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diff --git a/Master/texmf-dist/tex/latex/binomexp/binomexp.sty b/Master/texmf-dist/tex/latex/binomexp/binomexp.sty new file mode 100644 index 00000000000..1e17b5747ab --- /dev/null +++ b/Master/texmf-dist/tex/latex/binomexp/binomexp.sty @@ -0,0 +1,156 @@ +%% +%% This is file `binomexp.sty', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% binomexp.dtx (with options: `package') +%% This is a generated file. +%% Copyright (C) 2006 by David Roderick +%% This file may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either +%% version 1.2 of this license or (at your option) any later +%% version. The latest version of this license is in: +%% http://www.latex-project.org/lppl.txt +%% and version 1.2 or later is part of all distributions of +%% LaTeX version 1999/12/01 or later. +\NeedsTeXFormat{LaTeX2e}[2005/12/01] +\ProvidesPackage{binomexp} + [2007/01/07 v1.0 My first attempt] +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +%% +\RequirePackage{calc,ifthen} +\newcommand\binomexp@replicate[2]{% + \ifnum#1>\z@ \expandafter\@firstofone + \else + \expandafter\@gobble + \fi + {#2\expandafter\binomexp@replicate\expandafter{\number\numexpr#1-1\relax}{#2}}% +} +\newcommand{\binomexp@call}[1]{\rule[-0.125cm]{0mm}{0.5cm}\mbox{$#1$}} +\newcounter{binomexp@up} +\newcommand{\binomexp@up}{\number\value{binomexp@up} +\addtocounter{binomexp@up}{1}} +\newcounter{binomexp@down} +\newcommand{\binomexp@down}{\number\value{binomexp@down} +\addtocounter{binomexp@down}{-1}} +\newcounter{binomexp@columns} +\newcounter{binomexp@power} +\newcounter{binomexp@pascalstart} +\newcounter{binomexp@pascalstop} +\newcounter{binomexp@emptytimes} +\newcounter{binomexp@variable1} +\newcounter{binomexp@variable2} +\newcounter{binomexp@answervar} +\newcounter{binomexp@sub} +\protect\newcommand*{\binomexp@printpascal}{ +\addtocounter{binomexp@power}{1} +\expandafter\edef\csname +binomexp@morten\roman{binomexp@power}exporti\endcsname{1} +\setcounter{binomexp@sub}{2} +\setcounter{binomexp@variable1}{\numexpr\number\value{binomexp@power}+1\relax} +\whiledo{\number\numexpr\number\value{binomexp@power}+1\relax> +\value{binomexp@sub}}{ +\setcounter{binomexp@variable1}{\numexpr\number\value{binomexp@sub}-1\relax} +\setcounter{binomexp@variable2}{\value{binomexp@sub}} +\setcounter{binomexp@answervar}{\number\numexpr\csname +binomexp@x\roman{binomexp@variable1}\endcsname\relax+\number\numexpr\csname +binomexp@x\roman{binomexp@variable2}\endcsname\relax} +\expandafter\edef\csname binomexp@y\roman{binomexp@sub}\endcsname +{\number\value{binomexp@answervar}}\relax +\addtocounter{binomexp@sub}{1} +} +\setcounter{binomexp@sub}{2} +\whiledo{\numexpr\number\value{binomexp@power}+1\relax>\value{binomexp@sub}}{ +\setcounter{binomexp@answervar}{\number\numexpr\csname +binomexp@y\roman{binomexp@sub}\endcsname\relax} +\expandafter\edef\csname binomexp@x\roman{binomexp@sub}\endcsname +{\number\value{binomexp@answervar}} +\expandafter\edef\csname +binomexp@morten\roman{binomexp@power}export\roman{binomexp@sub}\endcsname +{\number\value{binomexp@answervar}} +\addtocounter{binomexp@sub}{1} +} +\setcounter{binomexp@variable1} +{\numexpr\number\value{binomexp@power}+1\relax} +\expandafter\edef\csname +binomexp@x\roman{binomexp@variable1}\endcsname{1} +\expandafter\edef\csname +binomexp@morten\roman{binomexp@power}export\roman{binomexp@variable1}\endcsname{1} +} +\newcommand*\binomexp@putpascal[6]{\par +\expandafter\edef\csname binomexp@xi\endcsname{1} +\expandafter\edef\csname binomexp@mortenexporti\endcsname{1} +\setcounter{binomexp@power}{0} +\setcounter{binomexp@pascalstart}{#1} +\setcounter{binomexp@pascalstop}{#2+1} +\setcounter{binomexp@emptytimes}{\value{binomexp@pascalstop}} +\whiledo{\value{binomexp@emptytimes}>1}{ +\binomexp@printpascal \addtocounter{binomexp@emptytimes}{-1} +} +\setcounter{binomexp@columns} +{\numexpr\number\value{binomexp@pascalstop}+2\relax} +\begin{math} \begin{array}{@{}|c|*{\value{binomexp@columns}}{|c}|@{}} +\whiledo{\value{binomexp@pascalstart}< +\numexpr\number\value{binomexp@pascalstop}-1\relax}{ +\setcounter{binomexp@up}{0} +\setcounter{binomexp@down}{\value{binomexp@pascalstart}} +\binomexp@call{(#3+#4)^{\number\numexpr\number\value{binomexp@pascalstart}\relax}} +\binomexp@replicate{\numexpr\number\value{binomexp@pascalstart}+1\relax} +{&\binomexp@call{\csname +binomexp@morten\romannumeral\numexpr\value{binomexp@pascalstart}\relax +export\romannumeral\numexpr\value{binomexp@up}+1\relax\endcsname +#5^{\binomexp@down} #6^{\binomexp@up}}}\\ +\addtocounter{binomexp@pascalstart}{1} +} +\setcounter{binomexp@up}{0} +\setcounter{binomexp@down}{\value{binomexp@pascalstart}} +\binomexp@call{(#3+#4)^{\number\numexpr\number\value{binomexp@pascalstart}\relax}} +\binomexp@replicate{\numexpr\number\value{binomexp@pascalstart}+1\relax} +{&\binomexp@call{\csname +binomexp@morten\romannumeral\numexpr\value{binomexp@pascalstart}\relax +export\romannumeral\numexpr\value{binomexp@up}+1\relax\endcsname +#5^{\binomexp@down} #6^{\binomexp@up}}} + \end{array} \end{math} +} +\newcommand{\binomexp@proof}[2]{ +\[ 7!=7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 \hspace*{5em} +{#1 \choose #2} = \frac{#1!}{(#1-#2)!\cdot #2!}= +\frac{#1!}{(#1-#2)!\cdot(#1-(#1-#2))!}={#1 \choose #1-#2} +\] +\begin{eqnarray*} {#1 - 1 \choose #2 - 1} + {#1 - 1 \choose #2} +&=& \frac{(#1 - 1)!}{(#2 - 1)!\cdot[(#1 - 1) - (#2 - 1)]!} + +\frac{(#1 - 1)!}{#2!\cdot[(#1 - 1) - #2)]!}\\ +&=& (#1 - 1)!\cdot\left(\frac{1}{(#2 - 1)!\cdot(#1 - #2)!} + +\frac{1}{#2!\cdot[(#1 - #2) - 1)]!}\right) \\ +&=& (#1 - 1)! \cdot\frac{#2 + (#1 - #2)}{#2! (#1 - #2)!} \\ +&=& \frac{#1!}{#2!(#1 - #2)!} = {#1 \choose #2} + \end{eqnarray*} +\[ \frac{#2}{#2!\cdot(#1-#2)!} = \frac{1}{(#2-1)!\cdot(#1-#2)!} +\hspace*{5em} \mbox{because} \hspace*{5em} \\ + \frac{6}{6!\cdot(#1-#2)!} = \frac{1}{5!\cdot(#1-#2)!} \] +\begin{eqnarray*} +(#2 + 1)\cdot {#1 + 1 \choose #2 + 1} &=& (#2 + 1)\cdot +\frac{(#1 + 1)!}{((#2 + 1)!\cdot ((#1 + 1) - (#2 + 1))!}\\ +&=& (#2 + 1)\cdot \frac{(#1 + 1)!}{(#2 + 1)!\cdot (#1 - #2)!}\\ +&=& (#1 + 1)\cdot \frac{#1!}{#2!\cdot (#1 - #2)!} = (#1 + 1)\cdot +{#1 \choose #2}\\ +\end{eqnarray*} +} +\endinput +%% +%% End of file `binomexp.sty'. |