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| author | Karl Berry <karl@freefriends.org> | 2016-10-18 22:21:39 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2016-10-18 22:21:39 +0000 |
| commit | 183d733f04955370f0044aadd316aabde0ddeb6b (patch) | |
| tree | c2224d9219da7d08d29752b1a2e956b2afd2c5a6 /Master/texmf-dist/doc | |
| parent | 67067bf3dea16a3ad7a67d81602f2dbfbb1e1956 (diff) | |
latex2nemeth (18oct16)
git-svn-id: svn://tug.org/texlive/trunk@42300 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc')
5 files changed, 2296 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/support/latex2nemeth/README b/Master/texmf-dist/doc/support/latex2nemeth/README new file mode 100644 index 00000000000..f71953163cf --- /dev/null +++ b/Master/texmf-dist/doc/support/latex2nemeth/README @@ -0,0 +1,72 @@ +Latex2Nemeth: A Latex to Nemeth direct transcriber. + +Requires Java 1.7 or newer. + +Usage: latex2nemeth [options] texFile auxFile + +Options: + -e,--encoding <arg> The encoding table for Braille Mathematical symbols + in the form of a JSON file. If not specified, default + Nemeth table is used. + + -m,--mode <arg> The mode of the parser which controls the type of + the output Braille files. It can be either 'nemeth' + or 'pef'. The default mode is nemeth. + + -o <arg> The output prefix of the Braille files. It can also + be prefixed with a path to a specific directory. + The default value is the name of the TeX file. The program + generates an output file for each chapter in the input TeX + file. + +Usage examples: + A simple example: + latex2nemeth examples/mathtest.tex examples/mathtest.aux + + A more complicated example: + latex2nemeth examples/mathtest.tex examples/mathtest.aux -o examples/ch -m nemeth -e examples/nemeth.json + + An example with pictures: + latex2nemeth examples/mathpics.tex examples/mathpics.aux + +Notes: + +1. Input tex files must be in utf-8. If using another encoding (such as iso-8859-7) + run first LaTeX to produce the aux file and then convert the source.tex to utf-8 + with a command such as + + iconv -f iso8859-7 -t utf-8 source.tex > source-utf8.tex + + or using your editor. Now run latex2nemeth as above with + source-utf8.tex as the tex file and source.aux as the aux file. If errors are + produced you need to modify the source-utf8.tex at the line indicated. + Usually the errors have to do either with non supported shortcuts for macros + (in which case replace the shortcut with the true code) or with macros that + are irrelevant to the blind (in which case remove them). + +2. Braille/Nemeth output files are encoded in UTF-16. + Convert them to utf-8 with a command such as + + iconv -f utf-16 -t utf-8 source.nemeth > source-utf8.nemeth + + (This step will be eliminated in future releases and the output will be directly + in utf-8.) + +3. To emboss the output open the produced source-utf8.nemeth in LibreOffice + with the odt2braille plugin installed, open it as "Unicode UTF-8 encoded text" + and emboss as usually. + +4. Pictures are exported separately in text files. Currently only pstricks pictures are supported. + +The project page is at http://myria.math.aegean.gr/labs/dt/braille/index-en.html + +The source is available at http://latex2nemeth.sourceforge.net/ under the GPL3 or newer license. + +Please report issues related to erratic output to andpapas@aegean.gr +and issues related to the tex file handling/modifying to antonis.tsolomitis@gmail.com + +The project was supported by the Research Unit of the University of the Aegean (project 2625). + + + + diff --git a/Master/texmf-dist/doc/support/latex2nemeth/examples/mathpics.tex b/Master/texmf-dist/doc/support/latex2nemeth/examples/mathpics.tex new file mode 100644 index 00000000000..09b559eeed7 --- /dev/null +++ b/Master/texmf-dist/doc/support/latex2nemeth/examples/mathpics.tex @@ -0,0 +1,93 @@ +\documentclass[a4paper,12pt]{article}% hvoss +\usepackage{pstricks-add,fullpage} +\usepackage{pst-3dplot,pst-solides3d} +\usepackage{pst-plot,pst-intersect,mathtools} + +%\pagestyle{empty} +\begin{document} + +\begin{pspicture}(-0.5,-3.5)(2.5,3.5) +%\psaxes[]{->}(0,0)(-0.5,-3.5)(3,3.5) +\psline[linewidth=1mm]{->}(-1,0)(3,0) +\psline[linewidth=1mm]{->}(-.1,-3.5)(-.1,3.5) +\psparametricplot[algebraic, + linewidth=1.8mm,plotpoints=200,yMaxValue=3]{-2}{2}{t^2|t*(t^2-1)} +\rput[lb](2.5,1.3){$y^2=(x-1)^2 x$} +\psline[linewidth=1mm](-0.3,1)(.1,1) +\rput(-.7,1){$1$} +\psline[linewidth=1mm](-0.3,2)(.1,2) +\rput(-.7,2){$2$} +\psline[linewidth=1mm](-0.3,3)(.1,3) +\rput(-.7,3){$3$} +\psline[linewidth=1mm](-0.3,-1)(.1,-1) +\rput(-.9,-1){$-1$} +\psline[linewidth=1mm](-0.3,-2)(.1,-2) +\rput(-.9,-2){$-2$} +\psline[linewidth=1mm](-0.3,-3)(.1,-3) +\rput(-.9,-3){$-3$} +\rput(1,-.7){$1$} +\psline[linewidth=1mm](2,-.2)(2,.2) +\rput(2,-.7){$2$} +\end{pspicture} + +\vspace*{2cm} + + + + +\psset{Alpha=75,unit=4} +\begin{pspicture}(-0.6,-1)(2,2) +\psset{arrowscale=1.5,arrowinset=0,dotstyle=*,dotscale=1.5,drawCoor} +\pstThreeDCoor[linecolor=black,xMin=-0.5,xMax=2,yMin=-0.5,yMax=2,zMin=-0.5,zMax=2,linewidth=1mm,% +nameX=$x$,spotX=270,nameY=$y$,nameZ=$z$] +\pstThreeDLine[linewidth=1.8mm](1.5,0,0)(0,1.5,0) +\pstThreeDLine[linewidth=1.8mm](0,1.5,0)(0,0,1.5) +\pstThreeDLine[linewidth=1.8mm](0,0,1.5)(1.5,0,0) + +%\pstThreeDDot[linecolor=blue]( 1.5 ,0 , 0) +%\pstThreeDDot[linecolor=blue]( 0 ,1.5 , 0) +%\pstThreeDDot[linecolor=blue]( 0 ,0 , 1.5) +\pstThreeDPut(1.5,0.1,-0.1){$\sqrt{E_s}$} +\pstThreeDPut(0.2,1.65,0.3){$\sqrt{E_s}$} +\pstThreeDPut(0.1,.2,1.7){$\sqrt{E_s}$} +\end{pspicture} + +\newpage +%\vspace*{4cm} + +\psset{unit=0.3,viewpoint=20 20 20 rtp2xyz} +\hspace*{1cm}\begin{pspicture}(-4,-3)(4,8) +\psSolid[object=grille,base=-2 2 -2 2,linewidth=1mm] +\axesIIID[axisnames={x,y,z},linewidth=1mm](0,0,0)(3.5,3,3) +\defFunction[algebraic]{mydensity}(t) + {cos(t)} + {sin(t)} + {10*(t/8)*(1-(t/6.5))^4} +\psSolid[object=courbe,r=.01,range=-1.3 10.5,linewidth=0.1,resolution=360,linewidth=1.8mm, + function=mydensity,linecolor=black,incolor=yellow,,hue=0 1] +\rput(-2,-8){$(\cos(t),\sin(t),10\cdot (t/8)\cdot(1-(t/6.5))^4)$} +\end{pspicture} + + +\newpage + +\psset{linewidth=1mm} +\begin{pspicture}(-2,-2)(8,8) +\psaxes[labels=none,ticks=none]{->}(0,0)(-2,-2)(8,8)[$M$,-90][$Y$,0] +\psset{linewidth=1.8mm,algebraic} +\pssavepath{A}{\psplot{-0.5}{8}{4*(1-1.2^(-3*x+1))}} +\psline(-2,4.2)(8,4.2) \uput[90](5,4.4){$Y=\frac{A}{\alpha+d}$} +\pssavepath{B}{\psplot{-0.5}{8}{2^(-x/2+3)-2}} +\pssavepath[linestyle=none]{C}{\psplot{-0.5}{8}{0}} +\psintersect[name=D, showpoints]{A}{B}\uput{5mm}[-5](D1){$M_3^*,Y^*$} +\psintersect[name=E, showpoints]{A}{C}\uput{4mm}[-70](E1){$M_c$} +\psdot(4,0)\uput{4mm}[45](4,0){$M_c^*$} +\end{pspicture} + + + + + + + +\end{document} diff --git a/Master/texmf-dist/doc/support/latex2nemeth/examples/mathtest.tex b/Master/texmf-dist/doc/support/latex2nemeth/examples/mathtest.tex new file mode 100644 index 00000000000..299b799b1f0 --- /dev/null +++ b/Master/texmf-dist/doc/support/latex2nemeth/examples/mathtest.tex @@ -0,0 +1,253 @@ +\documentclass[twoside,a4paper,leqno,11pt]{book} +\usepackage[greek]{babel} +\usepackage[utf8x]{inputenc} + +\usepackage{srcltx} + +\usepackage{latexsym} + +\usepackage{amsmath} + +\usepackage{amssymb} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%% New theorems %%%%%%%%%%%%%%%%%%%%%%%% +\newtheorem{theorem}{Θεώρημα}[section] +\newtheorem{lemma}[theorem]{Λήμμα} +\newtheorem{proposition}[theorem]{Πρόταση} +\newtheorem{application}[theorem]{Εφαρμογή} +\newtheorem{corollary}[theorem]{Πόρισμα} +\newtheorem{definition}[theorem]{Ορισμός} +\newtheorem{exercise}[theorem]{Άσκηση} +\newtheorem{example}[theorem]{Παράδειγμα} +\newtheorem{examples}[theorem]{Παραδείγματα} +\newtheorem{problem}[theorem]{Πρόβλημα} +\newtheorem{remark}[theorem]{Παρατήρηση} +\newtheorem{remarks}[theorem]{Παρατηρήσεις} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%% Document starts %%%%%%%%%%%% +\begin{document} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\textbf{Απειροστικός Λογισμός ΙΙ} +\textbf{Πρόχειρες Σημειώσεις} +\textbf{Τμήμα Μαθηματικών} +\textbf{Πανεπιστήμιο Αθηνών} +\textbf{2010--11} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Υπακολουθίες και βασικές ακολουθίες} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\section{Υπακολουθίες} + +\begin{definition} \upshape Έστω $(a_n)$ μια ακολουθία πραγματικών αριθμών. +Η ακολουθία $(b_n)$ λέγεται \textit{υπακολουθία} της $(a_n)$ αν υπάρχει +γνησίως αύξουσα ακολουθία φυσικών αριθμών $k_1 < k_2< \cdots < k_n < +k_{n+1}<\cdots $ ώστε +$$b_n = a_{k_n}\;\hbox{ για κάθε }\;n \in {\mathbb N}.\leqno (1.1.1)$$ +Με άλλα λόγια, οι όροι της $(b_n)$ είναι οι $a_{k_1}, a_{k_2}, +\ldots, a_{k_n}, \ldots $, όπου $k_1 < k_2< \cdots < k_n < +k_{n+1}<\cdots$. Γενικά, μια ακολουθία έχει πολλές (συνήθως άπειρες +το πλήθος) διαφορετικές υπακολουθίες. +\end{definition} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Σειρές πραγματικών αριθμών} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\section{Σύγκλιση σειράς} + +\begin{definition} \upshape Έστω $(a_k)$ μια ακολουθία πραγματικών +αριθμών. Θεωρούμε την ακολουθία $$s_n=a_1+\cdots +a_n.\leqno +(2.1.1)$$ Δηλαδή, +$$s_1=a_1,\ s_2=a_1+a_2,\ s_3=a_1+a_2+a_3,\ \ldots \leqno (2.1.2)$$ +Το σύμβολο $\sum_{k=1}^{\infty }a_k$ είναι η \textit{σειρά} με +$k$-οστό όρο τον $a_k$. Το άθροισμα $s_n=\sum_{k=1}^na_k$ +είναι το \textit{$n$-οστό μερικό άθροισμα} της σειράς +$\sum_{k=1}^{\infty }a_k$ και η $(s_n)$ είναι η {\it +ακολουθία των μερικών αθροισμάτων} της σειράς $ \sum_{k = +1}^{\infty }a_k$. + +Αν η $(s_n)$ συγκλίνει σε κάποιον πραγματικό αριθμό $s$, τότε +γράφουμε +$$s = a_1 + a_2 + \cdots + a_n + \cdots\ \hbox{ή}\ s=\sum_{k=1}^{\infty }a_k\leqno (2.1.3)$$ +και λέμε ότι η σειρά \textit{συγκλίνει} (στο $s$), το δε όριο +$s=\lim_{n\to\infty }s_n$ είναι το \textit{άθροισμα} της σειράς. +\end{definition} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Ολοκλήρωμα \textlatin{Riemann}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Ο ορισμός του \textlatin{Darboux}} + +Σε αυτήν την παράγραφο δίνουμε τον ορισμό του ολοκληρώματος +\textlatin{Riemann} για \textbf{φραγμένες} συναρτήσεις που ορίζονται σε ένα +κλειστό διάστημα. Για μια φραγμένη συνάρτηση $f:[a,b]\to {\mathbb +R}$ με μη αρνητικές τιμές, θα θέλαμε το ολοκλήρωμα να δίνει το +εμβαδόν του χωρίου που περικλείεται ανάμεσα στο γράφημα της +συνάρτησης, τον οριζόντιο άξονα $y=0$ και τις κατακόρυφες ευθείες +$x=a$ και $x=b$. + +\begin{definition} \upshape (α) Έστω $[a,b]$ ένα κλειστό διάστημα. +\textbf{Διαμέριση} του $[a,b]$ θα λέμε κάθε πεπερασμένο υποσύνολο +$$P +=\{ x_0,x_1,\ldots ,x_n\}\leqno (4.1.1)$$ του $[a,b]$ με $x_0=a$ +και $x_n=b$. Θα υποθέτουμε πάντα ότι τα $x_k\in P $ είναι +διατεταγμένα ως εξής: +$$a=x_0<x_1<\cdots <x_k<x_{k+1}<\cdots <x_n=b.\leqno (4.1.2)$$ +Θα γράφουμε +$$P =\{ a=x_0<x_1<\cdots <x_n=b\}\leqno (4.1.3)$$ για να τονίσουμε αυτήν +ακριβώς τη διάταξη. Παρατηρήστε ότι από τον ορισμό, κάθε διαμέριση +$ P $ του $[a,b]$ περιέχει τουλάχιστον δύο σημεία: το $a$ και το +$b$ (τα άκρα του $[a,b]$). + + + + (β) Κάθε διαμέριση $ P =\{ a=x_0<x_1<\cdots <x_n=b\}$ +χωρίζει το $[a,b]$ σε $n$ υποδιαστήματα $[x_k,x_{k+1}]$, +$k=0,1,\ldots ,n-1$. Ονομάζουμε \textbf{πλάτος} της διαμέρισης $ P $ +το μεγαλύτερο από τα μήκη αυτών των υποδιαστημάτων. Δηλαδή, το +πλάτος της διαμέρισης ισούται με +$$\| P\|:=\max\{ x_1-x_0,x_2-x_1,\ldots ,x_n-x_{n-1}\}.\leqno (4.1.4)$$ +Παρατηρήστε ότι δεν απαιτούμε να ισαπέχουν τα $x_k$ (τα $n$ +υποδιαστήματα δεν έχουν απαραίτητα το ίδιο μήκος). + + + + (γ) Η διαμέριση $ P_1$ λέγεται \textbf{εκλέπτυνση} της $ P +$ αν $ P \subseteq P_1$, δηλαδή αν η $P_1$ προκύπτει από την $ P $ +με την προσθήκη κάποιων (πεπερασμένων το πλήθος) σημείων. Σε αυτήν +την περίπτωση λέμε επίσης ότι η $ P_1$ είναι \textit{λεπτότερη} από +την $ P $. + + + + (δ) Έστω $ P_1, P_2$ δύο διαμερίσεις του $[a,b]$. Η +\textbf{κοινή εκλέπτυνση} των $ P_1, P_2$ είναι η διαμέριση $ P = P_1\cup +P_2$. Εύκολα βλέπουμε ότι η $ P $ είναι διαμέριση του $[a,b]$ και +ότι αν $ P^{\prime }$ είναι μια διαμέριση λεπτότερη τόσο από την $ +P_1$ όσο και από την $ P_2$ τότε $ P^{\prime }\supseteq P $ +(δηλαδή, η $ P = P_1\cup P_2$ είναι η μικρότερη δυνατή διαμέριση +του $[a,b]$ που εκλεπτύνει ταυτόχρονα την $ P_1$ και την $ P_2$). +\end{definition} + + +\section{Ιδιότητες του ολοκληρώματος \textlatin{Riemann}} + +Σε αυτή την παράγραφο αποδεικνύουμε αυστηρά μερικές από τις πιο +βασικές ιδιότητες του ολοκληρώματος \textlatin{Riemann}. Οι αποδείξεις +των υπολοίπων είναι μια καλή άσκηση που θα σας βοηθήσει να +εξοικειωθείτε με τις διαμερίσεις, τα άνω και κάτω αθροίσματα κλπ. + +\begin{theorem} +Αν $f(x)=c$ για κάθε $x\in [a,b]$, τότε +$$\int_a^bf(x)dx =c(b-a).\leqno (4.4.1)$$ +\end{theorem} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Τεχνικές ολοκλήρωσης} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Σε αυτό το Κεφάλαιο περιγράφουμε, χωρίς ιδιαίτερη αυστηρότητα, τις +βασικές μεθόδους υπολογισμού ολοκληρωμάτων. Δίνεται μια συνάρτηση +$f$ και θέλουμε να βρούμε μια αντιπαράγωγο της $f$, δηλαδή μια +συνάρτηση $F$ με την ιδιότητα $F^{\prime }=f$. Τότε, +$$\int f(x)dx =F(x)+c.$$ + +\section{Ολοκλήρωση με αντικατάσταση} + +\subsection{Πίνακας στοιχειωδών ολοκληρωμάτων} + +Κάθε τύπος παραγώγισης $F^{\prime }(x)=f(x)$ μας δίνει έναν τύπο +ολοκλήρωσης: η $F$ είναι αντιπαράγωγος της $f$. Μπορούμε έτσι να +δημιουργήσουμε έναν πίνακα βασικών ολοκληρωμάτων, αντιστρέφοντας +τους τύπους παραγώγισης των πιο βασικών συναρτήσεων: +\begin{eqnarray*} +\int x^adx =\frac{x^{a+1}}{a+1},\qquad a\neq -1, && +\int\frac{1}{x}\,dx = \ln |x| +c\\ +\int e^xdx = e^x+c, && +\int\sin x\,dx = -\cos x+c\\ +\int\cos x\,dx = \sin x+c, && +\int\frac{1}{\cos^2x}\,dx = \tan x+c\\ +\int\frac{1}{\sin^2x}\,dx = -\cot x+c , && +\int\frac{1}{\sqrt{1-x^2}}\,dx = \arcsin x+c\\ +\int\frac{1}{1+x^2}\,dx =\arctan x+c. && +\end{eqnarray*} + + +\section{Ολοκλήρωση ρητών συναρτήσεων} + +Σε αυτή την παράγραφο περιγράφουμε μια μέθοδο με την οποία μπορεί +κανείς να υπολογίσει το αόριστο ολοκλήρωμα οποιασδήποτε ρητής +συνάρτησης +$$f(x)=\frac{p(x)}{q(x)}=\frac{a_nx^n+a_{n-1}x^{n-1}+\cdots ++a_1x+a_0}{b_mx^m+b_{m-1}x^{m-1}+\cdots +b_1x+b_0}.\leqno (6.3.1)$$ +Η πρώτη παρατήρηση είναι ότι μπορούμε πάντα να υποθέτουμε ότι $n<m$. +Αν ο βαθμός $n$ του αριθμητή $p(x)$ είναι μεγαλύτερος ή ίσος από τον +βαθμό $m$ του παρονομαστή $q(x)$, τότε διαιρούμε το $p(x)$ με το +$q(x)$: υπάρχουν πολυώνυμα $\pi (x)$ και $\upsilon (x)$ ώστε ο +βαθμός του $\upsilon (x)$ να είναι μικρότερος από $m$ και $$p(x)=\pi +(x)q(x)+\upsilon (x).\leqno (6.3.2)$$ Τότε, +$$f(x)=\frac{\pi (x)q(x)+\upsilon (x)}{q(x)}=\pi (x)+\frac{\upsilon +(x)}{q(x)}.\leqno (6.3.3)$$ Συνεπώς, για τον υπολογισμό του $\int +f(x)\,dx$ μπορούμε τώρα να υπολογίσουμε χωριστά το $\int \pi +(x)\,dx$ (απλό ολοκλήρωμα πολυωνυμικής συνάρτησης) και το +$\int\frac{\upsilon (x)}{q(x)}\,dx$ (ρητή συνάρτηση με την πρόσθετη +ιδιότητα ότι $\mathrm{deg}(\upsilon )<\mathrm{deg}(q)$). + +Υποθέτουμε λοιπόν στη συνέχεια ότι $f=p/q$ και $\mathrm{deg}(p)< +\mathrm{deg}(q)$. Μπορούμε επίσης να υποθέσουμε ότι $a_n=b_m=1$. +Χρησιμοποιούμε τώρα το γεγονός ότι κάθε πολυώνυμο αναλύεται σε +γινόμενο πρωτοβάθμιων και δευτεροβάθμιων όρων. Το $q(x)=x^m+\cdots ++b_1x+b_0$ γράφεται στη μορφή +$$q(x)=(x-\alpha_1)^{r_1}\cdots +(x-\alpha_k)^{r_k}(x^2+\beta_1x+\gamma_1)^{s_1}\cdots +(x^2+\beta_lx+\gamma_l)^{s_l}.\leqno (6.3.4)$$ Οι $\alpha_1,\ldots +,\alpha_k$ είναι οι πραγματικές ρίζες του $q(x)$ (και $r_j$ είναι η +πολλαπλότητα της ρίζας $\alpha_j$) ενώ οι όροι +$x^2+\beta_ix+\gamma_i$ είναι τα γινόμενα +$(x-z_i)(x-\overline{z_i})$ όπου $z_i$ οι μιγαδικές ρίζες του $q(x)$ +(και $s_i$ είναι η πολλαπλότητα της ρίζας $z_i$). Παρατηρήστε ότι +κάθε όρος της μορφής $x^2+\beta_ix+\gamma_i$ έχει αρνητική +διακρίνουσα. Επίσης, οι $k,s\geq 0$ και $r_1+\cdots +r_k+2s_1+\cdots ++2s_l=m$ (ο βαθμός του $q(x)$). + +Γράφουμε την $f(x)$ στη μορφή +$$f(x)=\frac{x^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0}{(x-\alpha_1)^{r_1}\cdots +(x-\alpha_k)^{r_k}(x^2+\beta_1x+\gamma_1)^{s_1}\cdots +(x^2+\beta_lx+\gamma_l)^{s_l}},\leqno (6.3.5)$$ και την ((αναλύουμε +σε απλά κλάσματα)): υπάρχουν συντελεστές $A_{jt}$, +$B_{it},\Gamma_{it}$ ώστε +\begin{eqnarray*} +f(x) &=& +\frac{A_{11}}{x-\alpha_1}+\frac{A_{12}}{(x-\alpha_1)^2}+\cdots ++\frac{A_{1r_1}}{(x-\alpha_1)^{r_1}}\\ +&& +\cdots \\ +&& +\frac{A_{k1}}{x-\alpha_k}+\frac{A_{k2}}{(x-\alpha_k)^2}+\cdots ++\frac{A_{kr_1}}{(x-\alpha_k)^{r_k}}\\ +&& ++\frac{B_{11}x+\Gamma_{11}}{x^2+\beta_1x+\gamma_1}+\frac{B_{12}x+\Gamma_{12}}{(x^2+\beta_1x+\gamma_1)^2}+\cdots ++\frac{B_{1s_1}x+\Gamma_{1s_1}}{(x^2+\beta_1x+\gamma_1)^{s_1}}\\ +&& +\cdots \\ +&& ++\frac{B_{l1}x+\Gamma_{l1}}{x^2+\beta_lx+\gamma_l}+\frac{B_{l2}x+\Gamma_{l2}}{(x^2+\beta_lx+\gamma_l)^2}+\cdots ++\frac{B_{ls_1}x+\Gamma_{ls_l}}{(x^2+\beta_lx+\gamma_l)^{s_l}}. +\end{eqnarray*} + + +\end{document} diff --git a/Master/texmf-dist/doc/support/latex2nemeth/examples/nemeth.json b/Master/texmf-dist/doc/support/latex2nemeth/examples/nemeth.json new file mode 100644 index 00000000000..6c395dedd4c --- /dev/null +++ b/Master/texmf-dist/doc/support/latex2nemeth/examples/nemeth.json @@ -0,0 +1,1204 @@ +{ + "letters": { + ".": "\u2832", + ",": "\u2802", + ";": "\u2822", + "'": "\u2804", + "«": "\u2826", + "»": "\u2834", + "(": "\u2837", + ")": "\u283e", + "[": "\u2808\u2837", + "]": "\u2808\u283e", + "\\}": "\u2828\u283e", + "\\{": "\u2828\u2837", + "\\_": "\u2824\u2824", + ":": "\u2806", + "?": "\u2838\u2826", + "!": "\u2816", + "*": "\u2808\u283c", + "@": "\u2808\u2801\u281e", + "\\euro": "\u2808\u2811", + "+": "\u282e", + "-": "\u2824", + "=": "\u282d", + "\\backslash": "\u2838\u2821", + "\\#": "\u2828\u283c", + "\\&": "\u282f", + "\\ ": " ", + "\\,": "\u2802", + "--": "\u2824\u2824", + "---": "\u2824\u2824\u2824", + "/": "\u280c", + "\\\n": " ", + " ": " ", + "\\quad": " ", + "\\qquad": " ", + "#": "\u283c", + "0": "\u2834", + "1": "\u2802", + "2": "\u2806", + "3": "\u2812", + "4": "\u2832", + "5": "\u2822", + "6": "\u2816", + "7": "\u2836", + "8": "\u2826", + "9": "\u2814", + "a": "\u2801", + "b": "\u2803", + "c": "\u2809", + "d": "\u2819", + "e": "\u2811", + "f": "\u280b", + "g": "\u281b", + "h": "\u2813", + "i": "\u280a", + "j": "\u281a", + "k": "\u2805", + "l": "\u2807", + "m": "\u280d", + "n": "\u281d", + "o": "\u2815", + "p": "\u280f", + "q": "\u281f", + "r": "\u2817", + "s": "\u280e", + "t": "\u281e", + "u": "\u2825", + "v": "\u2827", + "w": "\u283a", + "x": "\u282d", + "y": "\u283d", + "z": "\u2835", + "A": "\u2820\u2801", + "B": "\u2820\u2803", + "C": "\u2820\u2809", + "D": "\u2820\u2819", + "E": "\u2820\u2811", + "F": "\u2820\u280b", + "G": "\u2820\u281b", + "H": "\u2820\u2813", + "I": "\u2820\u280a", + "J": "\u2820\u281a", + "K": "\u2820\u2805", + "L": "\u2820\u2807", + "M": "\u2820\u280d", + "N": "\u2820\u281d", + "O": "\u2820\u2815", + "P": "\u2820\u280f", + "Q": "\u2820\u281f", + "R": "\u2820\u2817", + "S": "\u2820\u280e", + "T": "\u2820\u281e", + "U": "\u2820\u2825", + "V": "\u2820\u2827", + "W": "\u2820\u283a", + "X": "\u2820\u282d", + "Y": "\u2820\u283d", + "Z": "\u2820\u2835", + "e-grave": "\u282e", + "e-accent": "\u283f", + "EN": "\u2830", + "αι": "\u2823", + "Αι": "\u2828\u2823", + "αυ": "\u2821", + "Αυ": "\u2828\u2821", + "ει": "\u2829", + "Ει": "\u2828\u2829", + "ευ": "\u2831", + "Ευ": "\u2828\u2831", + "οι": "\u282a", + "Οι": "\u2828\u282a", + "ου": "\u2825", + "Ου": "\u2828\u2825", + "υι": "\u283b", + "Υι": "\u2828\u283b", + "ηυ": "\u2833", + "Ηυ": "\u2828\u2833", + "Ηύ": "\u2828\u2833", + "αί": "\u2823", + "ηύ": "\u2833", + "Υί": "\u2828\u283b", + "υί": "\u283b", + "Ού": "\u2828\u2825", + "ού": "\u2825", + "Οί": "\u2828\u282a", + "οί": "\u282a", + "εύ": "\u2831", + "Εύ": "\u2828\u2831", + "Εί": "\u2828\u2829", + "Αί": "\u2828\u2823", + "Αύ": "\u2828\u2821", + "αύ": "\u2821", + "εί": "\u2829", + "α": "\u2801", + "β": "\u2803", + "γ": "\u281b", + "δ": "\u2819", + "ε": "\u2811", + "ζ": "\u2835", + "η": "\u281c", + "θ": "\u2839", + "ι": "\u280a", + "ϊ": "\u280a", + "κ": "\u2805", + "λ": "\u2807", + "μ": "\u280d", + "ν": "\u281d", + "ξ": "\u282d", + "ο": "\u2815", + "π": "\u280f", + "ρ": "\u2817", + "σ": "\u280e", + "ς": "\u280e", + "τ": "\u281e", + "υ": "\u283d", + "ϋ": "\u283d", + "φ": "\u280b", + "χ": "\u2813", + "ψ": "\u282f", + "ω": "\u281a", + "ά": "\u2801", + "έ": "\u2811", + "ή": "\u281c", + "ί": "\u280a", + "ό": "\u2815", + "ύ": "\u283d", + "ώ": "\u281a", + "Α": "\u2828\u2801", + "Β": "\u2828\u2803", + "Γ": "\u2828\u281b", + "Δ": "\u2828\u2819", + "Ε": "\u2828\u2811", + "Ζ": "\u2828\u2835", + "Η": "\u2828\u281c", + "Θ": "\u2828\u2839", + "Ι": "\u2828\u280a", + "Κ": "\u2828\u2805", + "Λ": "\u2828\u2807", + "Μ": "\u2828\u280d", + "Ν": "\u2828\u281d", + "Ξ": "\u2828\u282d", + "Ο": "\u2828\u2815", + "Π": "\u2828\u280f", + "Ρ": "\u2828\u2817", + "Σ": "\u2828\u280e", + "Τ": "\u2828\u281e", + "Υ": "\u2828\u283d", + "Φ": "\u2828\u280b", + "Χ": "\u2828\u2813", + "Ψ": "\u2828\u282f", + "Ω": "\u2828\u281a", + "Ά": "\u2828\u2801", + "\u00b6": "\u2828\u2801", + "Έ": "\u2828\u2811", + "Ή": "\u2828\u281c", + "Ί": "\u2828\u280a", + "Ό": "\u2828\u2815", + "Ύ": "\u2828\u283d", + "Ώ": "\u2828\u281a", + "Ά": "\u2828\u2810\u2801", + "Έ": "\u2828\u2810\u2811", + "Ή": "\u2828\u2810\u281c", + "Ί": "\u2828\u2810\u280a", + "Ό": "\u2828\u2810\u2815", + "Ύ": "\u2828\u2810\u283d", + "Ώ": "\u2828\u2810\u281a", + "\\textbf": "\u2838", + "\\textbf-open": "\u2820\u2804\u2838", + "\\textbf-close": "\u2838\u2820\u2804", + "\\textit": "\u2828", + "\\textit-open": "\u2820\u2804\u2838", + "\\textit-close": "\u2838\u2820\u2804" + }, + "mathSymbols": { + "#": "\u283c", + "0": "\u2834", + "1": "\u2802", + "2": "\u2806", + "3": "\u2812", + "4": "\u2832", + "5": "\u2822", + "6": "\u2816", + "7": "\u2836", + "8": "\u2826", + "9": "\u2814", + "#0": "\u283c\u2834", + "#1": "\u283c\u2802", + "#2": "\u283c\u2806", + "#3": "\u283c\u2812", + "#4": "\u283c\u2832", + "#5": "\u283c\u2822", + "#6": "\u283c\u2816", + "#7": "\u283c\u2836", + "#8": "\u283c\u2826", + "#9": "\u283c\u2814", + "a": "\u2801", + "b": "\u2803", + "c": "\u2809", + "d": "\u2819", + "e": "\u2811", + "f": "\u280b", + "g": "\u281b", + "h": "\u2813", + "i": "\u280a", + "j": "\u281a", + "k": "\u2805", + "l": "\u2807", + "m": "\u280d", + "n": "\u281d", + "o": "\u2815", + "p": "\u280f", + "q": "\u281f", + "r": "\u2817", + "s": "\u280e", + "t": "\u281e", + "u": "\u2825", + "v": "\u2827", + "w": "\u283a", + "x": "\u282d", + "y": "\u283d", + "z": "\u2835", + "A": "\u2820\u2801", + "B": "\u2820\u2803", + "C": "\u2820\u2809", + "D": "\u2820\u2819", + "E": "\u2820\u2811", + "F": "\u2820\u280b", + "G": "\u2820\u281b", + "H": "\u2820\u2813", + "I": "\u2820\u280a", + "J": "\u2820\u281a", + "K": "\u2820\u2805", + "L": "\u2820\u2807", + "M": "\u2820\u280d", + "N": "\u2820\u281d", + "O": "\u2820\u2815", + "P": "\u2820\u280f", + "Q": "\u2820\u281f", + "R": "\u2820\u2817", + "S": "\u2820\u280e", + "T": "\u2820\u281e", + "U": "\u2820\u2825", + "V": "\u2820\u2827", + "W": "\u2820\u283a", + "X": "\u2820\u282d", + "Y": "\u2820\u283d", + "Z": "\u2820\u2835", + "Α": "\u2828\u2801", + "Β": "\u2828\u2803", + "Ε": "\u2828\u2811", + "Ζ": "\u2828\u2835", + "Η": "\u2828\u281c", + "Ι": "\u2828\u280a", + "Κ": "\u2828\u2805", + "Μ": "\u2828\u280d", + "Ν": "\u2828\u281d", + "Ξ": "\u2828\u282d", + "Ο": "\u2828\u2815", + "Ρ": "\u2828\u2817", + "Τ": "\u2828\u281e", + "Υ": "\u2828\u283d", + "Χ": "\u2828\u2813", + "α": "\u2801", + "β": "\u2803", + "γ": "\u281b", + "δ": "\u2819", + "ε": "\u2811", + "ζ": "\u2835", + "η": "\u281c", + "θ": "\u2839", + "ι": "\u280a", + "ϊ": "\u280a", + "κ": "\u2805", + "λ": "\u2807", + "μ": "\u280d", + "ν": "\u281d", + "ξ": "\u282d", + "ο": "\u2815", + "π": "\u280f", + "ρ": "\u2817", + "σ": "\u280e", + "ς": "\u280e", + "τ": "\u281e", + "υ": "\u283d", + "ϋ": "\u283d", + "φ": "\u280b", + "χ": "\u2813", + "ψ": "\u282f", + "ω": "\u281a", + "\\sqrt-b": "\u281c", + "\\sqrt-e": "\u283b", + "\\sqrt-level": "\u2828", + "\\radical-index": "\u2823", + "\\frac-b": "\u2839", + "\\frac-e": "\u283c", + "frac-level": "\u2820", + "\\frac-separator": "\u280c", + "\\superscript": "\u2818", + "\\sub": "\u2830", + "\\base": "\u2810", + "\\arccos": "\u2801\u2817\u2809\u2809\u2815\u280e", + "\\cot": "\u2809\u2815\u281e", + "\\exp": "\u2811\u282d\u280f", + "\\lim": "\u2807\u280a\u280d", + "\\min": "\u280d\u280a\u281d", + "\\tan": "\u281e\u2801\u281d", + "\\arcsin": "\u2801\u2817\u2809\u280e\u280a\u281d", + "\\coth": "\u2809\u2815\u281e\u2813", + "\\gcd": "\u281b\u2809\u2819", + "\\liminf": "\u2829\u2807\u280a\u280d", + "\\varliminf": "\u2829\u2807\u280a\u280d", + "\\Pr": "\u2820\u280f\u2817", + "\\tanh": "\u281e\u2801\u281d\u2813", + "\\arctan": "\u2801\u2817\u2809\u281e\u2801\u281d", + "\\csc": "\u2809\u280e\u2809", + "\\hom": "\u2813\u2815\u280d", + "\\limsup": "\u2823\u2807\u280a\u280d", + "\\varlimsup": "\u2823\u2807\u280a\u280d", + "\\sec": "\u280e\u2811\u2809", + "\\arg": "\u2801\u2817\u281b", + "\\deg": "\u2819\u2811\u281b", + "\\inf": "\u280a\u281d\u280b", + "\\ln": "\u2807\u281d", + "\\sin": "\u280e\u280a\u281d ", + "\\cos": "\u2809\u2815\u280e ", + "\\det": "\u2819\u2811\u281e", + "\\ker": "\u2805\u2811\u2817", + "\\log": "\u2807\u2815\u281b ", + "\\sinh": "\u280e\u280a\u281d\u2813 ", + "\\cosh": "\u2809\u2815\u280e\u2813 ", + "\\dim": "\u2819\u280a\u280d", + "\\lg": "\u2807\u281b", + "\\max": "\u280d\u2801\u282d", + "\\sup": "\u280e\u2825\u280f", + " ": " ", + ".": "\u2832", + "\\qquad": " ", + "\\quad": " ", + "\\;": " ", + "\\:": " ", + "\\,": " ", + "\\!": "", + "\\\n": " ", + ":": "\u2806", + "+": "\u282c", + "-": "\u2824", + "*": "\u2808\u283c", + "/": "\u280c", + "=": "\u2828\u2805", + "!": "\u2816", + "--": "\u2824\u2824", + "---": "\u2824\u2824\u2824", + "\\&": "\u2838\u282f", + ",": "\u2820", + ";": "\u2822", + "(": "\u2837", + ")": "\u283e", + "[": "\u2808\u2837", + "]": "\u2808\u283e", + "\\left(": "\u2820\u2837", + "\\right)": "\u2820\u283e", + "\\bigl(": "\u2820\u2837", + "\\Bigl(": "\u2820\u2837", + "\\biggl(": "\u2820\u2837", + "\\Biggl(": "\u2820\u2837", + "\\bigr)": "\u2820\u283e", + "\\Bigr)": "\u2820\u283e", + "\\biggr)": "\u2820\u283e", + "\\Biggr)": "\u2820\u283e", + "\\right.": "", + "\\left.": "", + "\\big": "\u2820", + "\\bigg": "\u2820", + "\\right|": "\u2820\u2833", + "\\left|": "\u2820\u2833", + "\\ ": " ", + "\\hspace*": " ", + "\\left[": "\u2808\u2820\u2837", + "\\right]": "\u2808\u2820\u283e", + "\\bigl[": "\u2808\u2820\u2837", + "\\Bigl[": "\u2808\u2820\u2837", + "\\biggl[": "\u2808\u2820\u2837", + "\\Biggl[": "\u2808\u2820\u2837", + "\\bigr]": "\u2808\u2820\u283e", + "\\Bigr]": "\u2808\u2820\u283e", + "\\biggr]": "\u2808\u2820\u283e", + "\\Biggr]": "\u2808\u2820\u283e", + "\\setminus": "\u2838\u2821", + "\\sum": "\u2828\u2820\u280e", + "\\bigcap": "\u2828\u2829", + "\\bigodot": "\u282b\u2809\u2838\u282b\u2821\u283b", + "\\int": "\u282e", + "\\oint": "\u282e\u2808\u282b\u2809\u283b", + "\\prod": "\u2828\u2820\u280f", + "\\bigcup": "\u2828\u282c", + "\\bigotimes": "\u282b\u2809\u2838\u282b\u2808\u2821\u283b", + "\\bigvee": "\u2808\u282c", + "\\bigwedge": "\u2808\u2829", + "\\coprod": "INVERTED PI", + "\\AA": "\u2808\u2820\u2801", + "\\aa": "\u2801\u2823\u2828\u2821", + "@": "\u2808\u2801\u281e", + "\\P": "\u2808\u2820\u280f", + "\\dag": "\u2838\u283b", + "\\ddag": "\u2838\u2838\u283b", + "\\S": "\u2808\u2820\u280e", + "\\textsection": "\u2808\u2820\u280e", + "\\textregistered": "\u282b\u2809\u2838\u282b\u2820\u2817\u283b", + "\\copyright": "\u282b\u2809\u2838\u282b\u2820\u2809\u283b", + "\\pounds": "\u2808\u2807", + "\\textstirling": "\u2808\u2807", + "\\SS": "\u2820\u280e\u2820\u280e", + "\\lq": "\u2820\u2826", + "\\leftquote": "\u2820\u2826", + "\\rq": "\u2834\u2804", + "\\rightquote": "\u2834\u2804", + "\\texttrademark": "\u2818\u2820\u281e\u2820\u280d", + "\\textasciicircum": "\u2838\u2823", + "\\&": "\u2838\u282f", + "\\_": "\u2824\u2824", + "\\textbackslash": "\u2838\u2821", + "\\cent": "\u2808\u2809", + "\\checked": "\u2808\u281c", + "\\dj": "\u2808\u282b", + "\\barlambda": "\u2808\u2828\u2807", + "\\planck": "\u2808\u2813", + "\\$": "\u2808\u280e", + "\\bigoplus": "\u282b\u2809\u2838\u282b\u282c\u283b", + "\\biguplus": "\u2828\u282c\u2838\u282b\u282c\u283b", + "\\bigl\\|": "\u2820\u2833", + "\\bigr\\|": "\u2820\u2833", + "\\bigl|": "\u2820\u2833", + "\\bigr|": "\u2820\u2833", + "\\Bigl|": "\u2820\u2833", + "\\Bigr|": "\u2820\u2833", + "\\Bigl\\|": "\u2820\u2833", + "\\Bigr\\|": "\u2820\u2833", + "\\biggl|": "\u2820\u2833", + "\\biggr|": "\u2820\u2833", + "\\Biggl|": "\u2820\u2833", + "\\Biggr|": "\u2820\u2833", + "\\uparrow": "\u282b\u2823\u2812\u2812\u2815", + "\\{": "\u2828\u2837", + "\\left\\{": "\u2828\u2820\u2837", + "\\bigl\\{": "\u2828\u2820\u2837", + "\\Bigl\\{": "\u2828\u2820\u2837", + "\\biggl\\{": "\u2828\u2820\u2837", + "\\Biggl\\{": "\u2828\u2820\u2837", + "\\lfloor": "\u2808\u2830\u2837", + "\\langle": "\u2828\u2828\u2837", + "\\left\\langle": "\u2828\u2828\u2820\u2837", + "\\bigl\\langle": "\u2828\u2828\u2820\u2837", + "\\Biggl\\langle": "\u2828\u2828\u2820\u2837", + "\\biggl\\langle": "\u2828\u2828\u2820\u2837", + "\\Biggl\\langle": "\u2828\u2828\u2820\u2837", + "|": "\u2833", + "\\bigm|": "\u2820\u2833", + "\\Bigm|": "\u2820\u2833", + "\\biggm|": "\u2820\u2833", + "\\Biggm|": "\u2820\u2833", + "\\Uparrow": "\u282b\u2823\u2836\u2836\u2815", + "\\}": "\u2828\u283e", + "\\right\\}": "\u2828\u2820\u283e", + "\\bigr\\}": "\u2828\u2820\u283e", + "\\Bigr\\}": "\u2828\u2820\u283e", + "\\biggr\\}": "\u2828\u2820\u283e", + "\\Biggr\\}": "\u2828\u2820\u283e", + "\\rfloor": "\u2808\u2830\u283e", + "\\rangle": "\u2828\u2828\u283e", + "\\right\rangle": "\u2828\u2828\u2820\u283e", + "\\bigr\rangle": "\u2828\u2828\u2820\u283e", + "\\Bigr\rangle": "\u2828\u2828\u2820\u283e", + "\\biggr\rangle": "\u2828\u2828\u2820\u283e", + "\\Biggr\rangle": "\u2828\u2828\u2820\u283e", + "\\|": "\u2833\u2833", + "\\left\\|": "\u2820\u2833\u2820\u2833", + "\\right\\|": "\u2820\u2833\u2820\u2833", + "\\big\\|": "\u2820\u2833\u2820\u2833", + "\\Big\\|": "\u2820\u2833\u2820\u2833", + "\\bigg\\|": "\u2820\u2833\u2820\u2833", + "\\Bigg\\|": "\u2820\u2833\u2820\u2833", + "\\big(": "\u2820\u2837", + "\\big)": "\u2820\u283e", + "\\big\\{": "\u2828\u2820\u2837", + "\\big\\}": "\u2820\u2833\u2820\u2833", + "\\bigg(": "\u2820\u2837", + "\\bigg)": "\u2820\u283e", + "\\bigg\\{": "\u2828\u2820\u2837", + "\\bigg\\}": "\u2820\u2833\u2820\u2833", + "\\big|": "\u2820\u2833\u2820\u2833", + "\\bigg|": "\u2820\u2833\u2820\u2833", + "\\downarrow": "\u282b\u2829\u2812\u2812\u2815", + "\\updownarrow": "\u282b\u2823\u282a\u2812\u2812\u2815", + "\\lceil": "\u2808\u2818\u2837", + "\\Downarrow": "\u282b\u2829\u2836\u2836\u2815", + "\\Updownarrow": "\u282b\u2829\u282a\u2836\u2836\u2815", + "\\rceil": "\u2808\u2818\u283e", + "\\backslash": "\u2838\u2821", + "\\ulcorner": "\u2808\u2818\u2837", + "\\left\\ulcorner": "\u2808\u2818\u2820\u2837", + "\\bigl\\ulcorner": "\u2808\u2818\u2820\u2837", + "\\Bigl\\ulcorner": "\u2808\u2818\u2820\u2837", + "\\biggl\\ulcorner": "\u2808\u2818\u2820\u2837", + "\\Biggl\\ulcorner": "\u2808\u2818\u2820\u2837", + "\\urcorner": "\u2808\u2818\u283e", + "\\right\\urcorner": "\u2808\u2818\u2820\u283e", + "\\bigr\\urcorner": "\u2808\u2818\u2820\u283e", + "\\Bigr\\urcorner": "\u2808\u2818\u2820\u283e", + "\\biggr\\urcorner": "\u2808\u2818\u2820\u283e", + "\\Biggr\\urcorner": "\u2808\u2818\u2820\u283e", + "\\llcorner": "\u2808\u2830\u2837", + "\\left\\llcorner": "\u2808\u2830\u2820\u2837", + "\\bigl\\llcorner": "\u2808\u2830\u2820\u2837", + "\\Bigl\\llcorner": "\u2808\u2830\u2820\u2837", + "\\biggl\\llcorner": "\u2808\u2830\u2820\u2837", + "\\Biggl\\llcorner": "\u2808\u2830\u2820\u2837", + "\\lrcorner": "\u2808\u2830\u283e", + "\\right\\lrcorner": "\u2808\u2830\u2820\u283e", + "\\bigr\\lrcorner": "\u2808\u2830\u2820\u283e", + "\\Bigr\\lrcorner": "\u2808\u2830\u2820\u283e", + "\\biggr\\lrcorner": "\u2808\u2830\u2820\u283e", + "\\Biggr\\lrcorner": "\u2808\u2830\u2820\u283e", + "\\alpha": "\u2828\u2801", + "\\epsilon": "\u2828\u2811", + "\\theta": "\u2828\u2839", + "\\lambda": "\u2828\u2807", + "\\varrho": "\u2828\u2808\u2817", + "\\upsilon": "\u2828\u2825", + "\\psi": "\u2828\u283d", + "\\Gamma": "\u2828\u2820\u281b", + "\\Xi": "\u2828\u2820\u282d", + "\\Phi": "\u2828\u2820\u280b", + "\\beta": "\u2828\u2803", + "\\varepsilon": "\u2828\u2808\u2811", + "\\vartheta": "\u2828\u2808\u2839", + "\\mu": "\u2828\u280d", + "\\pi": "\u2828\u280f", + "\\sigma": "\u2828\u280e", + "\\phi": "\u2828\u280b", + "\\omega": "\u2828\u283a", + "\\Delta": "\u2828\u2820\u2819", + "\\Pi": "\u2828\u2820\u280f", + "\\Psi": "\u2828\u2820\u283d", + "\\gamma": "\u2828\u281b", + "\\zeta": "\u2828\u2835", + "\\iota": "\u2828\u280a", + "\\nu": "\u2828\u281d", + "\\varpi": "\u2828\u2808\u280f", + "\\varsigma": "\u2828\u2808\u280e", + "\\varphi": "\u2828\u2808\u280b", + "\\Theta": "\u2828\u2820\u2839", + "\\Sigma ": "\u2828\u2820\u280e", + "\\Omega": "\u2828\u2820\u283a", + "\\delta": "\u2828\u2819", + "\\eta": "\u2828\u2831", + "\\kappa": "\u2828\u2805", + "\\xi": "\u2828\u282d", + "\\rho": "\u2828\u2817", + "\\tau": "\u2828\u281e", + "\\chi": "\u2828\u282f", + "\\Lambda": "\u2828\u2820\u2807", + "\\Upsilon": "\u2828\u2820\u2825", + "\\digamma": "\u2828\u2827", + "\\varkappa": "\u2828\u2808\u2805", + "\\beth": "\u2820\u2820\u2827", + "\\daleth": "\u2820\u2820\u2819", + "\\gimel": "\u2820\u2820\u281b", + "\\stigma": "\u2828\u282e", + "\\Stigma": "\u2828\u2820\u282e", + "\\qoppa": "\u2828\u281f", + "\\sampi": "\u2828\u2809", + "\\Sampi ": "\u2828\u2820\u2809", + "\\Qoppa": "\u2828\u2820\u281f", + "\\pm": "\u282c\u2824", + "\\mp": "\u2824\u282c", + "\\times": "\u2808\u2821", + "\\div": "\u2828\u280c", + "\\ast": "\u2808\u283c", + "\\star": "\u282b\u280e", + "\\circ": "\u2828\u2821", + "\\bullet": "\u2838\u2832", + "\\cdot": "\u2821", + "\\cap": "\u2828\u2829", + "\\cup": "\u2828\u282c", + "\\uplus": "\u2828\u282c\u2838\u282b\u282c\u283b", + "\\vee": "\u2808\u282c", + "\\wedge": "\u2808\u2829", + "\\diamond": "\u282b\u2819", + "\\bigtriangleup": "\u282b\u281e", + "\\bigtriangledown": "\u2828\u282b", + "\\oplus": "\u282b\u2809\u2838\u282b\u282c\u283b", + "\\ominus": "\u282b\u2809\u2838\u282b\u2824\u283b", + "\\otimes": "\u282b\u2809\u2838\u282b\u2808\u2821\u283b", + "\\oslash": "\u282b\u2809\u2838\u282b\u2814\u283b", + "\\odot": "\u282b\u2809\u2838\u282b\u2821\u283b", + "\\bigcirc": "\u282b\u2809", + "\\dagger": "\u2838\u283b", + "\\ddagger": "\u2838\u2838\u283b", + "\\amalg": "????", + "\\dotplus": "\u2810\u282c\u2823\u2821\u283b", + "\\Cup": "\u2828\u282c\u2838\u282b\u2828\u282c\u283b", + "\\doublebarwedge": "\u2828\u2805\u2808\u2829", + "\\boxdot": "\u282b\u2832\u2838\u282b\u2821\u283b", + "\\circleddash": "\u282b\u2809\u2838\u282b\u2824\u283b", + "\\centerdot": "\u2821", + "\\smallsetminus": "\u2838\u2821", + "\\barwedge": "\u2831\u2808\u2829", + "\\boxminus": "\u282b\u2832\u2838\u282b\u2831\u283b", + "\\boxplus": "\u282b\u2832\u2838\u282b\u282c\u283b", + "\\circledast": "\u282b\u2809\u2838\u282b\u2808\u283c\u283b", + "\\intercal": "\u282b\u2823\u2812\u2812\u2833", + "\\Cap": "\u2828\u2829\u2838\u282b\u2828\u2829\u283b", + "\\veebar": "\u2808\u282c\u2831", + "\\boxtimes": "\u282b\u2832\u2838\u282b\u2808\u2821\u283b", + "\\divideontimes": "\u2808\u2821\u2838\u282b\u2828\u280c\u283b", + "\\circledcirc": "\u282b\u2809\u2838\u282b\u2828\u2821\u283b", + "\\leftarrow": "\u282b\u282a", + "\\Leftarrow": "\u282b\u282a\u2836\u2836", + "\\rightarrow": "\u282b\u2815", + "\\to": "\u282b\u2815", + "\\Rightarrow": "\u282b\u2836\u2836\u2815", + "\\leftrightarrow": "\u282b\u282a\u2812\u2812\u2815", + "\\Leftrightarrow": "\u282b\u282a\u2836\u2836\u2815", + "\\mapsto": "\u282b\u2833\u2812\u2815", + "\\hookleftarrow": "\u282b\u282a\u2812\u2812\u2808\u283d", + "\\leftharpoonup": "\u282b\u2808\u282a\u2812\u2812", + "\\leftharpoondown": "\u282b\u2820\u282a\u2812\u2812", + "\\leadsto": "\u282b\u2814\u2812\u2822\u2815", + "\\longleftarrow": "\u282b\u282a\u2812\u2812", + "\\Longleftarrow": "\u282b\u282a\u2812\u2812", + "\\longrightarrow": "\u282b\u2812\u2812\u2815", + "\\Longrightarrow": "\u282b\u282a\u2836\u2836", + "\\longleftrightarrow": "\u282b\u282a\u2812\u2812\u2815", + "\\Longleftrightarrow": "\u282b\u282a\u2836\u2836\u2815", + "\\longmapsto": "\u282b\u2833\u2812\u2812\u2815", + "\\hookrightarrow": "\u282b\u2808\u282f\u2812\u2812\u2815", + "\\rightharpoonup": "\u282b\u2812\u2812\u2808\u2815", + "\\rightharpoondown": "\u282b\u2812\u2812\u2820\u2815", + "\\uparrow": "\u282b\u2823\u2812\u2812\u2815", + "\\Uparrow": "\u282b\u2823\u2836\u2836\u2815", + "\\downarrow": "\u282b\u2829\u2812\u2812\u2815", + "\\Downarrow": "\u282b\u2829\u2836\u2836\u2815", + "\\updownarrow": "\u282b\u2823\u282a\u2812\u2812\u2815", + "\\Updownarrow": "\u282b\u2823\u282a\u2836\u2836\u2815", + "\\nearrow": "\u282b\u2818\u2812\u2812\u2815", + "\\searrow": "\u282b\u2830\u2812\u2812\u2815", + "\\swarrow": "\u282b\u2830\u282a\u2812\u2812", + "\\nwarrow": "\u282b\u2818\u282a\u2812\u2812", + "\\leftrightarrows": "\u282b\u282a\u2812\u2812\u282b\u2812\u2812\u2815", + "\\leftarrowtail": "\u282b\u282a\u2812\u2812\u282a", + "\\curvearrowleft": "\u282b\u2822\u2814\u2815", + "\\upuparrows": "\u282b\u2823\u2812\u2812\u2815\u2810\u282b\u2823\u2812\u2812\u2815", + "\\multimap": "\u282b\u2812\u2812\u2828\u2821", + "\\rightleftarrows": "\u282b\u2812\u2812\u2815\u282b\u282a\u2812\u2812", + "\\twoheadrightarrow": "\u282b\u2812\u2812\u2815\u2815", + "\\rightleftharpoons": "\u282b\u2812\u2812\u2808\u2815\u282b\u2820\u282a\u2812\u2812", + "\\downharpoonright": "\u282b\u2829\u2812\u2812\u2808\u2815", + "\\Lleftarrow": "\u282b\u282a\u283f\u283f", + "\\circlearrowleft": "\u282b\u2809\u2838\u282b\u282a\u283b", + "\\upharpoonleft": "\u282b\u2823\u2812\u2812\u2808\u2815", + "\\leftrightsquigarrow": "\u282b\u282a\u2814\u2822\u2814\u2815", + "\\rightrightarrows": "\u282b\u2812\u2812\u2815\u282b\u2812\u2812\u2815", + "\\curvearrowright": "\u282b\u282a\u2822\u2814", + "\\downdownarrows": "\u282b\u2829\u2812\u2812\u2815\u2810\u282b\u2829\u2812\u2812\u2815", + "\\rightsquigarrow": "\u282b\u2814\u2822\u2814\u2815", + "\\rightarrowtail": "\u282b\u2815\u2812\u2812\u2815", + "\\leftleftarrows": "\u282b\u282a\u2812\u2812\u282b\u282a\u2812\u2812", + "\\twoheadleftarrow": "\u282b\u282a\u282a\u2812\u2812", + "\\leftrightharpoons": "\u282b\u2820\u282a\u2812\u2812\u282b\u2812\u2812\u2808\u2815", + "\\downharpoonleft": "\u282b\u2829\u2812\u2812\u2820\u2815", + "\\circlearrowright": "\u282b\u2809\u2838\u282b\u2815\u283b", + "\\upharpoonright": "\u282b\u2823\u2812\u2812\u2820\u2815", + "\\Rrightarrow": "\u282b\u283f\u283f\u2815", + "\\nleftarrow": "\u280c\u282b\u282a", + "\\nRightarrow": "\u280c\u282b\u2836\u2836\u2815", + "\\nrightarrow": "\u280c\u282b\u2815", + "\\nleftrightarrow": "\u280c\u282b\u282a\u2812\u2812\u2815", + "\\nLeftarrow": "\u280c\u282b\u282a\u2836\u2836", + "\\nLeftrightarrow": "\u280c\u282b\u282a\u2836\u2836\u2815", + "\\leq": "\u2810\u2805\u2831", + "\\le": "\u2810\u2805\u2831", + "\\prec": "\u2828\u2810\u2805", + "\\preceq": "\u2828\u2810\u2805\u2831", + "\\ll": "\u2810\u2805\u2808\u2810\u2805\u283b", + "\\subset": "\u2838\u2810\u2805", + "\\subseteq": "\u2838\u2810\u2805\u2831", + "\\in": "\u2808\u2811", + "\\vdash": "\u282b\u2833\u2812\u2812", + "\\geq": "\u2828\u2802\u2831", + "\\succ": "\u2828\u2828\u2802", + "\\succeq": "\u2828\u2828\u2802\u2831", + "\\gg": "\u2828\u2802\u2808\u2828\u2802\u283b", + "\\supset": "\u2838\u2828\u2802", + "\\supseteq": "\u2838\u2828\u2802\u2831", + "\\ni": "\u2808\u2822", + "\\dashv": "\u282b\u2812\u2812\u2833", + "\\equiv": "\u2838\u2807", + "\\sim": "\u2808\u2831", + "\\simeq": "\u2808\u2831\u2831", + "\\asymp": "\u282b\u2801\u282b\u2804", + "\\approx": "\u2808\u2831\u2808\u2831", + "\\cong": "\u2808\u2831\u2828\u2805", + "\\neq": "\u280c\u2828\u2805", + "\\ne": "\u280c\u2828\u2805", + "\\not": "\u280c", + "\\doteq": "\u2810\u2828\u2805\u2823\u2821\u283b", + "\\propto": "\u2838\u283f", + "<": "\u2810\u2805", + "\\models": "\u282b\u2833\u2836\u2836", + "\\perp": "\u282b\u280f", + "\\mid": "\u2833", + "\\parallel": "\u282b\u2807", + "\\smile": "\u282b\u2804", + "\\frown": "\u282b\u2801", + ">": "\u2828\u2802", + "\\leqq": "\u2810\u2805\u2828\u2805", + "\\lesssim": "\u2810\u2805\u2808\u2831", + "\\lessdot": "\u2810\u2805\u2838\u282b\u2821\u283b", + "\\lesseqgtr": "\u2810\u2805\u2831\u2828\u2802", + "\\precsim": "\u2828\u2810\u2805\u2808\u2831", + "\\smallsmile": "\u282b\u2804", + "\\Bumpeq": "\u2808\u2823\u2820\u2823", + "\\eqslantgtr": "\u2831\u2828\u2802", + "\\gtrdot": "\u2828\u2802\u2838\u282b\u2821\u283b", + "\\gtreqless": "\u2828\u2802\u2831\u2810\u2805", + "\\circeq ": "\u2810\u2828\u2805\u2823\u2828\u2821\u283b", + "\\thickapprox": "\u2838\u2808\u2831\u2838\u2808\u2831", + "\\succsim": "\u2828\u2828\u2802\u2808\u2831", + "\\shortparallel": "\u282b\u2807", + "\\varpropto": "\u2838\u283f", + "\\backepsilon": "\u2808\u2822", + "\\leqslant": "\u2810\u2805\u2831", + "\\lessapprox": "\u2810\u2805\u2808\u2831\u2808\u2831", + "\\lll": "\u2810\u2805\u2808\u2810\u2805\u2808\u2810\u2805\u283b", + "\\lesseqqgtr": "\u2810\u2805\u2828\u2805\u2828\u2802", + "\\subseteqq": "\u2838\u2810\u2805\u2828\u2805", + "\\precapprox": "\u2828\u2810\u2805\u2808\u2831\u2808\u2831", + "\\vDash": "\u282b\u2833\u2836\u2836", + "\\smallfrown": "\u282b\u2801", + "\\geqq": "\u2828\u2802\u2828\u2805", + "\\gtrsim": "\u2828\u2802\u2808\u2831", + "\\ggg": "\u2828\u2802\u2808\u2828\u2802\u2808\u2828\u2802\u283b", + "\\gtreqqless": "\u2828\u2802\u2828\u2805\u2810\u2805", + "\\triangleq": "\u2810\u2828\u2805\u2823\u282b\u281e\u283b", + "\\supseteqq": "\u2838\u2828\u2802\u2828\u2805", + "\\succapprox": "\u2828\u2828\u2802\u2808\u2831\u2808\u2831", + "\\Vdash": "\u282b\u2833\u2833\u2812\u2812", + "\\blacktriangleleft": "\u282b\u2838", + "\\blacktriangleright": "\u282b\u2838", + "\\eqslantless": "\u2831\u2810\u2805", + "\\approxeq": "\u2808\u2831\u2808\u2831\u2831", + "\\lessgtr": "\u2810\u2805\u2828\u2802", + "\\doteqdot": "\u2810\u2828\u2805\u2829\u2821\u2823\u2821\u283b", + "\\Subset": "\u2838\u2810\u2805\u2838\u282b\u2838\u2810\u2805\u283b", + "\\Vvdash": "\u282b\u2833\u2833\u2833\u2812\u2812", + "\\geqslant": "\u2828\u2802\u2831", + "\\gtrapprox": "\u2828\u2802\u2808\u2831\u2808\u2831", + "\\gtrless": "\u2828\u2802\u2810\u2805", + "\\eqcirc ": "\u2828\u2821\u2808\u2828\u2805\u283b", + "\\thicksim": "\u2838\u2808\u2831", + "\\Supset": "\u2838\u2828\u2802\u2838\u282b\u2838\u2828\u2802\u283b", + "\\shortmid": "\u2833", + "\\therefore": "\u2820\u2821", + "\\because": "\u2808\u280c", + "\\nless": "\u280c\u2810\u2805", + "\\nleqq": "\u280c\u2810\u2805\u2828\u2805", + "\\nprec": "\u280c\u2828\u2810\u2805", + "\\precnapprox": "\u280c\u2828\u2810\u2805\u2808\u2831\u2808\u2831", + "\\nmid": "\u280c\u2833", + "\\subsetneq": "\u2838\u2810\u2805\u280c\u2831", + "\\varsubsetneqq": "\u2838\u2810\u2805\u280c\u2828\u2805", + "\\ngeqslant": "\u280c\u2828\u2802\u2831", + "\\gneqq ": "\u2828\u2802\u280c\u2828\u2805", + "\\gnapprox": "\u2828\u2802\u280c\u2808\u2831\u2808\u2831", + "\\succnsim": "\u2828\u2828\u2802\u280c\u2808\u2831", + "\\nshortparallel": "\u280c\u282b\u2807", + "\\nVDash": "\u280c\u282b\u2833\u2833\u2812\u2812", + "\\nsupseteq": "\u280c\u2838\u2828\u2802\u2831", + "\\varsupsetneq ": "\u2838\u2828\u2802\u280c\u2831", + "\\nleq": "\u280c\u2810\u2805\u2831", + "\\lneq": "\u2810\u2805\u280c\u2831", + "\\lnsim": "\u2810\u2805\u280c\u2808\u2831", + "\\npreceq": "\u280c\u2828\u2810\u2805\u2831", + "\\nsim": "\u280c\u2808\u2831", + "\\nvdash": "\u280c\u282b\u2833\u2812\u2812", + "\\varsubsetneq": "\u2838\u2810\u2805\u280c\u2831", + "\\ngtr": "\u280c\u2828\u2802", + "\\ngeqq": "\u280c\u2828\u2802\u2828\u2805", + "\\gvertneqq": "\u2828\u2802\u280c\u2828\u2805", + "\\nsucc": "\u2828\u2828\u2802", + "\\succnapprox": "\u2828\u2828\u2802\u280c\u2808\u2831\u2808\u2831", + "\\nparallel": "\u280c\u282b\u2807", + "\\nsupseteqq": "\u280c\u2838\u2828\u2802\u2828\u2805", + "\\supsetneqq": "\u2838\u2828\u2802\u280c\u2828\u2805", + "\\nleqslant": "\u280c\u2810\u2805\u2831", + "\\lneqq": "\u2810\u2805\u280c\u2828\u2805", + "\\lnapprox": "\u2810\u2805\u280c\u2808\u2831\u2808\u2831", + "\\precnsim": "\u2828\u2810\u2805\u280c\u2808\u2831", + "\\nshortmid": "\u280c\u2833", + "\\nvDash": "\u280c\u282b\u2833\u2836\u2836", + "\\nsubseteq": "\u280c\u2838\u2810\u2805\u2831", + "\\subsetneqq": "\u2838\u2810\u2805\u280c\u2828\u2805", + "\\ngeq": "\u280c\u2828\u2802\u2831", + "\\gneq": "\u2828\u2802\u280c\u2831", + "\\gnsim": "\u2828\u2802\u280c\u2808\u2831", + "\\nsucceq": "\u280c\u2828\u2828\u2802\u2831", + "\\ncong": "\u280c\u2808\u2831\u2828\u2805", + "\\nvDash": "\u280c\u282b\u2833\u2836\u2836", + "\\supsetneq": "\u2838\u2828\u2802\u280c\u2831", + "\\varsupsetneqq": "\u2838\u2828\u2802\u280c\u2828\u2805", + "\\ldots": "\u2804\u2804\u2804", + "\\dots": "\u2804\u2804\u2804", + "\\dotsc": "\u2804\u2804\u2804", + "\\aleph": "\u2820\u2820\u2801", + "\\hbar": "\u2808\u2813", + "\\surd": "\u281c", + "\\top": "\u282b\u2823\u2812\u2812\u2833", + "\\wp": "\u2808\u2830\u280f", + "\\Im": "\u2820\u280a\u280d", + "\\cdots": "\u2804\u2804\u2804", + "\\prime": "\u2804", + "\\emptyset": "\u2838\u2834", + "\\varnothing": "\u2838\u2834", + "\\Box": "\u282b\u2832", + "\\bot": "\u282b\u280f", + "\\angle": "\u282b\u282a", + "\\vdots": "\u282b\u2829\u2804\u2804\u2804", + "\\forall": "\u2808\u282f", + "\\exists": "\u2808\u283f", + "\\triangle": "\u282b\u281e", + "\\ell": "\u2820\u2807", + "\\partial": "\u2808\u2819", + "\\ddots": "\u282b\u2829\u2804\u2804\u2804", + "\\infty": "\u2820\u283f", + "\\nabla": "\u2828\u282b", + "\\Diamond": "\u282b\u2819", + "\\neg": "\u282b\u2812\u2812\u2820\u2833", + "\\sharp": "\u2828\u283c", + "\\Re": "\u2820\u2817\u2811", + "\\adots": "\u282b\u2823\u2804\u2804\u2804", + "\\lozenge": "\u282b\u2819", + "\\nexists": "\u280c\u2808\u283f", + "\\blacksquare": "\u282b\u2838\u2832", + "\\complement": "\u2828\u2809", + "\\square": "\u282b\u2832", + "\\blacktriangledown": "\u282b\u2838\u2828\u281e", + "\\vartriangle": "\u282b\u281e", + "\\circledS": "\u282b\u2809\u2838\u282b\u2820\u280e\u283b", + "\\varnothing": "\u2838\u2834", + "\\blacklozenge": "\u282b\u2838\u2819", + "\\measuredangle": "\u282b\u282a\u2808\u282b\u2801\u283b", + "\\blacktriangle": "\u282b\u2838\u281e", + "\\bigstar": "\u282b\u2838\u280e", + "\\diagup": "\u280c", + "\\Bbbk": "\u2838\u2805", + "\\diagdown": "\u2838\u2821", + "\\llbracket": "\u2808\u2838\u2837", + "\\left\\llbracket": "\u2808\u2838\u2820\u2837", + "\\bigl\\llbracket": "\u2808\u2838\u2820\u2837", + "\\Bigl\\llbracket": "\u2808\u2838\u2820\u2837", + "\\biggl\\llbracket": "\u2808\u2838\u2820\u2837", + "\\Biggl\\llbracket": "\u2808\u2838\u2820\u2837", + "\\rrbracket": "\u2808\u2838\u283e", + "\\right\rrbracket": "\u2808\u2838\u2820\u283e", + "\\bigr\rrbracket": "\u2808\u2838\u2820\u283e", + "\\Bigr\rrbracket": "\u2808\u2838\u2820\u283e", + "\\biggr\rrbracket": "\u2808\u2838\u2820\u283e", + "\\Biggr\rrbracket": "\u2808\u2838\u2820\u283e", + "\\varg": "\u2808\u281b", + "\\varv": "\u2808\u2827", + "\\varw": "\u2808\u283a", + "\\vary": "\u2808\u283d", + "\\medcirc": "\u282b\u2809", + "\\circledwedge": "\u282b\u2809\u2838\u282b\u2808\u2839\u283b", + "\\circledbslash": "\u282b\u2809\u2838\u282b\u2822\u283b", + "\\boxbslash": "\u282b\u2832\u2838\u282b\u2822\u283b", + "\\medbullet": "\u282b\u2838\u2809", + "\\circledvee": "\u282b\u2809\u2838\u282b\u2808\u283c\u283b", + "\\nplus": "\u2828\u2829\u2838\u282b\u282c\u283b", + "\\boxbar": "\u282b\u2832\u2838\u282b\u2833\u283b", + "\\circledbar": "\u282b\u2809\u2838\u282b\u2833\u283b", + "\\boxast": "\u282b\u2832\u2838\u282b\u2808\u283c\u283b", + "\\boxslash": "\u282b\u2832\u2838\u282b\u2814\u283b", + "\\Diamonddot": "\u282b\u2819\u2838\u282b\u2821\u283b", + "\\lambdabar": "\u2808\u2828\u2807", + "\\Bot": "\u282b\u2829\u2836\u2836\u2833", + "\\Diamondblack": "\u282b\u2838\u2819", + "\\Diamond": "\u282b\u2819", + "\\Top": "\u282b\u2823\u2836\u2836\u2833", + "\\bignplus": "\u2828\u2829\u2838\u282b\u282c\u283b", + "\\oiint": "\u282e\u282e\u2808\u282b\u2809\u283b", + "\\ointclockwise": "\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\sqint": "\u282e\u2808\u282b\u2832\u283b", + "\\fint": "\u280c\u282e", + "\\iiiint": "\u282e\u282e\u282e\u282e", + "\\oiintclockwise": "\u282e\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\oiiintctrclockwise": "\u282e\u282e\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\varoiiintclockwise": "\u282e\u282e\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\oiiint": "\u282e\u282e\u282e\u2808\u282b\u2809\u283b", + "\\varointctrclockwise": "\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\sqiintop": "\u282e\u282e\u2808\u282b\u2817\u283b", + "\\iint": "\u282e\u282e", + "\\idotsint": "\u282e\u2804\u2804\u2804\u282e", + "\\varoiintctrclockwise": "\u282e\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\oiiintclockwise": "\u282e\u282e\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\varprod": "\u2810\u2808\u2821", + "\\ointctrclockwise": "\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\varointclockwise": "\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\sqiiintop": "\u282e\u282e\u282e\u2808\u282b\u2817\u283b", + "\\iiint": "\u282e\u282e\u282e", + "\\iiiint": "\u282e\u282e\u282e\u282e", + "\\upint": "\u2823\u282e", + "\\lowint": "\u2829\u282e", + "\\oiintctrclockwise": "\u282e\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\varoiintclockwise": "\u282e\u282e\u2808\u282b\u282a\u2822\u2814\u283b", + "\\varoiiintctrclockwise": "\u282e\u282e\u282e\u2808\u282b\u2822\u2814\u2815\u283b", + "\\dashrightarrow": "\u282b\u2812", + "\\ntwoheadrightarrow": "\u280c\u282b\u2812\u2812\u2815\u2815", + "\\Searrow": "\u282b\u2830\u2836\u2836\u2815", + "\\Perp": "\u282b\u2829\u2836\u2836\u2833", + "\\boxright": "\u282b\u2832\u282b\u2815", + "\\boxdotleft": "\u282b\u282a\u282b\u2832\u2838\u282b\u2821\u283b", + "\\Diamonddotright": "\u282b\u2819\u2838\u282b\u2821\u283b\u282b\u2815", + "\\boxLeft": "\u282b\u282a\u2834\u2834\u282b\u2832", + "\\DiamondRight": "\u282b\u2819\u282b\u2836\u2836\u2815", + "\\DiamonddotLeft": "\u282b\u282a\u2836\u2836\u282b\u2819\u2838\u282b\u2821\u283b", + "\\circleddotright": "\u282b\u2809\u2838\u282b\u2821\u282b\u2815\u283b", + "\\multimapdotbothvert": "\u282b\u2823\u2821\u2812\u2812\u2821", + "\\dashleftrightarrow": "\u282b\u282a\u2812", + "\\ntwoheadleftarrow": "\u280c\u282b\u282a\u282a\u2812\u2812", + "\\Nwarrow": "\u282b\u2818\u282a\u2836\u2836", + "\\leadstoext": "\u2808\u2831", + "\\boxleft": "\u282b\u282a\u282b\u2832", + "\\Diamondright": "\u282b\u2819\u282b\u2815", + "\\Diamonddotleft": "\u282b\u282a\u282b\u2819\u2838\u282b\u2821\u283b", + "\\boxdotRight": "\u282b\u2832\u2838\u282b\u2821\u283b\u282b\u2836\u2836\u2815", + "\\DiamondLeft": "\u282b\u282a\u2836\u2836\u282b\u2819", + "\\circleright": "\u282b\u2809\u2838\u282b\u2815\u283b", + "\\circleddotleft": "\u282b\u2809\u2838\u282b\u2821\u282b\u282a\u283b", + "\\dashleftarrow": "\u282b\u282a\u2812", + "\\leftsquigarrow": "\u282b\u282a\u2814\u2822\u2814", + "\\Nearrow": "\u282b\u2818\u2836\u2836\u2815", + "\\Swarrow": "\u282b\u2830\u282a\u2836\u2836", + "\\leadsto": "\u282b\u2814\u2812\u2822\u2815", + "\\boxdotright": "\u282b\u2832\u2838\u2821\u283b\u282b\u2815", + "\\Diamondleft": "\u282b\u282a\u282b\u2819", + "\\boxRight": "\u282b\u2832\u282b\u2836\u2836\u2815", + "\\boxdotLeft": "\u282b\u282a\u2836\u2836\u282b\u2832\u2838\u282b\u2821\u283b", + "\\DiamonddotRight": "\u282b\u2819\u2838\u282b\u2821\u283b\u282b\u2836\u2836\u2815", + "\\circleleft": "\u282b\u2809\u2838\u282b\u282a\u283b", + "\\multimapbothvert": "\u282b\u2823\u2828\u2821\u2812\u2812\u2828\u2821", + "\\multimapdotbothBvert": "\u282b\u2823\u2828\u2821\u2812\u2812\u2821", + "\\mappedfrom": "\u282b\u282a\u2812\u2833", + "\\Longmapsto": "\u282b\u2833\u2836\u2836\u2815", + "\\mmapsto": "\u282b\u2833\u2833\u2812\u2815", + "\\longmmappedfrom": "\u282b\u282a\u2812\u2812\u2833\u2833", + "\\Mmappedfrom": "\u282b\u282a\u2836\u2833\u2833", + "\\varparallelinv": "\u2838\u2821\u2838\u2821", + "\\colonapprox": "\u2806\u2808\u2831\u2808\u2831", + "\\Colonsim": "\u2806\u2806\u2808\u2831", + "\\multimapboth": "\u282b\u2828\u2821\u2812\u2812\u2828\u2821", + "\\multimapdotboth": "\u282b\u2821\u2812\u2812\u2821", + "\\Vdash": "\u282b\u2833\u2833\u2836\u2836", + "\\preceqq": "\u2828\u2810\u2805\u2828\u2805", + "\\nsuccsim": "\u280c\u2828\u2828\u2802\u2808\u2831", + "\\nlessapprox": "\u280c\u2810\u2805\u2808\u2831\u2808\u2831", + "\\nequiv": "\u280c\u283f", + "\\nsubset": "\u280c\u2838\u2810\u2805", + "\\ngg": "\u280c\u2828\u2802\u2808\u2828\u2802\u283b", + "\\nprecapprox": "\u280c\u2828\u2810\u2805\u2808\u2831\u2808\u2831", + "\\nsucceqq": "\u280c\u2828\u2828\u2802\u2828\u2805", + "\\notni": "\u280c\u2808\u2822", + "\\notowns": "\u280c\u2808\u2822", + "\\eqqcolon": "\u2828\u2805\u2810\u2806", + "\\Coloneqq": "\u2806\u2806\u2810\u2828\u2805", + "\\Eqcolon": "\u2831\u2810\u2806\u2806", + "\\strictiff": "\u282b\u282f\u2812\u2812\u283d", + "\\longmappedfrom": "\u282b\u282a\u2812\u2812\u2833", + "\\Mappedfrom": "\u282b\u282a\u2836\u2833", + "\\longmmapsto": "\u282b\u2833\u2833\u2812\u2812\u2815", + "\\Mmapsto": "\u282b\u2833\u2833\u2836\u2815", + "\\Longmmappedfrom": "\u282b\u282a\u2836\u2836\u2833\u2833", + "\\nvarparallel": "\u280c\u282b\u2807", + "\\colonsim": "\u2806\u2810\u2808\u2831", + "\\doteq": "\u2810\u2828\u2805\u2823\u2821\u283b", + "\\multimapdot": "\u282b\u2812\u2812\u2821", + "\\multimapdotbothA": "\u282b\u2828\u2821\u2812\u2812\u2821", + "\\VvDash": "\u282b\u2833\u2833\u2833\u2836\u2836", + "\\succeqq": "\u2828\u2828\u2802\u2828\u2805", + "\\nlesssim": "\u280c\u2810\u2805\u2808\u2831", + "\\ngtrapprox": "\u280c\u2828\u2802\u2808\u2831\u2808\u2831", + "\\ngtrless": "\u280c\u2810\u2805\u2828\u2802", + "\\nBumpeq": "\u280c\u2808\u2823\u2820\u2823", + "\\nsim": "\u280c\u2808\u2831", + "\\nsupset": "\u280c\u2838\u2828\u2802", + "\\nthickapprox": "\u280c\u2838\u2808\u2831\u2838\u2808\u2831", + "\\nsuccapprox": "\u280c\u2828\u2828\u2802\u2808\u2831\u2808\u2831", + "\\nsimeq": "\u280c\u2808\u2831\u2831", + "\\nSubset": "\u280c\u2838\u2810\u2805\u2838\u282b\u2838\u2810\u2805\u283b", + "\\coloneq": "\u2806\u2810\u2831", + "\\Eqqcolon": "\u2828\u2805\u2810\u2806\u2806", + "\\strictif": "\u282b\u2812\u2812\u283d", + "\\circledless": "\u282b\u2809\u2838\u282b\u2810\u2805\u283b", + "\\Mapsto": "\u282b\u2833\u2836\u2815", + "\\Longmappedfrom": "\u282b\u282a\u2836\u2836\u2833", + "\\mmappedfrom": "\u282b\u282a\u2812\u2833\u2833", + "\\Longmmapsto": "\u282b\u2833\u2833\u2836\u2836\u2815", + "\\varparallel": "\u282b\u2807", + "\\nvarparallelinv": "\u280c\u2838\u2821\u2838\u2821", + "\\Colonapprox": "\u2806\u2806\u2810\u2808\u2831\u2808\u2831", + "\\multimapinv": "\u282b\u2828\u2821\u2812\u2812", + "\\multimapdotinv": "\u282b\u2821\u2812\u2812", + "\\multimapdotbothB": "\u282b\u2821\u2812\u2812\u2828\u2821", + "\\nprecsim": "\u280c\u2828\u2810\u2805\u2808\u2831", + "\\ngtrsim": "\u280c\u2828\u2802\u2808\u2831", + "\\nlessgtr": "\u280c\u2828\u2802\u2810\u2805", + "\\nasymp": "\u280c\u282b\u2801\u282b\u2804", + "\\napprox": "\u280c\u2808\u2831\u2808\u2831", + "\\nll": "\u280c\u2810\u2805\u2808\u2810\u2805\u283b", + "\\napproxeq": "\u280c\u2808\u2831\u2808\u2831\u2831", + "\\npreceqq": "\u280c\u2828\u2810\u2805\u2828\u2805", + "\\notin": "\u280c\u2808\u2811", + "\\nSupset": "\u280c\u2838\u2828\u2802\u2838\u282b\u2838\u2828\u2802\u283b", + "\\coloneqq": "\u2806\u2810\u2828\u2805", + "\\eqcolon": "\u2831\u2810\u2806", + "\\Coloneq": "\u2806\u2806\u2810\u2831", + "\\strictfi": "\u282b\u282f\u2812\u2812", + "\\circledgtr": "\u282b\u2809\u2838\u282b\u2828\u2802\u283b", + "\\mathbb": "\u2838", + "\\mathcal": "\u2808\u2830", + "\\underbrace-begin": "\u2810", + "\\underbrace-middle": "\u2829\u2828\u283e\u2829\u2829", + "\\underbrace-end": "\u283b", + "\\overbrace-begin": "\u2810", + "\\overbrace-middle": "\u2823\u2828\u2837\u2823\u2823", + "\\overbrace-end": "\u283b", + "\\overline-begin": "\u2810", + "\\overline-end": "\u2823\u2831", + "\\underline-begin": "\u2810", + "\\underline-end": "\u2829\u2831", + "?": "\u2838\u2826", + "'": "\u2804", + "{": "", + "}": "", + "\\displaystyle": "", + "\\tilde": "\u2808\u2831", + "\\widetilde-begin": "\u2810", + "\\widetilde-end": "\u2823\u2808\u2820\u2831", + "\\lenqno": " ", + "\\binom": "\u2829", + "\\atop": "\u2829", + "\\choose": "\u2829", + "\\under": "\u2829", + "\\under": "\u2829", + "\\leqno": " ", + "\\hat": "\u2823\u2838\u2823", + "\\%": "\u2808\u2834", + "\\bar": "\u2831", + "\\stackrel-begin": "\u2810", + "\\stackrel-middle": "\u2823", + "\\stackrel-end": "\u283B", + "\\sqcup": "⠈⠨⠬", + "\\sqcap": "⠈⠨⠩", + "\\bigsqcup": "⠈⠨⠬", + "\\bigsqcap": "⠈⠨⠩", + "\\wr": "", + "\\trangleleft": "⠫⠐⠅⠇⠻", + "\\triangleright": "⠫⠸⠨⠂⠻", + "\\lhd": "⠫⠐⠅⠇⠻", + "\\unlhd": "⠫⠐⠅⠇⠱⠻", + "\\rhd": "⠫⠸⠨⠂⠻", + "\\unrhd": "⠫⠸⠨⠂⠱⠻", + "\\amalg": "⠫⠨⠏⠻", + "\\ltimes": "⠫⠸⠈⠡⠻", + "\\rightthreetimes": "", + "\\rtimes": "⠫⠈⠡⠇⠻", + "\\curlywedge": "⠫⠈⠩⠻", + "\\leftthreetimes": "", + "\\curlyvee": "⠫⠈⠬⠻", + "\\sqsubset": "⠈⠸⠐⠅", + "\\sqsubseteq": "⠈⠸⠐⠅⠱", + "\\sqsupset": "⠈⠸⠨⠂", + "\\sqsupseteq": "⠈⠸⠨⠂⠱", + "\\bowtie": "⠫⠸⠈⠡⠇⠻", + "\\Join": "⠫⠸⠈⠡⠇⠻", + "\\risingdotseq": "", + "\\backsimeq": "⠈⠈⠱⠱", + "\\tianglelefteq": "⠫⠐⠅⠇⠱⠻", + "\\trianglerighteq": "⠫⠸⠨⠂⠱⠻", + "\\fallingdotseq": "", + "\\preccurlyeq": "⠫⠨⠐⠅⠱⠻", + "\\succcurlyeq": "⠫⠨⠨⠂⠱⠻", + "\\between": "⠷⠾", + "\\blacktriangleleft": "⠸⠫⠐⠅⠇⠻", + "\\blacktriangleright": "⠸⠫⠸⠨⠂⠻", + "\\backsim": "⠈⠈⠱", + "\\curlyeqprec": "⠫⠱⠨⠐⠅⠻", + "\\vartriangleleft": "⠫⠐⠅⠇⠻", + "\\curlyeqsucc": "⠫⠱⠨⠨⠂⠻", + "\\vartrianlgeright": "⠫⠸⠨⠂⠻", + "\\lvertneqq": "⠐⠅⠱⠌⠨⠅⠻", + "\\ntriangleleft": "⠌⠫⠐⠅⠇⠻", + "\\ntrianglelefteq": "⠌⠫⠐⠅⠇⠱⠻", + "\\ntriangleright": "⠌⠫⠸⠨⠂⠻", + "\\ntrianglerighteq": "⠌⠫⠸⠨⠂⠱⠻", + "\\mho": "⠫⠨⠚⠻", + "\\hslash": "⠫⠌⠓⠻", + "\\backprime": "⠈⠄", + "\\Finv": "⠫⠠⠋⠻", + "\\eth": "⠫⠌⠈⠙⠻", + "\\triangledown": "⠨⠫", + "\\Game": "⠫⠠⠛⠻", + "\\Wr": "", + "\\sqcupplus": "⠈⠨⠬⠸⠫⠬⠻", + "\\invamp": "⠫⠯⠻", + "\\sqcapplus": "⠈⠨⠩⠸⠫⠬⠻", + "\\lambdaslash": "⠫⠌⠨⠇⠻", + "\\bigsqcupplus": "⠈⠨⠬⠸⠫⠬⠻", + "\\bigsqcapplus": "⠈⠨⠩⠸⠫⠬⠻", + "\\nsqsubset": "⠌⠈⠸⠐⠅", + "\\nsqsupset": "⠌⠈⠸⠨⠂", + "\\nsucccurlyeq": "⠌⠫⠨⠨⠂⠱⠻", + "\\nbacksim": "⠌⠈⠈⠱", + "\\nsqsubseteq": "⠌⠈⠸⠐⠅⠱", + "\\lJoin": "⠫⠸⠈⠡⠻", + "\\openJoin": "⠈⠡", + "\\nsqsupseteq": "⠌⠈⠸⠨⠂⠱", + "\\lrtimes": "⠫⠸⠈⠡⠇⠻", + "\\rJoin": "⠫⠈⠡⠇⠻", + "\\npreccurlyeq": "⠌⠫⠨⠐⠅⠱⠻", + "\\nbacksim": "⠌⠈⠈⠱", + "\\textvisiblespace": "⠿", + "\\imath": "⠫⠊⠻", + "\\jmath": "⠫⠚⠻", + "\\check": "\u2823\u2808\u2838\u2823", + "\\acute": "\u2823\u2804", + "\\grave": "\u2831" + }, + "theoremSymbols": { + ".": "\u2828", + "#": "\u283c", + "0": "\u2834", + "1": "\u2802", + "2": "\u2806", + "3": "\u2812", + "4": "\u2832", + "5": "\u2822", + "6": "\u2816", + "7": "\u2836", + "8": "\u2826", + "9": "\u2814", + "#0": "\u283c\u2834", + "#1": "\u283c\u2802", + "#2": "\u283c\u2806", + "#3": "\u283c\u2812", + "#4": "\u283c\u2832", + "#5": "\u283c\u2822", + "#6": "\u283c\u2816", + "#7": "\u283c\u2836", + "#8": "\u283c\u2826", + "#9": "\u283c\u2814" + } +}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/latex2nemeth/gpl-3.0.txt b/Master/texmf-dist/doc/support/latex2nemeth/gpl-3.0.txt new file mode 100644 index 00000000000..94a9ed024d3 --- /dev/null +++ b/Master/texmf-dist/doc/support/latex2nemeth/gpl-3.0.txt @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. 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To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + <one line to give the program's name and a brief idea of what it does.> + Copyright (C) <year> <name of author> + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <http://www.gnu.org/licenses/>. + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + <program> Copyright (C) <year> <name of author> + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +<http://www.gnu.org/licenses/>. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +<http://www.gnu.org/philosophy/why-not-lgpl.html>. |