Renamed all LOs to match with their names in progress.org.

4 files changed, 378 insertions, 0 deletions

diff --git a/using_sage/quickref.tex b/using_sage/quickref.tex
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+Creating a linear array:\\
+{\ex \lstinline|    x = linspace(0, 2*pi, 50)|}
+
+Plotting two variables:\\
+{\ex \lstinline|    plot(x, sin(x))|}
+
+Plotting two lists of equal length x, y:\\
+{\ex \lstinline|    plot(x, y)|}
diff --git a/using_sage/script.rst b/using_sage/script.rst
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+.. Objectives
+.. ----------
+
+.. By the end of this tutorial you will --
+
+.. 1. Get an idea of the range of things for which Sage can be used. 
+.. #. Know some of the functions for Calculus
+.. #. Get some insight into Graphs in Sage. 
+
+
+.. Prerequisites
+.. -------------
+
+.. Getting Started -- Sage  
+     
+.. Author              : Puneeth 
+   Internal Reviewer   : Anoop Jacob Thomas<anoop@fossee.in>
+   External Reviewer   :
+   Language Reviewer   : Bhanukiran
+   Checklist OK?       : <06-11-2010, Anand, OK> [2010-10-05]
+
+Script
+------
+
+{{{ show the welcome slide }}}
+
+Hello Friends. Welcome to this tutorial on using Sage.
+
+{{{ show the slide with outline }}} 
+
+In this tutorial we shall quickly look at a few examples of using Sage
+for Linear Algebra, Calculus, Graph Theory and Number theory.
+
+{{{ show the slide with Calculus outline }}} 
+
+Let us begin with Calculus. We shall be looking at limits,
+differentiation, integration, and Taylor polynomial.
+
+{{{ show sage notebook }}}
+
+We have our Sage notebook running. In case, you don't have it running,
+start is using the command, ``sage --notebook``.
+
+To find the limit of the function x*sin(1/x), at x=0, we say
+::
+
+   lim(x*sin(1/x), x=0)
+
+We get the limit to be 0, as expected. 
+
+It is also possible to the limit at a point from one direction. For
+example, let us find the limit of 1/x at x=0, when approaching from
+the positive side.
+::
+
+    lim(1/x, x=0, dir='above')
+
+To find the limit from the negative side, we say,
+::
+
+    lim(1/x, x=0, dir='below')   
+
+Let us now see how to differentiate, using Sage. We shall find the
+differential of the expression ``exp(sin(x^2))/x`` w.r.t ``x``. We
+shall first define the expression, and then use the ``diff`` function
+to obtain the differential of the expression.
+::
+
+    var('x')
+    f = exp(sin(x^2))/x
+
+    diff(f, x)
+
+We can also obtain the partial differentiation of an expression w.r.t
+one of the variables. Let us differentiate the expression
+``exp(sin(y - x^2))/x`` w.r.t x and y.
+::
+
+    var('x y')
+    f = exp(sin(y - x^2))/x
+
+    diff(f, x)
+
+    diff(f, y)
+
+Now, let us look at integration. We shall use the expression obtained
+from the differentiation that we did before, ``diff(f, y)`` ---
+``e^(sin(-x^2 + y))*cos(-x^2 + y)/x``. The ``integrate`` command is
+used to obtain the integral of an expression or function.
+::
+
+    integrate(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y)
+
+We get back the correct expression. The minus sign being inside or
+outside the ``sin`` function doesn't change much. 
+
+Now, let us find the value of the integral between the limits 0 and
+pi/2. 
+::
+
+    integral(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y, 0, pi/2)
+
+Let us now see how to obtain the Taylor expansion of an expression
+using sage. Let us obtain the Taylor expansion of ``(x + 1)^n`` up to
+degree 4 about 0.
+::
+
+    var('x n')
+    taylor((x+1)^n, x, 0, 4)
+
+This brings us to the end of the features of Sage for Calculus, that
+we will be looking at. For more, look at the Calculus quick-ref from
+the Sage Wiki. 
+
+Next let us move on to Matrix Algebra. 
+
+{{{ show the equation on the slides }}}
+
+Let us begin with solving the equation ``Ax = v``, where A is the
+matrix ``matrix([[1,2],[3,4]])`` and v is the vector
+``vector([1,2])``. 
+
+To solve the equation, ``Ax = v`` we simply say
+::
+
+    x = solve_right(A, v)
+
+To solve the equation, ``xA = v`` we simply say
+::
+
+    x = solve_left(A, v)
+
+The left and right here, denote the position of ``A``, relative to x. 
+
+#[Puneeth]: any suggestions on what more to add?
+
+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
+::
+
+  G = Graph({0:[1,2,3], 2:[4]})
+
+We say 
+::
+
+  G.show()
+
+to view the visualization of the graph. 
+
+Similarly, we can obtain a directed graph using the ``DiGraph``
+function. 
+::
+
+  G = DiGraph({0:[1,2,3], 2:[4]})
+
+
+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. 
+::
+
+  G = graphs.CompleteGraph(5)
+
+  G.show()
+
+
+Sage provides other functions for Number theory and
+Combinatorics. Let's have a glimpse of a few of them.  
+
+
+::
+
+  prime_range(100, 200)
+
+gives primes in the range 100 to 200. 
+
+::
+
+  is_prime(1999) 
+
+checks if 1999 is a prime number or not. 
+
+::
+
+  factor(2001)
+
+gives the factorized form of 2001. 
+
+::
+
+  C = Permutations([1, 2, 3, 4])
+  C.list()
+
+gives the permutations of ``[1, 2, 3, 4]``
+
+::
+
+  C = Combinations([1, 2, 3, 4])
+  C.list()
+
+gives all the combinations of ``[1, 2, 3, 4]``
+  
+That brings us to the end of this session showing various features
+available in Sage. 
+
+.. #[[Anoop: I feel we should add more slides, a possibility is to add
+   the code which they are required to type in, I also feel we should
+   add some review problems for them to try out.]]
+
+{{{ Show summary slide }}}
+
+We have looked at some of the functions available for Linear Algebra,
+Calculus, Graph Theory and Number theory.   
+
+This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
+
+Hope you have enjoyed and found it useful.
+Thank you!
+
diff --git a/using_sage/slides.org b/using_sage/slides.org
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+++ b/using_sage/slides.org
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+#+LaTeX_CLASS: beamer
+#+LaTeX_CLASS_OPTIONS: [presentation]
+#+BEAMER_FRAME_LEVEL: 1
+
+#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent}
+#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra)
+#+PROPERTY: BEAMER_col_ALL 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 :ETC
+
+#+LaTeX_CLASS: beamer
+#+LaTeX_CLASS_OPTIONS: [presentation]
+
+#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl}
+#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet}
+
+#+LaTeX_HEADER: \usepackage{listings}
+
+#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries,
+#+LaTeX_HEADER:  commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},
+#+LaTeX_HEADER:  showstringspaces=false, keywordstyle=\color{blue}\bfseries}
+
+#+TITLE:    using Sage
+#+AUTHOR:    FOSSEE
+#+EMAIL:     
+#+DATE:    
+
+#+DESCRIPTION: 
+#+KEYWORDS: 
+#+LANGUAGE:  en
+#+OPTIONS:   H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t
+#+OPTIONS:   TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc
+
+* Outline
+  - Calculus
+  - Linear Algebra 
+  - Graph Theory
+  - Number Theory
+* Summary
+  - Differentiating and Integrating
+  - Taylor Expansions
+  - Solving Equations
+  - Initializing Graphs & Graph families
+  - Prime numbers
+  - Factors
+  - Combinations & Permutations
+* Thank you!
+#+begin_latex
+  \begin{block}{}
+  \begin{center}
+  This spoken tutorial has been produced by the
+  \textcolor{blue}{FOSSEE} team, which is funded by the 
+  \end{center}
+  \begin{center}
+    \textcolor{blue}{National Mission on Education through \\
+      Information \& Communication Technology \\ 
+      MHRD, Govt. of India}.
+  \end{center}  
+  \end{block}
+#+end_latex
+
+
diff --git a/using_sage/slides.tex b/using_sage/slides.tex
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+% Created 2010-10-27 Wed 13:16
+\documentclass[presentation]{beamer}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{fixltx2e}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{float}
+\usepackage{wrapfig}
+\usepackage{soul}
+\usepackage{t1enc}
+\usepackage{textcomp}
+\usepackage{marvosym}
+\usepackage{wasysym}
+\usepackage{latexsym}
+\usepackage{amssymb}
+\usepackage{hyperref}
+\tolerance=1000
+\usepackage[english]{babel} \usepackage{ae,aecompl}
+\usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet}
+\usepackage{listings}
+\lstset{language=Python, basicstyle=\ttfamily\bfseries,
+commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},
+showstringspaces=false, keywordstyle=\color{blue}\bfseries}
+\providecommand{\alert}[1]{\textbf{#1}}
+
+\title{using Sage}
+\author{FOSSEE}
+\date{}
+
+\usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent}
+\begin{document}
+
+\maketitle
+
+
+
+
+
+
+
+
+
+\begin{frame}
+\frametitle{Outline}
+\label{sec-1}
+
+\begin{itemize}
+\item Calculus
+\item Linear Algebra
+\item Graph Theory
+\item Number Theory
+\end{itemize}
+\end{frame}
+\begin{frame}
+\frametitle{Summary}
+\label{sec-2}
+
+\begin{itemize}
+\item Differentiating and Integrating
+\item Taylor Expansions
+\item Solving Equations
+\item Initializing Graphs \& Graph families
+\item Prime numbers
+\item Factors
+\item Combinations \& Permutations
+\end{itemize}
+\end{frame}
+\begin{frame}
+\frametitle{Thank you!}
+\label{sec-3}
+
+  \begin{block}{}
+  \begin{center}
+  This spoken tutorial has been produced by the
+  \textcolor{blue}{FOSSEE} team, which is funded by the 
+  \end{center}
+  \begin{center}
+    \textcolor{blue}{National Mission on Education through \\
+      Information \& Communication Technology \\ 
+      MHRD, Govt. of India}.
+  \end{center}  
+  \end{block}
+\end{frame}
+
+\end{document}