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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-03-02 10:23:02 +0100 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-03-02 10:23:02 +0100 |
commit | a04efb8ee3eef6ec32b1381801ee244744db1201 (patch) | |
tree | 7d3ac94373d0c4ad7e5fa01b24152742851a2357 /vorlesungen/slides/4/fp.tex | |
parent | add slides (diff) | |
download | SeminarMatrizen-a04efb8ee3eef6ec32b1381801ee244744db1201.tar.gz SeminarMatrizen-a04efb8ee3eef6ec32b1381801ee244744db1201.zip |
division in F_p
Diffstat (limited to 'vorlesungen/slides/4/fp.tex')
-rw-r--r-- | vorlesungen/slides/4/fp.tex | 25 |
1 files changed, 23 insertions, 2 deletions
diff --git a/vorlesungen/slides/4/fp.tex b/vorlesungen/slides/4/fp.tex index a893238..caa6ceb 100644 --- a/vorlesungen/slides/4/fp.tex +++ b/vorlesungen/slides/4/fp.tex @@ -13,6 +13,13 @@ \def\rot#1#2{ \fill[color=red!20] ({#1-0.5},{5-#2-0.5}) rectangle ({#1+0.5},{5-#2+0.5}); } +\definecolor{darkgreen}{rgb}{0,0.6,0} +\def\gruen#1#2{ + \fill[color=darkgreen!20] ({#1-0.5},{6-#2-0.5}) rectangle ({#1+0.5},{6-#2+0.5}); +} +\def\inverse#1#2{ + \node at (9,{6-#1}) {$#1^{-1}=#2\mathstrut$}; +} \begin{frame}[t] \frametitle{Galois-Körper} \vspace{-20pt} @@ -53,7 +60,9 @@ $\Rightarrow \quad \mathbb{F}_p$ ist ein Körper \vspace{-20pt} \begin{center} \begin{tikzpicture}[>=latex,thick,scale=0.45] -\begin{scope}[xshift=-7cm] +\fill[color=white] (-12,0) circle[radius=0.1]; +\fill[color=white] (12,0) circle[radius=0.1]; +\begin{scope}[xshift=-8cm] \rot{2}{3} \rot{4}{3} \rot{3}{2} @@ -98,7 +107,13 @@ $\Rightarrow \quad \mathbb{F}_p$ ist ein Körper \feld{4}{5}{2} \feld{5}{4}{2} \feld{5}{5}{1} \end{scope} -\begin{scope}[xshift=7cm] +\begin{scope}[xshift=6cm] +\gruen{1}{1} +\gruen{2}{4} +\gruen{3}{5} +\gruen{4}{2} +\gruen{5}{3} +\gruen{6}{6} \fill[color=gray!40] (-0.5,6.5) rectangle (6.5,7.5); \fill[color=gray!40] (-1.5,-0.5) rectangle (-0.5,6.5); \foreach \x in {-0.5,6.5}{ @@ -143,6 +158,12 @@ $\Rightarrow \quad \mathbb{F}_p$ ist ein Körper \geld{5}{5}{4} \geld{6}{5}{2} \geld{5}{6}{2} \geld{6}{6}{1} +\inverse{1}{1} +\inverse{2}{4} +\inverse{3}{5} +\inverse{4}{2} +\inverse{5}{3} +\inverse{6}{6} \end{scope} \end{tikzpicture} \end{center} |