doc/english/co-h

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diff --git a/Master/texmf-doc/doc/english/firststeps/Contents b/Master/texmf-doc/doc/english/firststeps/Contents
new file mode 100644
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--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/article.tpl b/Master/texmf-doc/doc/english/firststeps/article.tpl
new file mode 100644
index 00000000000..110b108671f
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/article2.tpl b/Master/texmf-doc/doc/english/firststeps/article2.tpl
new file mode 100644
index 00000000000..3075530cd2e
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/bibl.tpl b/Master/texmf-doc/doc/english/firststeps/bibl.tpl
new file mode 100644
index 00000000000..d7c40bb1e6c
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/gallery.tex b/Master/texmf-doc/doc/english/firststeps/gallery.tex
new file mode 100644
index 00000000000..2dee9d3ff09
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/ggamsart.tpl b/Master/texmf-doc/doc/english/firststeps/ggamsart.tpl
new file mode 100644
index 00000000000..1f4a0458813
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/ggart.tpl b/Master/texmf-doc/doc/english/firststeps/ggart.tpl
new file mode 100644
index 00000000000..15bd6718edc
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/ggart2.tpl b/Master/texmf-doc/doc/english/firststeps/ggart2.tpl
new file mode 100644
index 00000000000..f56c2f781cb
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/intrart.tex b/Master/texmf-doc/doc/english/firststeps/intrart.tex
new file mode 100644
index 00000000000..1f35c477230
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/lattice.sty b/Master/texmf-doc/doc/english/firststeps/lattice.sty
new file mode 100644
index 00000000000..2ebb04e90e9
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/math.tex b/Master/texmf-doc/doc/english/firststeps/math.tex
new file mode 100644
index 00000000000..fc96b999eb3
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/mathb.tex b/Master/texmf-doc/doc/english/firststeps/mathb.tex
new file mode 100644
index 00000000000..be97c541553
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/note1.tex b/Master/texmf-doc/doc/english/firststeps/note1.tex
new file mode 100644
index 00000000000..e4425f67797
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/note1b.tex b/Master/texmf-doc/doc/english/firststeps/note1b.tex
new file mode 100644
index 00000000000..4de05f5a2b6
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/note2.tex b/Master/texmf-doc/doc/english/firststeps/note2.tex
new file mode 100644
index 00000000000..7b218f21faf
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/noteslug.tex b/Master/texmf-doc/doc/english/firststeps/noteslug.tex
new file mode 100644
index 00000000000..04d2f46307e
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/sampart.tex b/Master/texmf-doc/doc/english/firststeps/sampart.tex
new file mode 100644
index 00000000000..1186358245a
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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/Master/texmf-doc/doc/english/firststeps/sampart2.tex b/Master/texmf-doc/doc/english/firststeps/sampart2.tex
new file mode 100644
index 00000000000..27a24e3a882
--- /dev/null
+++ b/Master/texmf-doc/doc/english/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