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-rw-r--r--using-sage/quickref.tex8
-rw-r--r--using-sage/script.rst197
-rw-r--r--using-sage/slides.tex106
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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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+========
+ Script
+========
+
+{{{ show the welcome slide }}}
+
+Welcome to this tutorial on using Sage.
+
+{{{ show the slide with outline }}}
+
+In this tutorial we shall quickly look at a few examples of the areas
+(name the areas, here) in which Sage can be used and how it can be
+used.
+
+{{{ 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='above')
+
+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.
+
+{{{ Show summary slide }}}
+
+We have looked at some of the functions available for Linear Algebra,
+Calculus, Graph Theory and Number theory.
+
+Thank You!
diff --git a/using-sage/slides.tex b/using-sage/slides.tex
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+++ b/using-sage/slides.tex
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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%Tutorial slides on Python.
+%
+% Author: FOSSEE
+% Copyright (c) 2009, FOSSEE, IIT Bombay
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\documentclass[14pt,compress]{beamer}
+%\documentclass[draft]{beamer}
+%\documentclass[compress,handout]{beamer}
+%\usepackage{pgfpages}
+%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
+
+% Modified from: generic-ornate-15min-45min.de.tex
+\mode<presentation>
+{
+ \usetheme{Warsaw}
+ \useoutertheme{infolines}
+ \setbeamercovered{transparent}
+}
+
+\usepackage[english]{babel}
+\usepackage[latin1]{inputenc}
+%\usepackage{times}
+\usepackage[T1]{fontenc}
+
+\usepackage{ae,aecompl}
+\usepackage{mathpazo,courier,euler}
+\usepackage[scaled=.95]{helvet}
+
+\definecolor{darkgreen}{rgb}{0,0.5,0}
+
+\usepackage{listings}
+\lstset{language=Python,
+ basicstyle=\ttfamily\bfseries,
+ commentstyle=\color{red}\itshape,
+ stringstyle=\color{darkgreen},
+ showstringspaces=false,
+ keywordstyle=\color{blue}\bfseries}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Macros
+\setbeamercolor{emphbar}{bg=blue!20, fg=black}
+\newcommand{\emphbar}[1]
+{\begin{beamercolorbox}[rounded=true]{emphbar}
+ {#1}
+ \end{beamercolorbox}
+}
+\newcounter{time}
+\setcounter{time}{0}
+\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
+
+\newcommand{\typ}[1]{\lstinline{#1}}
+
+\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} }
+
+% Title page
+\title{Your Title Here}
+
+\author[FOSSEE] {FOSSEE}
+
+\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
+\date{}
+
+% DOCUMENT STARTS
+\begin{document}
+
+\begin{frame}
+ \maketitle
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Outline}
+ \begin{itemize}
+ \item
+ \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% All other slides here. %%
+%% The same slides will be used in a classroom setting. %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
+ \frametitle{Summary}
+ \begin{itemize}
+ \item
+ \end{itemize}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Thank you!}
+ \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}