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typo in ALGZTH fixed
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5 changed files with 141 additions and 3 deletions
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@ -105,11 +105,11 @@ Sei $K$ ein Körper, $f \in K[X]$ mit $n = \deg(f) > 0$.
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\end{enumerate}
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\end{example}
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\begin{*example}
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Sei $f = x^3 -2 \in \Q[X]$, dann sind die Nullstellen von $f$: $\sqrt[2]{3} \in \R, \zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3}$
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Sei $f = x^3 -2 \in \Q[X]$, dann sind die Nullstellen von $f$: $\sqrt[2]{2} \in \R, \zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2}$
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\begin{itemize}
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\item $\Q(\sqrt[2]{3})$ ist Wurzelkörper von $f$. $\Q(\sqrt[2]{3}) \subseteq \R, \zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3} \notin \R$, aber kein Zerfällungskörper. Der Zerfällungskörper von $f$ ist
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\item $\Q(\sqrt[2]{2})$ ist Wurzelkörper von $f$. $\Q(\sqrt[2]{2}) \subseteq \R, \zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2} \notin \R$, aber kein Zerfällungskörper. Der Zerfällungskörper von $f$ ist
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\begin{align*}
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\Q(\sqrt[2]{3},\zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3}) = \Q(\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3})
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\Q(\sqrt[2]{2},\zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2}) = \Q(\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2})
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\end{align*}
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\end{itemize}
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\end{*example}
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Material/ALG/lemma_1_3_12.pdf
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Material/ALG/lemma_1_3_12.pdf
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Material/ALG/lemma_1_3_12.tex
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Material/ALG/lemma_1_3_12.tex
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@ -0,0 +1,40 @@
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\documentclass{standalone}
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\usepackage{tikz, amsmath}
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% \usepackage{tikz-qtree}
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\usepackage{tikz-cd}
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% \usetikzlibrary{cd}
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% \usetikzlibrary{arrows}
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% \usetikzlibrary{automata}
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% \usetikzlibrary{babel}
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% \usetikzlibrary{calc}
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% \usetikzlibrary{fit}
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% \usetikzlibrary{matrix}
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% \usetikzlibrary{positioning}
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% \usetikzlibrary{shapes.geometric}
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% \usetikzlibrary{arrows.meta,bending}
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\begin{document}
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\begin{align*}
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% \begin{tikzcd}[ampersand replacement=\&]
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% L \arrow[r, "\sigma"] \& L' K \arrow[r, "\varphi"]
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% \arrow[u] \& K' \arrow[u]
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% \end{tikzcd}
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\begin{tikzcd}[ampersand replacement=\&]
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L \arrow[r, "\sigma"] \arrow[d] \& L' \arrow[d] \\
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K \arrow[r, "\phi"] \& \tilde{K}
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\end{tikzcd}\\
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\begin{tikzcd}
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A \arrow[r, "\phi"] \arrow[d, red]
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\& B \arrow[d, "\psi" red] \\
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C \arrow[r, red, "\eta" blue]
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\& D
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\end{tikzcd}
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\end{align*}
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%
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% \begin{tikzcd}
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% L \arrow[dd] \arrow[rr] \& \& L' \arrow[dd] \\
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% K \arrow[rr] \& \& K'
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% \end{tikzcd}
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\end{document}
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98
cwl/mathscript - Copy.cwl
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cwl/mathscript - Copy.cwl
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@ -0,0 +1,98 @@
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#include:tabularx
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#include:longtable
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#include:multirow
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#include:colortbl
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#include:amsmath
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#include:amssymb
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#include:amsfonts
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#include:mathtools
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#include:latexsym
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#include:marvosym
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#include:stdmaryd
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#include:bbm
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#include:wasysym
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#include:mathafla
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#include:cancel
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#include:xfrac
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#include:xcolor
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#include:graphicx
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#include:tcolorbox
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#include:pgfplots
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#include:pgf
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#include:tikz
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#include:ulem
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#include:marginnote
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#include:enumerate
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#include:enumitem
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#include:listings
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#include:hyperref
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#include:cleveref
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#include:bookmark
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#include:ntheorem
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#include:mathoperators
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\begin{theorem}
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\begin{theorem}[title]
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\end{theorem}
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\begin{proposition}
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\begin{proposition}[title]
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\end{proposition}
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\begin{lemma}
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\begin{lemma}[title]
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\end{lemma}
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\begin{definition}
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\begin{definition}[title]
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\end{definition}
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\begin{conclusion}
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\begin{conclusion}[title]
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\end{conclusion}
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\begin{remark}
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\begin{remark}[title]
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\end{remark}
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\begin{erinnerung}
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\begin{erinnerung}[title]
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\end{erinnerung}
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\begin{example}
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\begin{example}[title]
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\end{example}
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\begin{algorithm}
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\begin{algorithm}[title]
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\end{algorithm}
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\begin{*definition}
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\begin{*definition}[title]
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\end{*definition}
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\begin{*remark}
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\begin{*remark}[title]
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\end{*remark}
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\begin{*example}
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\begin{*example}[title]
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\end{*example}
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\begin{*anmerkung}
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\begin{*anmerkung}[title]
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\end{*anmerkung}
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\begin{mathematica}
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\begin{mathematica}[title]
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\end{mathematica}
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\begin{overview}
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\begin{overview}[title]
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\end{overview}
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\begin{interpretation}[title]
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\end{interpretation}
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\begin{underlinedPlain}[title]
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\end{underlinedPlain}
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\begin{hint}
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\end{hint}
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\begin{plainenvironment}[title]
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\end{plainenvironment}
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\begin{underlinedenvironment}[title]
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\end{underlinedenvironment}
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\begin{boldEnvironment}[title]
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\end{boldEnvironment}
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\begin{repetition}
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\end{repetition}
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\begin{proof}
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\begin{proof}[title]
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\end{proof}
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\proplbl{label}#l
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\propref{ref}#r
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\begriff{term}%text
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\begriff[Ordnung]{term}[Unterordnung]%text
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