source: palm/tags/release-3.10/DOC/tec/methods/upstream_spline/sqrt.sty

Last change on this file was 481, checked in by raasch, 15 years ago

file structure of technical documentation revised; documents concerning numerical methods added

  • Property svn:executable set to *
File size: 6.3 KB
Line 
1%     plei.tex  =  sed-definitions  +  blei.tex   
2%
3%     abgeschlossene Wurzeln  \wu  ,  genau dann wenn  \gdw
4%       = mit Doppelpunkt     \gll  \glr
5%     Halbpfeil ueber         \vc  ,  Punkt(e) ueber   \p \pp 
6%     Punkt ueber Halbpfeil ueber  \pvc 
7%     Zwei Punkte ueber Halbpfeil  \ppvc
8%     Halbpfeil-Buchstaben "small"        \vcsm
9%     Halbpfeil ueber Schlange, kleine    \vcts   
10%              bzw. grosse Buchstabem     \vctl
11%     Gabel-Psi  \gps ,  Kurzer downarrow ueber  \apf
12%     Lange Doppelpfeile  \lpfr \lpfl \lpfu \lpfd
13%     Integral mit Kringel  \klint (in $ $)  \grint (in $$ $$) 
14%     Anfuehrungsstriche unten und oben      \anfu \anfo
15%     Stilisiertes Gross-A  \biga  \smala  , \ende .
16%
17%     Abkuerzungen vorhandener Befehle :
18%
19\typeout{sqrt.sty --> (c) by H. Schulz (verbessert von Michael Schroeter)}
20\def\nz{\par \noindent}  % 'neue Zeile' (ohne Einrueckung)
21\def\schl#1{ \widetilde{#1} }
22%  Klammern :
23   \def\({\left(} \def\){\right)} 
24   \def\lk{\,\left[ \,} \def\rk{\,\right] \,}
25   \def\lb{\left\{} \def\rb{\right\}} 
26   \def\lw{\left\langle} \def\rw{\right\rangle}
27
28\def\dis{ \displaystyle }   
29\def\lsim{\,\lower 4pt\hbox{$\sim\!\!\!\!\!$}\raise 2pt\hbox{$<$}\,}
30\def\gsim{\,\lower 4pt\hbox{$\sim\!\!\!\!\!$}\raise 2pt\hbox{$>$}\,}
31\def\be{ \begin{equation} }  \def\bea{ \begin{eqnarray} }
32\def\ee{ \end{equation} }    \def\eea{ \end{eqnarray} }
33\def\sgn{\,\mbox{sgn}\,}   
34%  ! !  :
35\def\6{\partial }
36%
37%    das alte blei.tex  :
38%
39   \def\wu#1{\sqrt{{#1} \,}^{ \hbox to0.19pt{\hss$
40          \vrule height 2.7pt width 0.4pt depth -0.1pt $} \;\! } }
41   \def\gdw{\leftharpoonup \hbox to-1pt{\hss $\rightharpoondown$} \;}
42          \font\dick=cmbx10  \font\duenn=cmbx8
43   \def\dop{\duenn \raise0.9pt\hbox to 0.2pt{: \hss}}
44   \def\dep{\duenn \raise0.9pt\hbox to 0.3pt{\hss :}}
45   \def\gll{\; \dop =}   \def\glr{= \dep \;}
46   \def\pbox{\dick _{\hbox{.}} }  \def\ppbox{\dick _{\hbox{..}} }
47   \def\pfeil{_\rightharpoonup}  \def\leer{\phantom{a}}
48   \def\opf{\buildrel \pfeil \over \leer}
49   \def\jvv{j \lower0.4pt\hbox to 2pt{\hss $\opf$}}
50   \def\jv{j \lower0.2pt\hbox to 1.4pt{\hss $\opf$}}
51   \def\ivv{i \lower0.4pt\hbox to 2pt{\hss $\opf$}}
52   \def\iv{i \lower0.2pt\hbox to 1.4pt{\hss $\opf$}}
53   \def\hq{h \raise0.2pt\hbox to 0.4pt{\hss $^-$}}   
54   \def\vk#1{\hbox{$\buildrel           \pfeil \over #1$}}
55   \def\vkk#1{\hbox{$\buildrel   \;     \pfeil \over #1$}}
56   \def\vkkk#1{\hbox{$\buildrel  \, \;  \pfeil \over #1$}}
57   \def\grpf{\displaystyle  _\rightharpoonup}
58   \def\vg#1{\hbox{$\buildrel       \grpf \over #1$}}
59   \def\vgg#1{\hbox{$\buildrel  \;  \grpf \over #1$}}
60\def\fzz{f} \def\bzz{b} \def\dzz{d} \def\gzz{g} \def\hzz{h} \def\jzz{j}
61\def\kzz{k} \def\lzz{l} \def\mzz{m} \def\wzz{w} \def\tzz{t} \def\izz{i}
62\def\bezz{\beta} \def\dezz{\delta} \def\xizz{\xi} \def\pszz{\psi}
63\def\vthzz{\vartheta}
64\def\uph{ \! \mathop{\vphantom{a}} } \def\dph{ \vphantom{a} }
65\def\vc#1{\def\tast{\noexpand#1} \def\test{#1}
66\ifcat\tast\bzz
67\ifx\test\fzz \vkkk f \uph \else   \ifx\test\bzz \vkk b \uph \else
68\ifx\test\dzz \vkkk d \uph \else   \ifx\test\gzz \vkk g \dph \else
69\ifx\test\hzz \vkk h \uph \else    \ifx\test\izz \ivv \dph \else
70\ifx\test\jzz \jvv \dph \else      \ifx\test\kzz \vkk k \uph \else
71\ifx\test\lzz \vkk l \uph \else    \ifx\test\tzz \vkk t \uph \else
72\ifx\test\mzz \vg m \dph \else     \ifx\test\wzz \vg w \dph \else
73\ifnum \lq#1<91 \vgg #1 \uph \else \vk #1 \dph
74  \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi \fi   \else
75\ifx\test\bezz \vkk \beta \uph \else  \ifx\test\pszz \vkk \psi \dph \else
76\ifx\test\dezz \vkk \delta \uph \else \ifx\test\xizz \vkk \xi \uph \else
77\ifx\test\vthzz \vkk \vartheta \uph \else \vk #1 \dph
78  \fi \fi \fi \fi \fi \fi }
79\def\abst#1{\def\tast{\noexpand#1} \ifcat\tast\bzz
80    \ifnum \lq#1<91 \; \else \, \fi      \else \, \fi}
81\def\absv#1{\def\tast{\noexpand#1} \def\test{#1}
82\ifcat\tast\bzz \ifx\test\fzz \, \; \else  \ifx\test\dzz \, \; \else
83\ifx\test\bzz \, \else \ifx\test\gzz \, \else \ifx\test\hzz \, \else
84\ifx\test\kzz \, \else \ifx\test\lzz \, \else \ifx\test\tzz \, \else
85\ifnum \lq#1<91 \; \else   
86  \fi \fi \fi \fi \fi \fi \fi \fi \fi \else
87\ifx\test\bezz \, \else \ifx\test\pszz \, \else \ifx\test\dezz \, \else
88\ifx\test\xizz \, \else \ifx\test\vthzz \, \else
89   \fi \fi \fi \fi \fi \fi }
90\def\vphan#1{\def\tast{\noexpand#1} \def\test{#1}
91\ifcat\tast\bzz \ifx\test\fzz  \uph \else \ifx\test\bzz  \uph \else
92\ifx\test\dzz  \uph \else   \ifx\test\hzz  \uph \else
93\ifx\test\kzz  \uph \else   \ifx\test\lzz  \uph \else
94\ifx\test\tzz  \uph \else   \ifnum \lq#1<91  \uph \else \dph
95  \fi \fi \fi \fi \fi \fi \fi \fi \else
96\ifx\test\bezz  \uph \else  \ifx\test\dezz  \uph \else
97\ifx\test\xizz  \uph \else  \ifx\test\vthzz  \uph \else \dph
98  \fi \fi \fi \fi \fi }
99\def\p#1{{\buildrel \abst #1 \pbox \over #1} \vphan #1 }
100\def\pp#1{{\buildrel \abst #1 \ppbox \over #1} \vphan #1 }
101\def\pvc#1{{\buildrel \absv #1 \pbox \over {\vc #1}} \vphan #1 }
102\def\ppvc#1{{\buildrel \absv #1 \ppbox \over {\vc #1}} \vphan #1 }
103\def\vcsm#1{ \def\sm{\raise 1.6pt\hbox to 5pt{\hss $_#1$}}
104             {\buildrel \pfeil \over \sm} \>\!\! }
105\def\vcts#1{\buildrel \absv #1 \pfeil \over {\schl #1} }
106\def\vctl#1{\buildrel \absv #1 \grpf \over {\schl #1} }
107\def\sinh{ {\rm sh} } \def\cosh{ {\rm ch} } \def\tanh{ {\rm th} }
108\def\cotanh{ {\rm cth} } \def\coth{ {\rm cth} } \def\sh{ {\rm sh} }
109\def\ch{ {\rm ch} }  \def\th{ {\rm th} }  \def\cth{ {\rm cth} }
110\def\gps{ \; \lower 2.6pt\hbox{$^\vert$} % 2.6
111           \raise 1.4pt\hbox to 2.2pt{\hss $\cup$} \,} %1.6
112\def\abpfeil{ \raise 1pt\hbox{ $_\vee$ \hskip -7.6pt
113           \vrule depth 0.7pt height 4.7pt width 0.3pt} \;\; }
114\def\apf#1{ \buildrel \abpfeil \over {#1} }
115\def\lpfr{\hbox{$\, =\!\!\!=\!\!\!=\!\!\!\Longrightarrow \,$} }
116\def\lpfl{\hbox{$\, \Longleftarrow\!\!\!=\!\!\!=\!\!\!= \,$} }
117\def\lpfu{\vbox to 15pt{\hbox{$\, \,\Uparrow \,$} \vss
118                        \hbox{$\, \>\Vert \,$} \vss}}
119\def\lpfd{\vbox to 15pt{\vss \hbox{$\, \>\Vert \,$} \vss
120                             \hbox{$\, \,\Downarrow \,$}}}
121\def\biga{ \raise 2pt\hbox{$ \bigcap \!\!\!\!\!\!\> $} \hbox{$-$}  }
122\def\smala{ \hbox{$ \cap \!\!\!\!\!\!\; $} \lower 0.7pt\hbox{$-$}  }
123\font\gital=cmti10 scaled \magstep4   \def\Vau{\hbox{{\gital v$\!\>$}}}
124\def\ende{ \hskip 5.64cm \vrule depth -2pt width 3cm height 2.5pt 
125           \hskip -1.55cm $\bullet$ \nz }
126%  ENDE           -1.55               -2               height 2.1
127
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