diff options
Diffstat (limited to 'vorlesungen/slides/1/algebrastruktur.tex')
| -rw-r--r-- | vorlesungen/slides/1/algebrastruktur.tex | 102 |
1 files changed, 61 insertions, 41 deletions
diff --git a/vorlesungen/slides/1/algebrastruktur.tex b/vorlesungen/slides/1/algebrastruktur.tex index 9647c04..d7794a3 100644 --- a/vorlesungen/slides/1/algebrastruktur.tex +++ b/vorlesungen/slides/1/algebrastruktur.tex @@ -13,34 +13,43 @@ \begin{tikzpicture}[>=latex,thick] \pgfmathparse{atan(7/4)} \xdef\a{\pgfmathresult} -\fill[color=red!40,opacity=0.5] - ({-4-2.5},{2+1.0}) - -- - ({-2.5},{-3-1.0}) - -- - ({2.5},{-3-1.0}) - -- - ({-4+2.5},{2+1.0}) - -- cycle; -\fill[color=blue!40,opacity=0.5] - ({4-2.5},{2+1.0}) - -- - ({-2.5},{-3-1.0}) - -- - ({2.5},{-3-1.0}) - -- - ({4+2.5},{2+1.0}) - -- cycle; -\fill[color=darkgreen!40,opacity=0.5] - ({-4-2.5},{2+1.0}) - -- - ({-4-2.5+2*(4/7)},{2-1}) - -- - ({+4+2.5-2*(4/7)},{2-1}) - -- - ({+4+2.5},{2+1}) - -- - cycle; +\uncover<2->{ + \fill[color=red!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({-4+2.5},{2+1.0}) + -- cycle; +} + +\uncover<4->{ + \fill[color=blue!40,opacity=0.5] + ({4-2.5},{2+1.0}) + -- + ({-2.5},{-3-1.0}) + -- + ({2.5},{-3-1.0}) + -- + ({4+2.5},{2+1.0}) + -- cycle; +} + +\uncover<6->{ + \fill[color=darkgreen!40,opacity=0.5] + ({-4-2.5},{2+1.0}) + -- + ({-4-2.5+2*(4/7)},{2-1}) + -- + ({+4+2.5-2*(4/7)},{2-1}) + -- + ({+4+2.5},{2+1}) + -- + cycle; +} + \node at ({-3-0.5},2) {Skalarmultiplikation}; \node at (3.5,2.2) {Multiplikation}; @@ -49,22 +58,33 @@ \node at (0,-2.8) {Addition}; \node at (0,-3.2) {\tiny Gruppe}; -\node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut}; -\node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut}; +\uncover<4->{ + \node[color=blue] at (4.8,-0.5) [rotate=\a] {Ring\strut}; +} + +\uncover<2->{ + \node[color=red] at (-4.8,-0.5) [rotate=-\a] {Vektorraum\strut}; +} -\node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$}; +\uncover<6->{ + \node[color=darkgreen] at (0,2.6) {$(\lambda a)b=\lambda(ab)$}; +} -\node[color=red] at (-2.5,-0.5) {$\displaystyle -\begin{aligned} -\lambda(a+b)&=\lambda a + \lambda b\\ -(\lambda+\mu)a&=\lambda a +\mu a -\end{aligned}$}; +\uncover<3->{ + \node[color=red] at (-2.5,-0.5) {$\displaystyle + \begin{aligned} + \lambda(a+b)&=\lambda a + \lambda b\\ + (\lambda+\mu)a&=\lambda a +\mu a + \end{aligned}$}; +} -\node[color=blue] at (2.5,-0.5) {$\displaystyle -\begin{aligned} -a(b+c)&=ab+ac\\ -(a+b)c&=ac+bc -\end{aligned}$}; +\uncover<5->{ + \node[color=blue] at (2.5,-0.5) {$\displaystyle + \begin{aligned} + a(b+c)&=ab+ac\\ + (a+b)c&=ac+bc + \end{aligned}$}; +} \end{tikzpicture} \end{center} |