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author | Karl Berry <karl@freefriends.org> | 2011-02-20 00:40:24 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2011-02-20 00:40:24 +0000 |
commit | 1dd9292b81ca92a5b6c5baec8bbdd192f17a0ebc (patch) | |
tree | d686bfbb0005b6b092206247c5f6fa0e40ba97b5 | |
parent | 4f69ba13b48d4c5143e6914991c448b8c36147b9 (diff) |
rm firststeps, no license info, examples from 1999 book
git-svn-id: svn://tug.org/texlive/trunk@21479 c570f23f-e606-0410-a88d-b1316a301751
23 files changed, 1 insertions, 1803 deletions
diff --git a/Master/texmf-dist/doc/latex/firststeps/Contents b/Master/texmf-dist/doc/latex/firststeps/Contents deleted file mode 100644 index ccfa66eefb0..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/Contents +++ /dev/null @@ -1,23 +0,0 @@ -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-dist/doc/latex/firststeps/article.tpl b/Master/texmf-dist/doc/latex/firststeps/article.tpl deleted file mode 100644 index 110b108671f..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/article.tpl +++ /dev/null @@ -1,94 +0,0 @@ -% 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-dist/doc/latex/firststeps/article2.tpl b/Master/texmf-dist/doc/latex/firststeps/article2.tpl deleted file mode 100644 index 3075530cd2e..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/article2.tpl +++ /dev/null @@ -1,100 +0,0 @@ -% 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-dist/doc/latex/firststeps/bibl.tpl b/Master/texmf-dist/doc/latex/firststeps/bibl.tpl deleted file mode 100644 index d7c40bb1e6c..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/bibl.tpl +++ /dev/null @@ -1,135 +0,0 @@ -% 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-dist/doc/latex/firststeps/gallery.tex b/Master/texmf-dist/doc/latex/firststeps/gallery.tex deleted file mode 100644 index 2dee9d3ff09..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/gallery.tex +++ /dev/null @@ -1,254 +0,0 @@ -% 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-dist/doc/latex/firststeps/ggamsart.tpl b/Master/texmf-dist/doc/latex/firststeps/ggamsart.tpl deleted file mode 100644 index 1f4a0458813..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/ggamsart.tpl +++ /dev/null @@ -1,112 +0,0 @@ -% 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-dist/doc/latex/firststeps/ggart.tpl b/Master/texmf-dist/doc/latex/firststeps/ggart.tpl deleted file mode 100644 index 15bd6718edc..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/ggart.tpl +++ /dev/null @@ -1,97 +0,0 @@ -% 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-dist/doc/latex/firststeps/ggart2.tpl b/Master/texmf-dist/doc/latex/firststeps/ggart2.tpl deleted file mode 100644 index f56c2f781cb..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/ggart2.tpl +++ /dev/null @@ -1,101 +0,0 @@ -% 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-dist/doc/latex/firststeps/intrart.tex b/Master/texmf-dist/doc/latex/firststeps/intrart.tex deleted file mode 100644 index 1f35c477230..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/intrart.tex +++ /dev/null @@ -1,127 +0,0 @@ -% 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-dist/doc/latex/firststeps/lattice.sty b/Master/texmf-dist/doc/latex/firststeps/lattice.sty deleted file mode 100644 index 2ebb04e90e9..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/lattice.sty +++ /dev/null @@ -1,122 +0,0 @@ -% 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-dist/doc/latex/firststeps/math.tex b/Master/texmf-dist/doc/latex/firststeps/math.tex deleted file mode 100644 index fc96b999eb3..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/math.tex +++ /dev/null @@ -1,21 +0,0 @@ -% 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-dist/doc/latex/firststeps/mathb.tex b/Master/texmf-dist/doc/latex/firststeps/mathb.tex deleted file mode 100644 index be97c541553..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/mathb.tex +++ /dev/null @@ -1,24 +0,0 @@ -% 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-dist/doc/latex/firststeps/note1.tex b/Master/texmf-dist/doc/latex/firststeps/note1.tex deleted file mode 100644 index e4425f67797..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/note1.tex +++ /dev/null @@ -1,22 +0,0 @@ -% 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-dist/doc/latex/firststeps/note1b.tex b/Master/texmf-dist/doc/latex/firststeps/note1b.tex deleted file mode 100644 index 4de05f5a2b6..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/note1b.tex +++ /dev/null @@ -1,22 +0,0 @@ -% 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-dist/doc/latex/firststeps/note2.tex b/Master/texmf-dist/doc/latex/firststeps/note2.tex deleted file mode 100644 index 7b218f21faf..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/note2.tex +++ /dev/null @@ -1,14 +0,0 @@ -% 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-dist/doc/latex/firststeps/noteslug.tex b/Master/texmf-dist/doc/latex/firststeps/noteslug.tex deleted file mode 100644 index 04d2f46307e..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/noteslug.tex +++ /dev/null @@ -1,22 +0,0 @@ -% 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-dist/doc/latex/firststeps/sampart.tex b/Master/texmf-dist/doc/latex/firststeps/sampart.tex deleted file mode 100644 index 1186358245a..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/sampart.tex +++ /dev/null @@ -1,258 +0,0 @@ -% 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-dist/doc/latex/firststeps/sampart2.tex b/Master/texmf-dist/doc/latex/firststeps/sampart2.tex deleted file mode 100644 index 27a24e3a882..00000000000 --- a/Master/texmf-dist/doc/latex/firststeps/sampart2.tex +++ /dev/null @@ -1,252 +0,0 @@ -% 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 diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds index 821e847a80f..81029821288 100755 --- a/Master/tlpkg/libexec/ctan2tds +++ b/Master/tlpkg/libexec/ctan2tds @@ -309,6 +309,7 @@ $Master = "$mydir/../.."; 'featpost', "&MAKEfeatpost", 'feynmf', "&MAKEfeynmf", 'findhyph', "&MAKEflatten", + 'firststeps', "die 'skipping, noinfo license, 1999 book examples'", 'fldigigal', "die 'skipping, per author request'", 'floatflt', "die 'skipping, nosell license'", 'fnlineno', "die 'skipping, use lineno'", diff --git a/Master/tlpkg/tlpsrc/collection-documentation-english.tlpsrc b/Master/tlpkg/tlpsrc/collection-documentation-english.tlpsrc index 49e0caba9a6..27d27bb7f1e 100644 --- a/Master/tlpkg/tlpsrc/collection-documentation-english.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-documentation-english.tlpsrc @@ -10,7 +10,6 @@ depend components-of-TeX depend comprehensive depend dtxtut depend first-latex-doc -depend firststeps depend free-math-font-survey depend gentle depend guide-to-latex diff --git a/Master/tlpkg/tlpsrc/firststeps.tlpsrc b/Master/tlpkg/tlpsrc/firststeps.tlpsrc deleted file mode 100644 index e69de29bb2d..00000000000 --- a/Master/tlpkg/tlpsrc/firststeps.tlpsrc +++ /dev/null diff --git a/Master/tlpkg/tlpsrc/scheme-gust.tlpsrc b/Master/tlpkg/tlpsrc/scheme-gust.tlpsrc index 9b135a35342..65a2106dca9 100644 --- a/Master/tlpkg/tlpsrc/scheme-gust.tlpsrc +++ b/Master/tlpkg/tlpsrc/scheme-gust.tlpsrc @@ -15,7 +15,6 @@ depend concrete depend cyklop depend dvidvi depend dviljk -depend firststeps depend gustprog depend impatient depend iwona diff --git a/Master/tlpkg/tlpsrc/scheme-tetex.tlpsrc b/Master/tlpkg/tlpsrc/scheme-tetex.tlpsrc index 96fed90fd01..10178b0ffc3 100644 --- a/Master/tlpkg/tlpsrc/scheme-tetex.tlpsrc +++ b/Master/tlpkg/tlpsrc/scheme-tetex.tlpsrc @@ -26,7 +26,6 @@ depend cmbright depend cweb depend eplain depend eulervm -depend firststeps depend gentle depend lshort-english depend mathmode |