Added the script to plotting_using_sage

3 files changed, 374 insertions, 0 deletions

diff --git a/plotting_using_sage/quickref.tex b/plotting_using_sage/quickref.tex
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+Creating a tuple:\\
+{\ex \lstinline|    t = (1, "hello", 2.5)|}
+
+Accessing elements of tuples:\\
+{\ex \lstinline|    t[index] Ex: t[2]|}
+
+Accessing slices of tuples:\\
+{\ex \lstinline|    t[start:stop:step]|}
+
+Swapping values:\\
+{\ex \lstinline|    a, b = b, a|}
diff --git a/plotting_using_sage/script.rst b/plotting_using_sage/script.rst
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+.. Objectives
+.. ----------
+
+.. A - Students and teachers from Science and engineering backgrounds
+   B -
+   C - 
+   D - 
+
+.. Prerequisites
+.. -------------
+
+..   1. Getting started with lists
+     
+.. Author              : Nishanth Amuluru
+   Internal Reviewer   : 
+   External Reviewer   :
+   Checklist OK?       : <put date stamp here, if OK> [2010-10-05]
+
+Script
+------
+
+Hello friends, welcome to the tutorial on "Plotting using SAGE".
+
+{{{ Show the outline slide }}}
+
+In this tutorial we shall look at 
+ 
+ * 2D plotting in SAGE
+ * 3D plotting in SAGE
+
+We shall first create a symbolic variable ``x``
+::
+
+    x = var('x')
+
+We shall plot the function ``sin(x) - cos(x) ^ 2`` in the range (-5, 5).
+::
+
+    plot(sin(x) - cos(x) ^ 2, (x, -5, 5))
+
+As we can see, the plot is shown.
+
+``plot`` command takes the symbolic function as the first argument and the
+range as the second argument.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 1 %% Define a variable ``y`` and plot the function ``y^2 + 5y - 7`` in the
+        range (-3, 3)
+
+{{{ continue from paused state }}}
+
+::
+
+    y = var('y')
+    plot(y^2 + 5*y -7, (y, -3, 3))
+
+We have seen that plot command plots the given function on a linear range.
+
+What if the x and y values are functions of another variable.
+For instance, lets plot the trajectory of a projectile.
+
+A projectile was thrown at 50 m/s^2 and at an angle of 45 degrees from the 
+ground. We shall plot the trajectory of the particle for 5 seconds.
+
+These types of plots can be drawn using the parametric_plot function.
+We first define the time variable.
+::
+
+    t = var('t')
+
+Then we define the x and y as functions of t.
+::
+
+    f_x = 50 * cos(pi/4)
+    f_y = 50 * sin(pi/4) * t - 1/2 * 9.81 * t^2 )
+
+We then call the ``parametric_plot`` function as
+::
+
+    parametric_plot((f_x, f_y), (t, 0, 5))
+
+And we can see the trajectory of the projectile.
+
+The ``parametric_plot`` funciton takes a tuple of two functions as the first
+argument and the range over which the independent variable varies as the second
+argument.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 2 %% A particle is thrown into the air at 10 m/s^2 and at angle of 60 degrees
+        from the top of a 100 m tower. Plot the trajectory of the particle.
+
+{{{ continue from paused state }}}
+
+::
+
+    t = var('t')
+    f_x = 10 * cos(pi/3) * t
+    f_y = 100 + 10 * sin(pi/3) * t - 1/2 * 9.81 * t^2
+    parametric_plot((f_x, f_y), (t,0,5))
+
+Now we shall look at how to plot a set of points.
+
+We have the ``line`` function to acheive this.
+
+We shall plot sin(x) at few points and join them.
+
+First we need the set of points.
+::
+
+    points = [ (x, sin(x)) for x in srange(-2*float(pi), 2*float(pi), 0.75) ]
+
+``srange`` takes a start, a stop and a step argument and returns a list of
+point. We generate list of tuples in which the first value is ``x`` and second
+is ``sin(x)``.
+
+::
+
+    line(points)
+
+plots the points and joins them with a line.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 3 %% Plot the cosine function using line function.
+
+{{{ continue from paused state }}}
+
+::
+
+    points = [ (x, cos(x)) for x in srange(-2*float(pi), 2*float(pi), 0.75) ]
+    line(points)
+
+The ``line`` function behaves like the plot command in matplotlib. The
+difference is that ``plot`` command takes two sequences while line command
+expects a sequence of co-ordinates.
+
+As we can see, the axes limits are set by SAGE. Often we would want to set them
+ourselves. Moreover, the plot is shown here since the last command that is
+executed produces a plot. 
+
+Let us try this example
+::
+
+    plot(cos(x), (x,0,2*pi))
+    # Does the plot show up??
+
+As we can see here, the plot is not shown since the last command does not
+produce a plot.
+
+The actual way of showing a plot is to use the ``show`` command.
+
+::
+
+    p1 = plot(cos(x), (x,0,2*pi))
+    show(p1)
+    # What happens now??
+
+As we can see the plot is shown since we used it with ``show`` command.
+
+``show`` command is also used set the axes limits.
+
+::
+
+    p1 = plot(cos(x), (x,0,2*pi))
+    show(p1, xmin=0, xmax=2*pi, ymin=-1.2, ymax=1.2)
+
+As we can see, we just have to pass the right keyword arguments to the ``show``
+command to set the axes limits.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 4 %% Plot the cosine function in the range (-2pi, 2pi) and set the x-axis
+        limits to (-5, 5) and y-axis limits to (-2, 2) respectively.
+
+{{{ continue from paused state }}}
+
+::
+
+    p1 = plot(cos(x), (x, 0, 2*pi))
+    show(p1, xmin=-5, xmax=5, ymin=-2, ymax=2)
+
+The ``show`` command can also be used to show multiple plots.
+::
+
+    p1 = plot(cos(x), (x, 0, 2*pi))
+    p2 = plot(sin(x), (x, 0, 2*pi))
+    show(p1+p2)
+
+As we can see, we can add the plots and use them in the ``show`` command.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 5 %% Plot sin(x) and sin(2*x) in the range (0, 2pi)
+
+{{{ continue from paused state }}}
+
+::
+
+    p1 = plot(sin(x), (x, 0, 2*pi))
+    p2 = plot(sin(2*x), (x, 0, 2*pi))
+    show(p1+p2)
+
+Now we shall look at 3D plotting in SAGE.
+
+We have the ``plot3d`` function that takes a function in terms of two 
+independent variables and the range over which they vary.
+
+::
+
+    x, y = var('x y')
+    plot3d(x^2 + y^2, (x, 0, 2), (y, 0, 2))
+
+We get a 3D plot which can be rotated and zoomed using the mouse.
+
+{{{ Pause here and try out the following exercises }}}
+
+%% 6 %% Plot the function sin(x)^2 + cos(y)^2 for x in range (0,2) and y in
+        range (-2, 2)
+
+{{{ continue from paused state }}}
+
+::
+
+    x, y = var("x y")
+    plot3d( sin(x)^2 + cos(y)^2, (x, 0, 2), (y, -2, 2))
+
+``parametric_plot3d`` function plots the surface in which x, y and z are
+functions of another variable.
+
+::
+
+   u, v = var("u v")
+   f_x = u
+   f_y = v
+   f_z = u^2 + v^2
+   parametric_plot3d((f_x, f_y, f_z), (u, 0, 2), (v, 0, 2))
+
+{{{ Show summary slide }}}
+
+This brings us to the end of the tutorial.
+we have learnt
+
+ * How to draw 2D plots using plot comand
+ * How to use the parametric_plot and line functions
+ * How to use show command for multiple plots and setting axes limits
+ * How to draw 3D plots
+
+{{{ Show the "sponsored by FOSSEE" slide }}}
+
+#[Nishanth]: Will add this line after all of us fix on one.
+This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
+
+Hope you have enjoyed and found it useful.
+Thankyou
+
diff --git a/plotting_using_sage/slides.tex b/plotting_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}