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authorAndreas Müller <andreas.mueller@ost.ch>2021-08-22 21:52:24 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-08-22 21:52:24 +0200
commite5bc54895bd698524f14b8c33f324bf6343e40c4 (patch)
tree7b16162fa18d49d19501dadd03d8cb3aabb02ff7 /buch/chapters
parenteuler char, traces, telescoping sums (diff)
downloadSeminarMatrizen-e5bc54895bd698524f14b8c33f324bf6343e40c4.tar.gz
SeminarMatrizen-e5bc54895bd698524f14b8c33f324bf6343e40c4.zip
some improvements
Diffstat (limited to 'buch/chapters')
-rw-r--r--buch/chapters/95-homologie/images/complexbasis.pdfbin26502 -> 27036 bytes
-rw-r--r--buch/chapters/95-homologie/images/complexbasis.tex50
2 files changed, 33 insertions, 17 deletions
diff --git a/buch/chapters/95-homologie/images/complexbasis.pdf b/buch/chapters/95-homologie/images/complexbasis.pdf
index 536f04f..3a627d4 100644
--- a/buch/chapters/95-homologie/images/complexbasis.pdf
+++ b/buch/chapters/95-homologie/images/complexbasis.pdf
Binary files differ
diff --git a/buch/chapters/95-homologie/images/complexbasis.tex b/buch/chapters/95-homologie/images/complexbasis.tex
index 365789c..6accb2a 100644
--- a/buch/chapters/95-homologie/images/complexbasis.tex
+++ b/buch/chapters/95-homologie/images/complexbasis.tex
@@ -44,36 +44,52 @@
\fill[color=gray!20]
({\s},{(2*(#1)+1)*\s})
--
- ({3-\s},{-\s})
+ ({3.5-\s},{-\s})
--
- ({3-\s},{(2*(#3)+1)*\s})
+ ({3.5-\s},{(2*(#3)+1)*\s})
--
- ({\s},{(2*(#1)+1)*\s});
+ ({\s},{(2*(#1)+1)*\s})
+ --
+ cycle;
\fill[color=gray!40]
({\s},{(2*(#1+1)-1)*\s})
--
- ({3-\s},{(2*(#3+1)-1)*\s})
+ ({3.5-\s},{(2*(#3+1)-1)*\s})
+ --
+ ({3.5-\s},{(2*(#4)+1)*\s})
+ --
+ ({\s},{(2*(#2)+1)*\s})
--
- ({3-\s},{(2*(#4)+1)*\s})
+ cycle;
+ \draw[<-,color=gray]
+ ({\s},{(2*(#1+1)-1)*\s})
+ --
+ ({3.5-\s},{(2*(#3+1)-1)*\s});
+ \draw[->,color=gray]
+ ({3.5-\s},{(2*(#4)+1)*\s})
--
({\s},{(2*(#2)+1)*\s});
+ \draw[<-,color=gray!40]
+ ({\s},{(2*(#1)+1)*\s})
+ --
+ ({3.5-\s},{-\s});
}
-\clip (-4.5,-1.2) rectangle (7.5,11.7);
+\clip (-5.5,-1.2) rectangle (8.5,11.7);
-\begin{scope}[xshift=-6cm]
+\begin{scope}[xshift=-7cm]
\abbildung{6}{7}{10}{11}
\end{scope}
-\begin{scope}[xshift=-3cm]
+\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 (1.5,{9*2*\s}) {$\Delta_{k-1}$};
- \node at (1.5,{-\s}) [above] {$\partial_{k-1\mathstrut}$};
+ \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] {$Z_{k-2\mathstrut}$};
@@ -88,14 +104,14 @@
\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 (1.5,{6.5*2*\s}) {$\Delta_k$};
- \node at (1.5,{-\s}) [above] {$\partial_{k\mathstrut}$};
+ \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=3cm]
+\begin{scope}[xshift=3.5cm]
\abbildung{3}{5}{5}{7}
\rechteck{6}{10}{blue}
\rechteck{4}{5}{darkgreen}
@@ -116,21 +132,21 @@
\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 (1.5,{5.5*2*\s}) {$\Delta_{k+1}$};
- \node at (1.5,{-\s}) [above] {$\partial_{k+1\mathstrut}$};
+ \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=6cm]
+\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},{(2.5*2+1)*\s})
+ \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});