From 3c4b834382461bf8959446e95f7c90cccc2e243d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jonathan=20Schmidt-Domin=C3=A9?= <git@the-user.org>
Date: Thu, 12 Apr 2012 04:19:18 +0200
Subject: [PATCH] =?UTF-8?q?Sage-Pr=C3=A4sentation?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 kiss/sage/cantor.png | Bin 0 -> 40146 bytes
 kiss/sage/sage.pdf   | Bin 0 -> 118412 bytes
 kiss/sage/sage.tex   | 288 +++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 288 insertions(+)
 create mode 100644 kiss/sage/cantor.png
 create mode 100644 kiss/sage/sage.pdf
 create mode 100644 kiss/sage/sage.tex

diff --git a/kiss/sage/cantor.png b/kiss/sage/cantor.png
new file mode 100644
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diff --git a/kiss/sage/sage.tex b/kiss/sage/sage.tex
new file mode 100644
index 0000000..385944a
--- /dev/null
+++ b/kiss/sage/sage.tex
@@ -0,0 +1,288 @@
+\documentclass{beamer}
+
+\usepackage[ngerman]{babel}
+
+\usepackage{savesym}
+
+\usepackage{kpfonts} %varprod
+
+\savesymbol{approx}
+\savesymbol{colonapprox}
+\savesymbol{colonsim}
+
+\usepackage{colonequals} %colonequals ≔
+\usepackage{ulsy} %blitza
+
+\newcommand{\ccode}[1]{\texttt{\lstinline[basicstyle=]!#1!}}
+
+\usepackage{iftex}
+\ifPDFTeX
+  \usepackage[utf8]{inputenc}
+  \usepackage[T1]{fontenc}
+  \usepackage{uniinput}
+  \usepackage{lmodern}
+  \usepackage{amsmath}
+  \usepackage{amssymb}
+\else
+  \ifLuaTeX
+    \usepackage{luatextra}
+    \usepackage{amsmath}
+    \usepackage{amssymb}
+    \usepackage{lmodern}
+    \usepackage{uniinput-lualatex}
+    \usepackage{fontspec}
+  \fi
+\fi
+
+\usepackage{amsthm}
+
+\usepackage{sagetex}
+
+\beamertemplatenavigationsymbolsempty
+\usetheme{Anadyr}
+\newcommand{\hideinstitute}{}
+\renewcommand{\footerauthorwidth}{0.25}
+\renewcommand{\footertitlewidth}{0.5}
+\renewcommand{\footerdatewidth}{0.25}
+\newcommand{\blackframe}{{\setbeamercolor{normal text}{bg=black!100} \frame[plain]{}}}
+
+\usepackage{hyperref}
+
+\usepackage{float}
+
+\usepackage{tikz}
+\usetikzlibrary{shapes,arrows}
+
+\newcommand{\symdiff}{\ensuremath{\ominus}} % some math symbols
+\newcommand{\dsum}{\ensuremath{\bigoplus}}
+\newcommand{\ps}[1]{\ensuremath{\mathcal P\left(#1\right)}}
+
+\savesymbol{corollary}
+\savesymbol{lemma}
+\savesymbol{theorem}
+\newcounter{satz}
+\newcounter{definition}
+\newtheorem{lemma}[satz]{Lemma}
+\newtheorem{corollary}[satz]{Korollar}
+\newtheorem{theorem}[satz]{Satz}
+\theoremstyle{definition}
+\newtheorem{defi}[definition]{Definition}
+
+\title{Kurzeinführung Sage}
+\author{Jonathan Schmidt-Dominé}
+\institute{RWTH Aachen}
+
+\setcounter{tocdepth}{1} % short tocs are usually better in presentations
+
+\begin{document}
+
+\frame{
+  \titlepage
+}
+
+\frame[allowframebreaks]{
+  \tableofcontents
+}
+
+\section{Allgemeines}
+\subsection{Was ist Sage?}
+\begin{frame}
+ \begin{itemize}
+  \item<+-> Computeralgebrasystem, Computeralgebra im weitesten Sinne
+  \item<+-> Verwendung üblicher Programmiersprache: Python
+  \item<+-> Frei (und kostenlos)
+  \item<+-> Integriert Features verschiedenster anderer freier Software: Maxima, R, Singular, GAP, …
+ \end{itemize}
+\end{frame}
+
+\subsection{Frontends}
+\begin{frame}
+ \begin{block}{Web-Frontend}
+  \begin{itemize}
+   \item Arbeitet als lokaler HTTP-Server\pause
+   \item Über Browser zu bedienen, mit MathJax
+  \end{itemize}
+ \end{block}
+ \pause
+ \begin{block}{Cantor}
+  \begin{center}
+    \includegraphics[scale=0.3]{./cantor.png}
+ % cantor.png: 855x672 pixel, 96dpi, 22.62x17.78 cm, bb=
+  \end{center}
+ \end{block}
+\end{frame}
+
+\section{Grundlagen}
+\subsection{Umgang mit Variablen und Ausdrücken}
+\begin{frame}[fragile]
+ \begin{itemize}
+  \item<+-> Alle Ausdrücke sind ganz normale Python-Objekte
+  \item<+-> Symbolischer Ausdrück erzeugt durch \ccode{var} (wenn nicht standardmäßig vorhanden)
+  \begin{sageblock}
+   var('x,y')
+  \end{sageblock}
+  \item<+-> Rechnen liefert symbolische Ausdrücke
+  \begin{sageblock}
+   product = x*y
+  \end{sageblock}
+  \item<+-> Einsetzen möglich:
+  \begin{sageblock}
+   product(y=1)
+  \end{sageblock}
+  ergibt
+  \[
+   \sage{(x*y)(y=1)}
+  \]
+  \item<+-> Hilfe
+  \begin{verbatim}
+   plot?
+  \end{verbatim}
+ \end{itemize}
+\end{frame}
+
+\subsection{Gleichungen lösen}
+\begin{frame}[fragile]
+ \begin{itemize}
+  \item<+-> Gleichung lösen mittels \ccode{solve}:
+    \begin{sagesilent}var('n')\end{sagesilent}
+    \begin{sageblock}
+     s=solve(sin(n*x)==1, x)
+    \end{sageblock}
+    \[
+     \sage{s[0]}
+    \]
+  \item<+-> Gleichungssystem:
+    \begin{sageblock}
+     s=solve([x + 2*y == 1, x - y == 0], (x, y))
+    \end{sageblock}
+    \[
+     \sage{s[0]}
+    \]
+ \end{itemize}
+\end{frame}
+
+\subsection{Plots}
+\begin{frame}[fragile]
+ \begin{block}{Kreishälfte}
+  \begin{sageblock}
+   r=2
+   p=plot(sqrt(r^2 - x^2), (x, -r, r))
+  \end{sageblock}
+  \begin{center}
+   \sageplot[scale=.4]{p}
+  \end{center}
+ \end{block}
+\end{frame}
+
+
+
+\section{Analysis}
+\subsection{Differentiation}
+\begin{frame}[fragile]
+\begin{itemize}
+ \item<+-> Erste Ableitung
+  \begin{sageblock}
+   d=diff(x^3, x)
+  \end{sageblock}
+  \[
+   \sage{d}
+  \]
+ \item<+-> Zweite Ableitung
+  \begin{sageblock}
+   d=diff(x^3, x, x) # oder diff(x^3, x, 2)s
+  \end{sageblock}
+  \[
+   \sage{d}
+  \]
+ \item<+-> Mehrere Richtungen
+  \begin{sagesilent}
+   var('z')
+  \end{sagesilent}
+  \begin{sageblock}
+   f(x,y) = [x*y*z, x*y^2*z]
+   d = diff(f)
+  \end{sageblock}
+  \[
+   \sage{d}
+  \]
+ \end{itemize}
+\end{frame}
+
+
+\subsection{Grenzwerte}
+\begin{frame}[fragile]
+ \begin{itemize}
+  \item<+-> Geometrische Reihe
+    \begin{sagesilent}
+     var('n,b')
+    \end{sagesilent}
+    \begin{sageblock}
+     assume(b>1)
+     l = sum(1/b^n, n, 1, infinity)
+    \end{sageblock}
+    \[
+     l = \sage{l}
+    \]
+  \item<+-> Asymptote
+    \begin{sageblock}
+     l = limit(log(exp(x) + exp(-x)) / x, x=infinity)
+    \end{sageblock}
+    \[
+     l=\sage{l}
+    \]
+ \end{itemize}
+\end{frame}
+
+\subsection{Gewöhnliche Differentialgleichung}
+
+\begin{frame}[fragile]
+\begin{block}{Harmonischer Oszillator}
+\begin{sagesilent}
+ f = function('f', x)
+ omega = var('omega')
+\end{sagesilent}
+
+\begin{sageblock}
+ assume(omega != 0)
+ s=desolve(diff(diff(f, x), x) == -omega^2*f, f, ivar=x)
+\end{sageblock}
+\[
+ \sage{s}
+\]
+\begin{center}
+ \sageplot[scale=0.3]{plot(s(omega=1, k1=1, k2=0), (x, 0, 2*pi))}
+\end{center}
+\end{block}
+\end{frame}
+
+\section{Abstraktes}
+\subsection{Zahlbereiche etc.}
+\begin{frame}[fragile]
+ \begin{itemize}
+  \item<+-> Ganze Zahlen \ccode{ZZ}
+  \item<+-> Rationale Zahlen \ccode{QQ}
+  \item<+-> Gleitkommazahlen mit gewisser Anzahl an Stellen \ccode{RealField(n)} oder einfach \ccode{RR}
+  \begin{sageblock}
+   RF = RealField
+   s = RF(2)(2.2) + RF(2)(2.5)
+  \end{sageblock}
+  \[
+   s = \sage{s}
+  \]
+  \item<+-> Komplexe Gleitkommazahlen \ccode{ComplexField(n)} oder einfach \ccode{CC}
+  \item<+-> Polynome \ccode{QQ['x']}
+  \item<+-> Restklassenringe \ccode{ZZ.quotient(n*ZZ)}
+  \begin{sageblock}
+   ZZ5 = ZZ.quotient(5*ZZ)
+   s = ZZ5(3) + ZZ5(4)
+  \end{sageblock}
+  \[
+   s = \sage{s}
+  \]
+
+
+ \end{itemize}
+
+\end{frame}
+
+\end{document}
-- 
GitLab