# HG changeset patch
# User amit
# Date 1288089482 -19800
# Node ID 054117c9dd593fac471e068f183ca38a3d552a2a
# Parent  d14bc84feca16e45fb2c66cef01c79f52c1529cd
changed the name of symbolics to getting started with symbolics

diff -r d14bc84feca1 -r 054117c9dd59 getting-started-with-lists/getting_started_with_lists.rst
--- a/getting-started-with-lists/getting_started_with_lists.rst	Tue Oct 26 16:04:50 2010 +0530
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,137 +0,0 @@
-Hello friends and welcome to the tutorial on getting started with
-lists.
-
- {{{ Show the slide containing title }}}
-
- {{{ Show the slide containing the outline slide }}}
-
-In this tutorial we will be getting acquainted with a python data
-structure called lists.  We will learn ::
- 
- * How to create lists
- * Structure of lists
- * Access list elements
- * Append elements to lists
- * Deleting elements from lists
-
-List is a compound data type, it can contain data of other data
-types. List is also a sequence data type, all the elements are in
-order and there order has a meaning.
-
-We will first create an empty list with no elements. On your IPython
-shell type ::
-
-   empty = [] 
-   type(empty)
-   
-
-This is an empty list without any elements.
-
-* Filled lists
-
-Lets now define a list, nonempty and fill it with some random elements.
-
-nonempty = ['spam', 'eggs', 100, 1.234]
-
-Thus the simplest way of creating a list is typing out a sequence 
-of comma-separated values (items) between square brackets. 
-All the list items need not have the same data type.
-
-
-
-As we can see lists can contain different kinds of data. In the
-previous example 'spam' and 'eggs' are strings and 100 and 1.234
-integer and float. Thus we can put elements of heterogenous types in
-lists. Thus list themselves can be one of the element types possible
-in lists. Thus lists can also contain other lists.  Example ::
-
-      list_in_list=[[4,2,3,4],'and', 1, 2, 3, 4]
-
-We access list elements using the number of index. The
-index begins from 0. So for list nonempty, nonempty[0] gives the
-first element, nonempty[1] the second element and so on and
-nonempty[3] the last element. ::
-
-	    nonempty[0] 
-	    nonempty[1] 
-	    nonempty[3]
-
-We can also access the elememts from the end using negative indices ::
-   
-   nonempty[-1] 
-   nonempty[-2] 
-   nonempty[-4]
-
--1 gives the last element which is the 4th element , -2 second to last and -4 gives the fourth
-from last element which is first element.
-
-We can append elements to the end of a list using append command. ::
-
-   nonempty.append('onemore') 
-   nonempty
-   nonempty.append(6) 
-   nonempty
-   
-As we can see non empty appends 'onemore' and 6 at the end.
-
-
-
-Using len function we can check the number of elements in the list
-nonempty. In this case it being 6 ::
-	 
-	 len(nonempty)
-
-
-
-Just like we can append elements to a list we can also remove them.
-There are two ways of doing it. One is by using index. ::
-
-      del(nonempty[1])
-
-
-
-deletes the element at index 1, i.e the second element of the
-list, 'eggs'. The other way is removing element by content. Lets say
-one wishes to delete 100 from nonempty list the syntax of the command
-should be :: 
-      
-      a.remove(100)
-
-but what if their were two 100's. To check that lets do a small
-experiment. ::
-
-	   a.append('spam') 
-	   a 
-	   a.remove('spam') 
-	   a
-
-If we check a now we will see that the first occurence 'spam' is removed
-thus remove removes the first occurence of the element in the sequence
-and leaves others untouched.
-
-
-{{{Slide for Summary }}}
-
-
-In this tutorial we came across a sequence data type called lists. ::
-
- * We learned how to create lists.  
- * How to access lists.
- * Append elements to list.
- * Delete Element from list.  
- * And Checking list length.
- 
-
-
-{{{ Sponsored by Fossee Slide }}}
-
-This tutorial was created as a part of FOSSEE project.
-
-I hope you found this tutorial useful.
-
-Thank You
-
-
- * Author : Amit Sethi 
- * First Reviewer : 
- * Second Reviewer : Nishanth
diff -r d14bc84feca1 -r 054117c9dd59 getting-started-with-symbolics/questions.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-with-symbolics/questions.rst	Tue Oct 26 16:08:02 2010 +0530
@@ -0,0 +1,61 @@
+Objective Questions
+-------------------
+
+.. A mininum of 8 questions here (along with answers)
+
+1. How do you define a name 'y' as a symbol?
+
+
+   Answer: var('y')
+
+2. List out some constants pre-defined in sage?
+
+   Answer: pi, e ,euler_gamma
+
+3. List the functions for differentiation and integration in sage?
+
+   Answer: diff and integral
+
+4. Get the value of pi upto precision 5 digits using sage?
+
+   Answer: n(pi,5)
+
+5.  Find third order differential of function.
+
+    f(x)=sin(x^2)+exp(x^3)
+
+    Answer: diff(f(x),x,3) 
+
+6. What is the function to find factors of an expression?
+
+   Answer: factor
+
+7. What is syntax for simplifying a function f?
+
+   Answer f.simplify_full()
+
+8. Find the solution for x between pi/2 to pi for the given equation?
+   
+   sin(x)==cos(x^3)+exp(x^4)
+   find_root(sin(x)==cos(x^3)+exp(x^4),pi/2,pi)
+
+9. Create a simple two dimensional matrix with two symbolic variables?
+
+   var('a,b')
+   A=matrix([[a,1],[2,b]])
+
+Larger Questions
+----------------
+
+.. A minimum of 2 questions here (along with answers)
+
+1.Find the points of intersection of the circles
+
+ x^2 + y^2 - 4x = 1 
+ x^2 + y^2 - 2y = 9  
+
+2. Integrate the function 
+
+x^2*cos(x)
+
+between 1 to 3.
diff -r d14bc84feca1 -r 054117c9dd59 getting-started-with-symbolics/quickref.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-with-symbolics/quickref.tex	Tue Oct 26 16:08:02 2010 +0530
@@ -0,0 +1,8 @@
+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 -r d14bc84feca1 -r 054117c9dd59 getting-started-with-symbolics/script.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-with-symbolics/script.rst	Tue Oct 26 16:08:02 2010 +0530
@@ -0,0 +1,277 @@
+Symbolics with Sage
+-------------------
+
+Hello friends and welcome to the tutorial on symbolics with sage.
+
+{{{ Show welcome slide }}}
+
+
+.. #[Madhu: What is this line doing here. I don't see much use of it]
+
+During the course of the tutorial we will learn
+
+{{{ Show outline slide  }}}
+
+* Defining symbolic expressions in sage.  
+* Using built-in costants and functions. 
+* Performing Integration, differentiation using sage. 
+* Defining matrices. 
+* Defining Symbolic functions.  
+* Simplifying and solving symbolic expressions and functions.
+
+We can use Sage for symbolic maths. 
+
+On the sage notebook type::
+   
+    sin(y)
+
+It raises a name error saying that y is not defined. But in sage we
+can declare y as a symbol using var function.
+
+
+::
+    var('y')
+   
+Now if you type::
+
+    sin(y)
+
+sage simply returns the expression.
+
+
+Thus sage treats sin(y) as a symbolic expression . We can use
+this to do  symbolic maths using sage's built-in constants and
+expressions..
+
+
+So let us try ::
+   
+   var('x,alpha,y,beta') 
+   x^2/alpha^2+y^2/beta^2
+ 
+taking another example
+   
+   var('theta')
+   sin^2(theta)+cos^2(theta)
+
+
+Similarly, we can define many algebraic and trigonometric expressions
+using sage .
+
+
+Sage also provides a few built-in constants which are commonly used in
+mathematics .
+
+example : pi,e,infinity , Function n gives the numerical values of all these
+    constants.
+
+{{{ Type n(pi)
+   	n(e)
+	n(oo) 
+    On the sage notebook }}}  
+
+
+
+If you look into the documentation of function "n" by doing
+
+.. #[Madhu: "documentation of the function "n"?]
+
+::
+   n(<Tab>
+
+You will see what all arguments it takes and what it returns. It will be very
+helpful if you look at the documentation of all functions introduced through
+this script.
+
+
+
+Also we can define the no. of digits we wish to use in the numerical
+value . For this we have to pass an argument digits.  Type
+
+.. #[Madhu: "no of digits"? Also "We wish to obtain" than "we wish to
+     use"?]
+::
+
+   n(pi, digits = 10)
+
+Apart from the constants sage also has a lot of builtin functions like
+sin,cos,log,factorial,gamma,exp,arcsin etc ...
+lets try some of them out on the sage notebook.
+
+
+::
+     
+   sin(pi/2)
+   
+   arctan(oo)
+     
+   log(e,e)
+
+
+Given that we have defined variables like x,y etc .. , We can define
+an arbitrary function with desired name in the following way.::
+
+       var('x') 
+       function('f',x)
+
+
+Here f is the name of the function and x is the independent variable .
+Now we can define f(x) to be ::
+
+     f(x) = x/2 + sin(x)
+
+Evaluating this function f for the value x=pi returns pi/2.::
+	   
+	   f(pi)
+
+We can also define functions that are not continuous but defined
+piecewise.  Let us define a function which is a parabola between 0
+to 1 and a constant from 1 to 2 .  Type the following as given on the
+screen
+
+::
+      
+
+      var('x') 
+      h(x)=x^2 g(x)=1 
+      f=Piecewise(<Tab>
+
+{{{ Show the documentation of Piecewise }}} 
+    
+::
+      f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) f
+
+
+
+
+We can also define functions which are series 
+
+
+We first define a function f(n) in the way discussed above.::
+
+   var('n') 
+   function('f', n)
+
+
+To sum the function for a range of discrete values of n, we use the
+sage function sum.
+
+For a convergent series , f(n)=1/n^2 we can say ::
+   
+   var('n') 
+   function('f', n)
+
+   f(n) = 1/n^2
+
+   sum(f(n), n, 1, oo)
+
+ 
+Lets us now try another series ::
+
+
+    f(n) = (-1)^(n-1)*1/(2*n - 1)
+    sum(f(n), n, 1, oo)
+
+
+This series converges to pi/4. 
+
+
+Moving on let us see how to perform simple calculus operations using Sage
+
+For example lets try an expression first ::
+
+    diff(x**2+sin(x),x) 
+    2x+cos(x)
+
+The diff function differentiates an expression or a function. Its
+first argument is expression or function and second argument is the
+independent variable.
+
+We have already tried an expression now lets try a function ::
+
+   f=exp(x^2)+arcsin(x) 
+   diff(f(x),x)
+
+To get a higher order differential we need to add an extra third argument
+for order ::
+ 
+   diff(<tab> diff(f(x),x,3)
+
+in this case it is 3.
+
+
+Just like differentiation of expression you can also integrate them ::
+
+     x = var('x') 
+     s = integral(1/(1 + (tan(x))**2),x) 
+     s
+
+
+
+Many a times we need to find factors of an expression ,we can use the "factor" function
+
+::
+    factor(<tab> 
+    y = (x^100 - x^70)*(cos(x)^2 + cos(x)^2*tan(x)^2) 
+    f = factor(y)
+
+One can  simplify complicated expression ::
+    
+    f.simplify_full()
+
+This simplifies the expression fully . We can also do simplification
+of just the algebraic part and the trigonometric part ::
+
+    f.simplify_exp() 
+    f.simplify_trig()
+    
+
+
+One can also find roots of an equation by using find_root function::
+
+    phi = var('phi') 
+    find_root(cos(phi)==sin(phi),0,pi/2)
+
+Lets substitute this solution into the equation and see we were
+correct ::
+
+     var('phi') 
+     f(phi)=cos(phi)-sin(phi)
+     root=find_root(f(phi)==0,0,pi/2) 
+     f.substitute(phi=root)
+
+as we can see when we substitute the value the answer is almost = 0 showing 
+the solution we got was correct.
+
+
+
+
+Lets us now try some matrix algebra symbolically ::
+
+
+
+   var('a,b,c,d') 
+   A=matrix([[a,1,0],[0,b,0],[0,c,d]]) 
+   A
+
+Now lets do some of the matrix operations on this matrix
+
+
+::
+    A.det() 
+    A.inverse()
+
+
+
+{{{ Part of the notebook with summary }}}
+
+So in this tutorial we learnt how to
+
+
+* We learnt about defining symbolic expression and functions.  
+* Using built-in constants and functions.  
+* Using <Tab>  to see the documentation of a function.  
+* Simple calculus operations .  
+* Substituting values in expression using substitute function.
+* Creating symbolic matrices and performing operation on them .
+
diff -r d14bc84feca1 -r 054117c9dd59 getting-started-with-symbolics/slides.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-with-symbolics/slides.tex	Tue Oct 26 16:08:02 2010 +0530
@@ -0,0 +1,67 @@
+% Created 2010-10-21 Thu 00:06
+\documentclass[presentation]{beamer}
+\usetheme{Warsaw}\useoutertheme{infolines}\usecolortheme{default}\setbeamercovered{transparent}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{float}
+\usepackage{wrapfig}
+\usepackage{soul}
+\usepackage{amssymb}
+\usepackage{hyperref}
+
+
+\title{Plotting Data }
+\author{FOSSEE}
+\date{2010-09-14 Tue}
+
+\begin{document}
+
+\maketitle
+
+
+
+
+
+
+\begin{frame}
+\frametitle{Tutorial Plan}
+\label{sec-1}
+\begin{itemize}
+
+\item Defining symbolic expressions in sage.\\
+\label{sec-1.1}%
+\item Using built-in costants and functions.\\
+\label{sec-1.2}%
+\item Performing Integration, differentiation using sage.\\
+\label{sec-1.3}%
+\item Defining matrices.\\
+\label{sec-1.4}%
+\item Defining Symbolic functions.\\
+\label{sec-1.5}%
+\item Simplifying and solving symbolic expressions and functions.\\
+\label{sec-1.6}%
+\end{itemize} % ends low level
+\end{frame}
+\begin{frame}
+\frametitle{Summary}
+\label{sec-2}
+\begin{itemize}
+
+\item We learnt about defining symbolic expression and functions.\\
+\label{sec-2.1}%
+\item Using built-in constants and functions.\\
+\label{sec-2.2}%
+\item Using <Tab>  to see the documentation of a function.\\
+\label{sec-2.3}%
+\item Simple calculus operations .\\
+\label{sec-2.4}%
+\item Substituting values in expression using substitute function.\\
+\label{sec-2.5}%
+\item Creating symbolic matrices and performing operation on them .\\
+\label{sec-2.6}%
+\end{itemize} % ends low level
+\end{frame}
+
+\end{document}