{\Prodm}[2]{\gP(\,#1\mid#2\,)}
+ % product with a middle
+\newcommand{\Prodsm}[2]{\gP^{*}(\,#1\mid#2\,)}
+ % product * with a middle
+\newcommand{\vct}[2]{\vv<\dots,0,\dots,\overset{#1}{#2},%
+\dots,0,\dots>}% special vector
+\newcommand{\fp}{\F{p}}% Fraktur p
+\newcommand{\Ds}{D^{\langle2\rangle}}
+
+\begin{document}
+\title[Complete-simple distributive lattices]
+ {A construction of complete-simple\\
+ distributive lattices}
+\author{George~A. Menuhin}
+\address{Computer Science Department\\
+ University of Winnebago\\
+ Winnebago, Minnesota 23714}
+\email{menuhin@ccw.uwinnebago.edu}
+\urladdr{http://math.uwinnebago.ca/homepages/menuhin/}
+\thanks{Research supported by the NSF under grant number~23466.}
+\keywords{Complete lattice, distributive lattice, complete
+ congruence, congruence lattice}
+\subjclass{Primary: 06B10; Secondary: 06D05}
+\date{March 15, 1995}
+
+\begin{abstract}
+ In this note we prove that there exist \emph{complete-simple
+ distributive lattices,} that is, complete distributive
+ lattices in which there are only two complete congruences.
+\end{abstract}
+\maketitle
+
+\section{Introduction}\label{S:intro}
+In this note we prove the following result:
+
+\begin{main}
+ There exists an infinite complete distributive lattice
+ $K$ with only the two trivial complete congruence relations.
+\end{main}
+
+\section{The $\Ds$ construction}\label{S:Ds}
+For the basic notation in lattice theory and universal algebra,
+see Ferenc~R. Richardson~\cite{fR82} and George~A. Menuhin~\cite{gM68}.
+We start with some definitions:
+
+\begin{definition}\label{D:prime}
+ Let $V$ be a complete lattice, and let $\fp = [u, v]$ be
+ an interval of $V$. Then $\fp$ is called
+ \emph{complete-prime} if the following three conditions are satisfied:
+ \begin{enumerate}
+ \item[(1)] $u$ is meet-irreducible but $u$ is \emph{not}
+ completely meet-irreducible;
+ \item[(2)] $v$ is join-irreducible but $v$ is \emph{not}
+ completely join-irreducible;
+ \item[(3)] $[u, v]$ is a complete-simple lattice.
+ \end{enumerate}
+\end{definition}
+
+Now we prove the following result:
+
+\begin{lemma}\label{L:ds}
+ Let $D$ be a complete distributive lattice satisfying
+ conditions~\textup{(1)} and~\textup{(2)}.
+ Then $\Ds$ is a sublattice of $D^{2}$; hence $\Ds$ is
+ a lattice, and $\Ds$ is a complete distributive lattice
+ satisfying conditions~~\textup{(1)} and~~\textup{(2)}.
+\end{lemma}
+
+\begin{proof}
+ By conditions~(1) and (2), $\Ds$ is a sublattice of
+ $D^{2}$. Hence, $\Ds$ is a lattice.
+
+ Since $\Ds$ is a sublattice of a distributive lattice, $\Ds$ is
+ a distributive lattice. Using the characterization of
+ standard ideals in Ernest~T. Moynahan~\cite{eM57},
+ $\Ds$ has a zero and a unit element, namely,
+ $\vv<0, 0>$ and $\vv<1, 1>$. To show that $\Ds$ is
+ complete, let $\es \ne A \ci \Ds$, and let $a = \JJ A$
+ in $D^{2}$. If $a \in \Ds$, then
+ $a = \JJ A$ in $\Ds$; otherwise, $a$ is of the form
+ $\vv<b, 1>$ for some $b \in D$ with $b < 1$. Now
+ $\JJ A = \vv<1, 1>$ in $D^{2}$, and
+ the dual argument shows that $\MM A$ also exists in
+ $D^{2}$. Hence $D$ is complete. Conditions~(1) and (2)
+ are obvious for $\Ds$.
+\end{proof}
+
+\begin{corollary}\label{C:prime}
+ If $D$ is complete-prime, then so is $\Ds$.
+\end{corollary}
+
+The motivation for the following result comes from Soo-Key
+Foo~\cite{sF90}.
+
+\begin{lemma}\label{L:ccr}
+ Let $\gQ$ be a complete congruence relation of $\Ds$ such
+ that
+ \begin{equation}\label{E:rigid}
+ \vv<1, d> \equiv \vv<1, 1> \pod{\gQ},
+ \end{equation}
+ for some $d \in D$ with $d < 1$. Then $\gQ = \gi$.
+\end{lemma}
+
+\begin{proof}
+ Let $\gQ$ be a complete congruence relation of $\Ds$
+ satisfying \eqref{E:rigid}. Then $\gQ = \gi$.
+\end{proof}
+
+\section{The $\gP^{*}$ construction}\label{S:P*}
+The following construction is crucial to our proof of the
+Main~Theorem:
+
+\begin{definition}\label{D:P*}
+ Let $D_{i}$, for $i \in I$, be complete distributive
+ lattices satisfying condition~\tup{(2)}. Their $\gP^{*}$
+ product is defined as follows:
+ \[
+ \Prodsm{ D_{i} }{i \in I} = \Prodm{ D_{i}^{-} }{i \in I} +1;
+ \]
+ that is, $\Prodsm{ D_{i} }{i \in I}$ is
+ $\Prodm{ D_{i}^{-} }{i \in I}$ with a new unit element.
+\end{definition}
+
+\begin{notation}
+ If $i \in I$ and $d \in D_{i}^{-}$, then
+ \[
+ \vct{i}{d}
+ \]
+ is the element of $\Prodsm{ D_{i} }{i \in I}$ whose
+ $i$-th component is $d$ and all the other
+ components are $0$.
+\end{notation}
+
+See also Ernest~T. Moynahan~\cite{eM57a}. Next we verify:
+
+\begin{theorem}\label{T:P*}
+ Let $D_{i}$, for $i \in I$, be complete distributive
+ lattices satisfying condition~\tup{(2)}. Let $\gQ$ be a
+ complete congruence relation on
+ $\Prodsm{ D_{i} }{i \in I}$. If there exist
+ $i \in I$ and $d \in D_{i}$ with $d < 1_{i}$ such
+ that for all $d \leq c < 1_{i}$,
+ \begin{equation}\label{E:cong1}
+ \vct{i}{d} \equiv \vct{i}{c} \pod{\gQ},
+ \end{equation}
+ then $\gQ = \gi$.
+\end{theorem}
+
+\begin{proof}
+ Since
+ \begin{equation}\label{E:cong2}
+ \vct{i}{d} \equiv \vct{i}{c} \pod{\gQ},
+ \end{equation}
+ and $\gQ$ is a complete congruence relation, it follows
+ from condition~(3) that
+ \begin{align}\label{E:cong}
+ &\vct{i}{d} \equiv \notag\\
+ &\qq\q{\JJm{\vct{i}{c}}{d \leq c < 1}=1} \pod{\gQ}.
+ \end{align}
+ Let $j \in I$ for $j \neq i$, and let
+ $a \in D_{j}^{-}\). Meeting both sides of the congruence
+ \eqref{E:cong} with $\vct{j}{a}$, we obtain
+ \begin{align}\label{E:comp}
+ 0 &= \vct{i}{d} \mm \vct{j}{a}\\
+ &\equiv \vct{j}{a}\pod{\gQ}. \notag
+ \end{align}
+ Using the completeness of $\gQ$ and \eqref{E:comp}, we get:
+ \begin{equation}\label{E:cong3}
+ 0=\JJm{ \vct{j}{a} }{ a \in D_{j}^{-} } \equiv 1 \pod{\gQ},
+ \end{equation}
+ hence $\gQ = \gi$.
+\end{proof}
+
+\begin{theorem}\label{T:P*a}
+ Let $D_{i}$ for $i \in I$ be complete distributive
+ lattices satisfying
+ conditions~\tup{(2)} and \tup{(3)}. Then
+ $\Prodsm{ D_{i} }{i \in I}$ also satisfies
+ conditions~\tup{(2)} and \tup{(3)}.
+\end{theorem}
+
+\begin{proof}
+ Let $\gQ$ be a complete congruence on
+ $\Prodsm{ D_{i} }{i \in I}$. Let $i \in I$. Define
+ \begin{equation}\label{E:dihat}
+ \widehat{D}_{i} = \setm{ \vct{i}{d} }{ d \in D_{i}^{-} }
+ \uu \set{1}.
+ \end{equation}
+ Then $\widehat{D}_{i}$ is a complete sublattice of
+ $\Prodsm{ D_{i} }{i \in I}$, and $\widehat{D}_{i}$
+ is isomorphic to $D_{i}$. Let $\gQ_{i}$ be the
+ restriction of $\gQ$ to $\widehat{D}_{i}$. Since
+ $D_{i}$ is complete-simple, so is $\widehat{D}_{i}$,
+ hence $\gQ_{i}$ is $\go$ or $\gi$. If $\gQ_{i} = \go$
+ for all $i \in I$, then $\gQ = \go$.
+ If there is an $i \in I$, such that $\gQ_{i} = \gi$,
+ then $0 \equiv 1 \pod{\gQ}$, and hence $\gQ = \gi$.
+\end{proof}
+
+The Main Theorem follows easily from Theorems~\ref{T:P*} and
+\ref{T:P*a}.
+
+\begin{thebibliography}{9}
+
+ \bibitem{sF90}
+ Soo-Key Foo, \emph{Lattice Constructions,} Ph.D. thesis, University
+ of Winnebago, Winnebago, MN, December, 1990.
+
+ \bibitem{gM68}
+ George~A. Menuhin, \emph{Universal Algebra,} D.~van Nostrand,
+ Princeton-Toronto-London-Mel\-bourne, 1968.
+
+ \bibitem{eM57}
+ Ernest~T. Moynahan, \emph{On a problem of M.H. Stone,} Acta Math.
+ Acad.Sci. Hungar. \textbf{8} (1957), 455--460.
+
+ \bibitem{eM57a}
+ \bysame, \emph{Ideals and congruence relations in lattices.~II,}
+ Magyar Tud. Akad. Mat. Fiz. Oszt. K\"{o}zl. \textbf{9} (1957),
+ 417--434 (Hungarian).
+
+ \bibitem{fR82}
+ Ferenc~R. Richardson, \emph{General Lattice Theory,} Mir, Moscow,
+ expanded and revised ed., 1982 (Russian).
+
+\end{thebibliography}
+
+\end{document} \ No newline at end of file