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%MODULE 1: Intro to SAGE
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%USER DEFINED COMMANDS
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%INPUT THE INSTRUCTIONS PAGE 
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%BUILD  TITLE PAGE 
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\begin_layout Title
An Introduction to SAGE
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\begin_layout Subtitle
Because SAGE is essential for this aspect of the course, this lesson is
 designed to serve as an introduction to some basic constructions of SAGE.
 
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\begin_layout BeginFrame
Why SAGE?
\end_layout

\begin_layout Standard
These modules are aimed as a series of online, interactive lessons and labs
 to help you learn Calculus.
 An essential component of the modules is the use of the computer algebra
 package SAGE.
 SAGE is a state-of-the-art, free computer algebra system that allows you
 to do many different kinds of mathematics, from basic arithmetic to calculus
 and beyond.
 Similar commercial systems include Maple and Mathematica.
\end_layout

\begin_layout Standard
Some of the lessons advise you to use SAGE.
 In some cases you will use prebuilt applications we call SAGE applets;
 in other cases you will start a blank worksheet and go from there.
 You are welcome to use it on your own to try to answer your questions or
 explore your ideas.
 The reason we include SAGE is because 
\emph on
we want you to experiment, even play with the mathematics.
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{
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Getting started
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}
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\noindent
You have several options for obtaining and running SAGE.
 All of them are free.
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Visit the department's SAGE server at 
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\backslash
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\end_inset

 please insert your own server's address here!
\family default
 There you can login as guest (no password), or create your own username.
 This can be slow if there is a great deal of demand for the server, and
 the server might be down sometimes.
 
\end_layout

\begin_layout Itemize
Obtain a copy of SAGE on a CD-ROM from the math department, and run it on
 your own computer.
 
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\begin_layout Itemize
Download SAGE from 
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 http://www.sagemath.org/
\family default
 and run it on your own computer.
 
\end_layout

\begin_layout Standard
You will sometimes need to use worksheets that the math department has prepared
 for this course.
 You should be able to find these at the same website where you find the
 modules, 
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 http://www.math.usm.edu/sage/
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If you need help obtaining SAGE or the worksheets, your professor should
 be able to help you.
 If not, s/he will tell you whom you can contact.
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Start SAGE
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}
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\begin_layout Standard
\noindent
At this point we assume that you have obtained SAGE and have started it,
 either by navigating to the web address online or by double-clicking an
 icon on your computer.
 You may receive some security warnings; allow any certificates to pass.
 (The Firefox web browser calls this 
\begin_inset Quotes eld
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adding an exception.
\begin_inset Quotes erd
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) You should see a welcome screen:
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(Colors and some minor details may vary.)
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{
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Log in to SAGE
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}
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\noindent
SAGE's worksheet interface works best with the Firefox web browser, which
 you can download (for free!) at 
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 http://www.mozilla.com/
\family default
 It should also work with Internet Explorer, Safari, Opera, and any web
 browser.
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\begin_layout Standard
Go ahead and sign up for a new SAGE Notebook account.
 Then log in to your account.
 You should see a screen like this:
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{
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Your first SAGE worksheet
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}
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\noindent
In the upper-left hand region of the window, you will see a link for creating
 a new worksheet.
 Click on that, and you will see something like the following.
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	scale 20

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\begin_layout Standard
Pay particular attention to the two circled objects.
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\begin_layout Itemize
The one on the left is the title of your worksheet.
 You can change it by clicking on it and typing a new name.
 Do that now; change the title to 
\emph on
My first SAGE worksheet!
\emph default
 
\end_layout

\begin_layout Itemize
The one on the right is a link to help.
 SAGE comes with a substantial amount of documentation, and you may want
 to explore it from time to time.
 However, we will try to include in this module everything you need to know
 to make SAGE work.
 
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Cells
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\begin_layout Standard
\noindent
When you want SAGE to do something, you type instructions into a 
\emph on
cell
\emph default
.
 A cell looks like a rectangle; we have written the word "CELL" in the screensho
t below to show you where it is.
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Click in the cell, and you will be ready to work with SAGE.
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{
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Basic Arithmetic
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\noindent
SAGE will perform basic arithmetic like any calculator.
 Type 
\begin_inset Formula $\ec2+(-4)$
\end_inset

 into the cell.
 To make SAGE perform an instruction, hold the 
\family typewriter

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 SHIFT
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\family default
 key and press 
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 RETURN
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\family default
 (or 
\family typewriter

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 ENTER
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\family default
).
 You should see this:
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	scale 20

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\end_layout

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\begin_layout Standard
Personally, I find it highly reassuring that SAGE agrees with every other
 calculator on this point.
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{
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Symbolic calculator
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\noindent
SAGE is more than a calculator, however; it is a 
\emph on
Computer Algebra System
\emph default
.
 Unlike ordinary calculators, SAGE can compute with polynomials, matrices,
 and esoteric mathematical objects that you've probably never heard of,
 such as Gr
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{
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ö
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bner bases, modular forms, elliptic curves, finite fields, and lots more.
\end_layout

\begin_layout Standard
Let's add two polynomials.
 We'll shoot for something that you should be able to check yourself: 
\begin_inset Formula $\ec\left(x^{2}-3x+2\right)+\left(4x^{3}-2x+3\right)$
\end_inset

.
 To type this in, use the caret (‸) to show exponentiation, and a star (*)
 to show multiplication.
 Unlike written mathematics, you will need to include the star for every
 multiplication.
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We get this:
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\end_layout

\begin_layout Plain Layout
\align center
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	scale 40

\end_inset

 
\end_layout

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{
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Declaring variables
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\begin_layout Standard
\noindent
SAGE recognizes 
\begin_inset Formula $\ec x$
\end_inset

 as a variable.
 If you want your functions to use variables other than 
\begin_inset Formula $\ec x$
\end_inset

, you will have to tell this to SAGE.
 Otherwise you could get an error like the following.
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\begin_layout Plain Layout
 
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\begin_layout Plain Layout
\align center
\begin_inset Graphics
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	scale 30

\end_inset

 
\end_layout

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\begin_layout Standard
To declare 
\begin_inset Formula $\ec y$
\end_inset

 as a variable to be used for functions, type 
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{
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 var('y')
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}
\end_layout

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.
 After that you can manipulate it to your heart's content.
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	scale 30

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You can declare more than one variable by typing, for example, 
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 a, b, c = var('a b c')
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.
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Simplifying expressions
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\begin_layout Standard
\noindent
You may have noticed in the previous slide that SAGE did not expand the
 product 
\begin_inset Formula $\ec(x+y)(x-y)$
\end_inset

, but returned it to us in the same form.
 If you want SAGE to expand the product, you can tell it to do so explicitly.
\end_layout

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\begin_layout Plain Layout
 
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\begin_layout Plain Layout
\align center
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	filename figures/sage_expand_product.png
	scale 20

\end_inset

 
\end_layout

\end_inset


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\begin_layout Standard
Likewise, if you want it to factor a polynomial, it will do so if it can.
\end_layout

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\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_factor_poly.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
SAGE will also solve equations, but you have to use two equality signs instead
 of one:
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\begin_layout Plain Layout
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	filename figures/sage_solve.png
	scale 20

\end_inset

 
\end_layout

\end_inset


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\begin_layout Standard
SAGE has a large number of useful functions like these.
 We will introduce the functions that you need when necessary.
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{
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Multiple commands
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\noindent
You can enter multiple commands into a cell, separating each one by pressing
 
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 ENTER
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\family default
.
 Do not hold the 
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 SHIFT
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\family default
 key when you want to enter multiple commands into a cell.
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\begin_inset Float figure
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\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_multiple_commands.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Notice that SAGE only printed the result of the 
\emph on
last
\emph default
 command in the cell.
 To print the results of all the commands in a cell, surround each command
 with the 
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{
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 print
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 function.
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\begin_layout Plain Layout
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\begin_inset Graphics
	filename figures/sage_print.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
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{
\end_layout

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Naming expressions
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}
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\end_layout

\begin_layout Standard
\noindent
It can grow tiresome to retype the same expressions.
 Assigning names to expressions makes this less burdensome.
 You can make an assignment this way: 
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\begin_layout Standard
\align center
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{
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\backslash
ec
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 name
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\begin_inset space \space{}
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=
\begin_inset space \space{}
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 expression
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}
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\begin_layout Standard
\noindent
To illustrate, create two polynomials 
\begin_inset Formula $\ec f$
\end_inset

 and 
\begin_inset Formula $\ec g$
\end_inset

, then perform a series of operations on them.
 Notice that SAGE does not print the result of an assignment.
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\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_assignments.png
	scale 20

\end_inset

 
\end_layout

\end_inset


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\begin_layout BeginFrame
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Special names
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\begin_layout Standard
\noindent
SAGE reserves some names for mathematical expressions.
 The ones that matter for Calculus are 
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 pi
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 for 
\begin_inset Formula $\pi$
\end_inset

 and 
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{
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 e
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\end_inset

 for 
\begin_inset Formula $e$
\end_inset

.
 
\end_layout

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\begin_inset Float figure
placement h!
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sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_pi_and_e.png
	scale 40

\end_inset

 
\end_layout

\end_inset


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Plotting graphs
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\noindent
You can plot a graph using the commands 
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{
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\backslash
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 plot()
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 and 
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\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 show()
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset

.
 To plot 
\begin_inset Formula $\ec x^{2}-4$
\end_inset

 on the interval 
\begin_inset Formula $\ec\left[-3,3\right]$
\end_inset

, type 
\end_layout

\begin_layout Standard
\align center
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 plot(x‸2-4,-3,3)
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
You can also assign the plot to a name such as 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 f_plot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset

 and then type 
\end_layout

\begin_layout Standard
\align center
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 f_plot.show()
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
You would see something like this:
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_plot.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Combining the plots of graphs
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
You can also combine several plots into one.
 Assign the plots of 
\begin_inset Formula $\ec x^{2}-4$
\end_inset

 and 
\begin_inset Formula $\ec x+2$
\end_inset

 over the interval 
\begin_inset Formula $\ec\left[-3,3\right]$
\end_inset

to the names 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 f_plot
\family default
 and 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 g_plot
\family default
, then type 
\end_layout

\begin_layout Standard
\align center

\family typewriter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 (f_plot + g_plot).show()
\end_layout

\begin_layout Standard
You will see something like this:
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_combine_plots.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Colored plots
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
When combining plots, it can be hard to tell them apart if they are all
 the same color.
 SAGE has an option for changing the color of a plot.
 Type the following:
\end_layout

\begin_layout Standard

\family typewriter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 f_plot = plot(x‸2-4,-3,4,color="red")
\end_layout

\begin_layout Standard

\family typewriter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 g_plot = plot(x+2,-3,4,color="blue")
\end_layout

\begin_layout Standard

\family typewriter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 (f_plot + g_plot).show()
\end_layout

\begin_layout Standard
You will see this:
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_colored_plots.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Adjusting the aspect ratio
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
You may have noticed that the 
\begin_inset Formula $x$
\end_inset

-axis is a little longer than the 
\begin_inset Formula $y$
\end_inset

-axis.
 The result is that the graphs are a little distorted; a circle, for example,
 would look like an ellipse.
\end_layout

\begin_layout Standard
You can fix this by adding an option in the 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 show()
\family default
 command called 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 aspect_ratio
\family default
.
 If you specify 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 aspect_ratio=1
\family default
, then the graph will look square.
 For example,
\end_layout

\begin_layout Standard
\align center

\family typewriter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 (f_plot + g_plot).show(aspect_ratio=1)
\end_layout

\begin_layout Standard
generates the following graph.
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_combine_plots_square.png
	lyxscale 50
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Adding, removing cells
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
If you want to insert a cell between two others, hover the mouse slightly
 above an old cell.
 A line should appear:
\end_layout

\begin_layout Standard
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_create_cell.png
	scale 20

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
If you click on that line, a new cell will appear.
\end_layout

\begin_layout Standard
To delete a cell, delete its contents, place the cursor inside the cell,
 then press 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Backspace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\family default
.
\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Values of names
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
SAGE remembers the value of a name based on the order it was executed, 
\emph on
not
\emph default
 the order it appears in the worksheet.
 If you insert a cell between two others and each of the three assigns a
 value to the name 
\begin_inset Formula $\ec f$
\end_inset

, you could see something like this: 
\begin_inset Float figure
placement h!
wide false
sideways false
status open

\begin_layout Plain Layout
 
\end_layout

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename figures/sage_assignment_order.png
	scale 30

\end_inset

 
\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
 Why is 
\begin_inset Formula $\ec a$
\end_inset

 equal to 
\begin_inset Formula $\ec8$
\end_inset

 in the last cell?!? 
\begin_inset CommandInset label
LatexCommand label
name "fig:ooe"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout BeginFrame
Values of names
\end_layout

\begin_layout Standard
\noindent
Why does 
\begin_inset Formula $\ec a$
\end_inset

 have the value 8 in the last cell? Because the second cell was executed
 
\emph on
after
\emph default
 the third one.
 This is not something that we can show you in the slides, but you can try
 it yourself: 
\end_layout

\begin_layout Itemize
type what is written in the first three cells of 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
RefFig
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

fig:ooe
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset

 and execute them (hold 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 SHIFT
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\family default
 and press 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 ENTER
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\family default
); 
\end_layout

\begin_layout Itemize
execute the second cell again (click within the cell, hold 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 SHIFT
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\family default
, and press 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 ENTER
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\family default
; 
\end_layout

\begin_layout Itemize

\emph on
without executing the third cell again
\emph default
, click within the fourth cell, type what you see in 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
RefFig
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

fig:ooe
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset

, and execute it.
 
\end_layout

\begin_layout Standard
If calculations aren't working the way the worksheet suggests, it is probably
 because something has been executed out of order.
 You can fix this by executing the cells again in the proper order.
\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Saving a worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
You can --- and should --- save your work frequently using the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Save
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button in the upper right.
 If you want to work on a new worksheet, or just leave SAGE, you have several
 options: 
\end_layout

\begin_layout Itemize
the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Save and quit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button; 
\end_layout

\begin_layout Itemize
the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Discard and quit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button; 
\end_layout

\begin_layout Itemize
the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 New worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 option in the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 File\SpecialChar \ldots{}

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 drop-down, and 
\end_layout

\begin_layout Itemize
the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Home
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 link, 
\end_layout

\begin_layout Standard
For now choose the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Save and quit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 option.
 It will return you to the home screen, and you will find your worksheet
 listed!
\end_layout

\begin_layout BeginFrame
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Loading a worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout OverlayArea
\begin_inset ERT
status open

\begin_layout Plain Layout

{
\backslash
textwidth}{6in}
\end_layout

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
\noindent
For many of the modules you will have to load a SAGE worksheet that contains
 a SAGE applet.
 We will describe three ways that you can do this.
\end_layout

\begin_layout Pause

\end_layout

\begin_layout Only
\begin_inset ERT
status open

\begin_layout Plain Layout

<2>
\end_layout

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
First, you can visit the SAGE homepage and download the module.
 
\end_layout

\begin_layout Itemize
The SAGE homepage is 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 http://www.math.usm.edu/sage/
\family default
.
 
\end_layout

\begin_layout Itemize
Find the link to module worksheets, and click on it.
 
\end_layout

\begin_layout Itemize
Find the link to the worksheet that you want, and click on it.
 
\end_layout

\begin_layout Itemize
On the SAGE homepage, you will see a link named 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Upload
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 in the upper left, next to the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 New worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 link.
 
\end_layout

\begin_layout Itemize
Click on the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Browse\SpecialChar \ldots{}

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button, and browse to the location where you saved the worksheet on your
 computer.
 Select your worksheet.
 
\end_layout

\begin_layout Itemize
Press the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Upload Worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button.
 You will now return to the list of worksheets, and the worksheet that you
 uploaded will be available.
 
\end_layout

\end_deeper
\begin_layout Pause

\end_layout

\begin_layout Only
\begin_inset ERT
status open

\begin_layout Plain Layout

<3>
\end_layout

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
Second, you can load it from a disk, such as a CD-ROM that your instructor
 gave you.
 
\end_layout

\begin_layout Itemize
On the SAGE homepage, you will see a link named 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Upload
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 in the upper left, next to the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 New worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 link.
 
\end_layout

\begin_layout Itemize
Click on the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Browse\SpecialChar \ldots{}

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button, and browse to the location where the worksheet lies on the CD-ROM.
 (Look for a directory called 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ttcolor
\end_layout

\end_inset

 Worksheets
\family default
.) 
\end_layout

\begin_layout Itemize
Press the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Upload Worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 button.
 You will now return to the list of worksheets, and the worksheet that you
 uploaded will be available.
 
\end_layout

\end_deeper
\begin_layout Pause

\end_layout

\begin_layout Only
\begin_inset ERT
status open

\begin_layout Plain Layout

<4>
\end_layout

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
Third, you can load it directly from another website.
 In this case your instructor may have created his own worksheet that he
 wants you to use.
\end_layout

\begin_layout Itemize
On the SAGE homepage, you will see a link named 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 Upload
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 in the upper left, next to the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textless
\end_layout

\end_inset

 New worksheet
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textgreater
\end_layout

\end_inset


\series default
 link.
 
\end_layout

\begin_layout Itemize
There is a box labeled, 
\emph on
Or enter the url of a worksheet file on the web:
\emph default
.
 In this box, type the address that your instructor gave you.
 
\end_layout

\begin_layout Itemize
Press the 
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
color{blue}
\end_layout

\end_inset


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 Upload Worksheet
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\series default
 button.
 You will now return to the list of worksheets, and the worksheet that you
 uploaded will be available.
 
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{
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Programming
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\begin_layout Standard
\noindent
One of the strengths of the SAGE computer algebra system is that it relies
 on a computer programming language called Python.
 You don't have to know any Python in order to complete the worksheets for
 this course.
 However, you will learn a little bit about Python programming indirectly,
 and if you do know how to program in Python then you can do many powerful
 things in SAGE.
 
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\end_body
\end_document
