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author | hardythe1 | 2015-03-10 11:58:22 +0530 |
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committer | hardythe1 | 2015-03-10 11:58:22 +0530 |
commit | 4f190be89aaf9413c2dc93910cd09991e230b6b7 (patch) | |
tree | f0750811d65adb7705ba5cd6067fe8e25f1120f9 /using_sage_for_graphs | |
parent | 86d4d1e402c52ae5a8e92dbb12fda7d996a4dd49 (diff) | |
download | st-scripts-4f190be89aaf9413c2dc93910cd09991e230b6b7.tar.gz st-scripts-4f190be89aaf9413c2dc93910cd09991e230b6b7.tar.bz2 st-scripts-4f190be89aaf9413c2dc93910cd09991e230b6b7.zip |
modified 'using_sage' script cut it to 2
Diffstat (limited to 'using_sage_for_graphs')
-rw-r--r-- | using_sage_for_graphs/part2.rst | 178 | ||||
-rw-r--r-- | using_sage_for_graphs/script.odt | bin | 0 -> 33593 bytes | |||
-rw-r--r-- | using_sage_for_graphs/slides.tex | 149 |
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diff --git a/using_sage_for_graphs/part2.rst b/using_sage_for_graphs/part2.rst new file mode 100644 index 0000000..7eaca67 --- /dev/null +++ b/using_sage_for_graphs/part2.rst @@ -0,0 +1,178 @@ +########## Break Here ########## + +Now, let us look at Graph Theory in Sage. + +We shall look at some ways to create graphs and some of the graph +families available in Sage. + +The simplest way to define an arbitrary graph is to use a dictionary +of lists. We create a simple graph by using the ``Graph()`` function. + +.. L17 +:: + + G = Graph({0:[1,2,3], 2:[4]}) + +.. R18 + +to view the visualization of the graph, we say + +.. L18 +:: + + G.show() + +.. R19 + +Similarly, we can obtain a directed graph using the ``DiGraph`` +function. + +.. L19 +:: + + G = DiGraph({0:[1,2,3], 2:[4]}) + +.. R20 + +Sage also provides a lot of graph families which can be viewed by +typing ``graph.<tab>``. Let us obtain a complete graph with 5 vertices +and then show the graph. + +.. L20 +:: + + G = graphs.CompleteGraph(5) + + G.show() + +.. R21 + +Sage provides other functions for Number theory and +Combinatorics. Let's have a glimpse of a few of them. +``prime_range`` gives primes in the range 100 to 200. + +.. L21 +:: + + prime_range(100, 200) + +.. R22 + +``is_prime`` checks if 1999 is a prime number or not. + +.. L22 +:: + + is_prime(1999) + +.. R23 + +``factor(2001)`` gives the factorized form of 2001. + +.. L23 +:: + + factor(2001) + +.. R24 + +The ``Permutations()`` gives the permutations of ``[1, 2, 3, 4]`` + +.. L24 +:: + + C = Permutations([1, 2, 3, 4]) + C.list() + +.. R25 + +And the ``Combinations()`` gives all the combinations of ``[1, 2, 3, 4]`` + +.. L25 +:: + + C = Combinations([1, 2, 3, 4]) + C.list() + +.. L26 + +{{{ Show summary slide }}} + +.. R26 + +This brings us to the end of the tutorial.In this tutorial, +we have learnt to, + + 1. Use functions for calculus like -- + - lim()-- to find out the limit of a function + - diff()-- to find out the differentiation of an expression + - integrate()-- to integrate over an expression + - integral()-- to find out the definite integral of an + expression by specifying the limits + - solve()-- to solve a function, relative to it's position. + #. Create Both a simple graph and a directed graph, using the + functions ``graph`` and ``digraph`` respectively. + #. Use functions for Number theory.For eg: + - primes_range()-- to find out the prime numbers within the + specified range + - factor()-- to find out the factorized form of the number specified + - Permutations(), Combinations()-- to obtain the required permutation + and combinations for the given set of values. + +.. L27 + +{{{Show self assessment questions slide}}} + +.. R27 + +Here are some self assessment questions for you to solve + +1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends + to ``0`` from the negative side. + + +2. List all the primes between 2009 and 2900 + + +3. Solve the system of linear equations + + x-2y+3z = 7 + 2x+3y-z = 5 + x+2y+4z = 9 + +.. L28 + +{{{solution of self assessment questions on slide}}} + +.. R28 + +And the answers, + +1. To find out the limit of an expression from the negative side,we add + an argument dir="left" as +:: + + lim(x/sin(x), x=0, dir="left") + +2. The prime numbers from 2009 and 2900 can be obtained as, +:: + + prime_range(2009, 2901) + +3. We shall first write the equations in matrix form and then use the + solve() function +:: + + A = Matrix([[1, -2, 3], + [2, 3, -1], + [1, 2, 4]]) + + b = vector([7, 5, 9]) + + x = A.solve_right(b) + +To view the output type x +:: + + x + diff --git a/using_sage_for_graphs/script.odt b/using_sage_for_graphs/script.odt Binary files differnew file mode 100644 index 0000000..53dd5f4 --- /dev/null +++ b/using_sage_for_graphs/script.odt diff --git a/using_sage_for_graphs/slides.tex b/using_sage_for_graphs/slides.tex new file mode 100644 index 0000000..18e2d1c --- /dev/null +++ b/using_sage_for_graphs/slides.tex @@ -0,0 +1,149 @@ +\documentclass[17pt]{beamer} +\usetheme{Madrid} +\useoutertheme{noslidenum} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\usepackage{ae,aecompl} +\usepackage[scaled=.95]{helvet} +\usepackage[english]{babel} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{mathpazo,courier,euler} +\usepackage{listings} + +\lstset{language=sh, + basicstyle=\ttfamily\bfseries, + showstringspaces=false, + keywordstyle=\color{black}\bfseries} + +\definecolor{NavyBlue}{RGB}{0, 76, 153} +\setbeamercolor{structure}{fg=NavyBlue} +\author[FOSSEE]{} +\institute[IIT Bombay]{} +\date[]{} + +% theme split +\usepackage{verbatim} +\newenvironment{colorverbatim}[1][]% +{% +\color{blue} +\verbatim +}% +{% +\endverbatim +}% + +% logo +\logo{\includegraphics[height=1.30 cm]{../images/3t-logo.pdf}} +\logo{\includegraphics[height=1.30 cm]{../images/fossee-logo.png} + +\hspace{7.5cm} +\includegraphics[scale=0.3]{../images/fossee-logo.png}\\ +\hspace{281pt} +\includegraphics[scale=0.80]{../images/3t-logo.pdf}} + +\begin{document} + +\sffamily \bfseries +\title +[Graph Theory in Sage] +{Grapy Theory in Sage} +\author +[FOSSEE] +{\small Talk to a Teacher\\{\color{blue}\url{http://spoken-tutorial.org}}\\National Mission on Education + through ICT\\{\color{blue}\url{http://sakshat.ac.in}} \\ [0.8cm]Script by: Hardik Ghaghada \\Narration by: \\ [0.7cm] +{\small 15 May 2013}} + +% slide 1 +\begin{frame} + \titlepage +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Objectives} + By the end of this tutorial, you will, +\begin{itemize} +\item Learn about graph theory using Sage +\item Learn about number theory using Sage +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Summary} +In this tutorial, we have learnt to, +\begin{itemize} +\item Create Both a simple graph and a directed graph, using the functions +graph() and DiGraph() respectively +\item Create a complete graph using CompleteGraph() function +\item Use functions like primes_range(), factor(), Permutations(), +Combinations() +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Evaluation} +\begin{enumerate} +\item Find Permutations for the list ['a', 'b', 'c', 'd'] +\item List all the primes between 2009 and 2900 including 2900 +\end{enumerate} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Solutions} +\begin{enumerate} +\item C = Permutations(['a', 'b', 'c', 'd']) +\item prime_range(2009, 2901) +\end{enumerate} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{FOSSEE} +{\color{blue}Free and Open-source Software for \\Science and Engineering Education} \\ +\begin{itemize} +\item Goal - enabling all to use open source software tools +\item For more details, please visit {\color{blue}\url{http://fossee.in/}} +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{About the Spoken Tutorial Project} +\begin{itemize} +\item Watch the video available at {\color{blue}\url{http://spoken-tutorial.org /What\_is\_a\_Spoken\_Tutorial}} +\item It summarises the Spoken Tutorial project +\item If you do not have good bandwidth, you can download and watch it +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Spoken Tutorial Workshops}The Spoken Tutorial Project Team +\begin{itemize} +\item Conducts workshops using spoken tutorials +\item Gives certificates to those who pass an online test +\item For more details, please write to \\ \hspace {0.5cm}{\color{blue}contact@spoken-tutorial.org} +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Acknowledgements} +\begin{itemize} +\item Spoken Tutorial Project is a part of the Talk to a Teacher project +\item It is supported by the National Mission on Education through ICT, MHRD, Government of India +\item More information on this Mission is available at: \\{\color{blue}\url{http://spoken-tutorial.org/NMEICT-Intro}} +\end{itemize} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} + \begin{block}{} + \begin{center} + \textcolor{blue}{\Large THANK YOU!} + \end{center} + \end{block} +\begin{block}{} + \begin{center} + For more Information, visit our website\\ + \url{http://fossee.in/} + \end{center} + \end{block} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\end{document} |