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Diffstat (limited to 'buch/chapters/95-homologie/images/complexbasis.tex')
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diff --git a/buch/chapters/95-homologie/images/complexbasis.tex b/buch/chapters/95-homologie/images/complexbasis.tex new file mode 100644 index 0000000..bab89d2 --- /dev/null +++ b/buch/chapters/95-homologie/images/complexbasis.tex @@ -0,0 +1,158 @@ +% +% complexbasis.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\usetikzlibrary{decorations.pathreplacing} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\s{0.5} +\def\h{0.02} + +\def\rechteck#1#2#3{ + \fill[color=#3!20,rounded corners=2pt] + ({-\s+\h},{(2*(#1)-1)*\s+\h}) + rectangle + ({\s-\h},{(2*(#2)+1)*\s-\h}); + \draw[color=#3,rounded corners=2pt] + ({-\s+\h},{(2*(#1)-1)*\s+\h}) + rectangle + ({\s-\h},{(2*(#2)+1)*\s-\h}); + \foreach \y in {{#1},...,{#2}}{ + \fill[color=#3] (0,{2*\y*\s}) circle[radius=0.05]; + } +} +\def\Rechteck#1#2{ + \draw[rounded corners=3pt] + ({-\s-\h},{(2*(#1)-1)*\s-\h}) + rectangle + ({\s+\h},{(2*(#2)+1)*\s+\h}); +} + +\def\abbildung#1#2#3#4{ + \fill[color=gray!20] + ({\s+\h},{(2*(#1)+1)*\s}) + -- + ({3.5-\s-\h},{-\s}) + -- + ({3.5-\s-\h},{(2*(#3)+1)*\s}) + -- + ({\s+\h},{(2*(#1)+1)*\s}) + -- + cycle; + \fill[color=gray!40] + ({\s+\h},{(2*(#1+1)-1)*\s}) + -- + ({3.5-\s-\h},{(2*(#3+1)-1)*\s}) + -- + ({3.5-\s-\h},{(2*(#4)+1)*\s}) + -- + ({\s+\h},{(2*(#2)+1)*\s}) + -- + cycle; + \draw[<-,color=gray] + ({\s+\h},{(2*(#1+1)-1)*\s}) + -- + ({3.5-\s-\h},{(2*(#3+1)-1)*\s}); + \draw[->,color=gray] + ({3.5-\s-\h},{(2*(#4)+1)*\s}) + -- + ({\s+\h},{(2*(#2)+1)*\s}); + \draw[<-,color=gray!40] + ({\s+\h},{(2*(#1)+1)*\s}) + -- + ({3.5-\s-\h},{-\s}); +} + +\clip ({-3.5-1.7},-1.2) rectangle ({7+1.7},11.7); + +\begin{scope}[xshift=-7cm] + \abbildung{6}{7}{10}{11} +\end{scope} + +\begin{scope}[xshift=-3.5cm] + \abbildung{6}{10}{7}{11} + \rechteck{0}{6}{red} + \rechteck{7}{10}{darkgreen} + \rechteck{11}{11}{blue} + \Rechteck{0}{11} + \node[color=darkgreen] at ({0},{(9*2-1)*\s}) {$B_{k-2\mathstrut}$}; + \node at (1.75,{9*2*\s}) {$\Delta_{k-1}$}; + \node at (1.75,{-\s}) [above] {$\partial_{k-1\mathstrut}$}; + \draw[decorate,decoration={brace,amplitude=4pt}] + ({-\s-0.1},{-\s}) -- ({-\s-0.1},{(2*10+1)*\s}); + \node at ({-\s-0.17},{10*\s}) [left] {$Z_{k-2\mathstrut}$}; + \node at (0,{-\s}) [below] {$C_{k-2\mathstrut}$}; +\end{scope} + +\begin{scope} + \abbildung{2}{7}{5}{10} + \rechteck{8}{11}{blue} + \rechteck{3}{7}{darkgreen} + \rechteck{0}{2}{red} + \Rechteck{0}{11} + \node at (0,{-\s}) [below] {$C_{k-1\mathstrut}$}; + \node[color=darkgreen] at ({0},{(5*2-1)*\s}) {$B_{k-1\mathstrut}$}; + \node at (1.75,{6.5*2*\s}) {$\Delta_k$}; + \node at (1.75,{-\s}) [above] {$\partial_{k\mathstrut}$}; + \draw[decorate,decoration={brace,amplitude=4pt}] + ({-\s-0.1},{-\s}) -- ({-\s-0.1},{(2*7+1)*\s}); + \node at ({-\s-0.17},{7*\s}) [left] {$Z_{k-1\mathstrut}$}; +\end{scope} + +\begin{scope}[xshift=3.5cm] + \abbildung{3}{5}{5}{7} + \rechteck{6}{10}{blue} + \rechteck{4}{5}{darkgreen} + \rechteck{0}{3}{red} + \Rechteck{0}{10} + \node at (0,{-\s}) [below] {$C_{k\mathstrut}$}; + \node[color=darkgreen] at ({-0.25},{9*\s}) + {$B_{k\mathstrut}$}; + \node[color=darkgreen] at (0.24,{2*4*\s}) {$b_1$}; + \node[color=darkgreen] at (0.24,{2*4.5*\s+0.1}) {$\vdots$}; + \node[color=darkgreen] at (0.24,{2*5*\s}) {$b_r$}; + \node[color=red] at (0.24,{2*0*\s}) {$z_1$}; + \node[color=red] at (0.24,{2*1*\s}) {$z_2$}; + \node[color=red] at (0.24,{2*2*\s+0.1}) {$\vdots$}; + \node[color=red] at (0.24,{2*3*\s}) {$z_l$}; + \node[color=blue] at (0.24,{2*6*\s}) {$c_1$}; + \node[color=blue] at (0.24,{2*7*\s}) {$c_2$}; + \node[color=blue] at (0.24,{2*8*\s}) {$c_3$}; + \node[color=blue] at (0.24,{2*9*\s}) {$\vdots$}; + \node[color=blue] at (0.24,{2*10*\s}) {$c_s$}; + \node at (1.75,{5.5*2*\s}) {$\Delta_{k+1}$}; + \node at (1.75,{-\s}) [above] {$\partial_{k+1\mathstrut}$}; + \draw[decorate,decoration={brace,amplitude=4pt}] + ({-\s-0.1},{-\s}) -- ({-\s-0.1},{(2*5+1)*\s}); + \node at ({-\s-0.17},{5*\s}) [left] {$Z_{k\mathstrut}$}; +\end{scope} + +\begin{scope}[xshift=7cm] + \abbildung{0}{5}{4}{8} + \rechteck{5}{7}{blue} + \rechteck{1}{5}{darkgreen} + \rechteck{0}{0}{red} + \Rechteck{0}{7} + \node at (0,{-\s}) [below] {$C_{k+1\mathstrut}$}; + \node[color=darkgreen] at ({0},{(2.0*2+1)*\s}) + {$B_{k+1\mathstrut}$}; + \draw[decorate,decoration={brace,amplitude=4pt}] + ({-\s-0.1},{-\s}) -- ({-\s-0.1},{(2*5+1)*\s}); + \node at ({-\s-0.17},{5*\s}) [left] {$Z_{k+1\mathstrut}$}; +\end{scope} + +\end{tikzpicture} +\end{document} + |