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%TCIDATA{<META NAME="Title" CONTENT="Basic Guidelines for Computing with Scientific Notebook">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 16:35:30 1997}
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\input{tcilatex}
\begin{document}


\section{Basic Guidelines for Computing with Scientific Notebook \label%
{Computing}}

When you respond to the request ``place the insertion point in the
expression,'' place the insertion point within, or immediately to the right
of, the expression. The position immediately to the left of a mathematical
expression is not valid. You can check the state of \textsf{Toggle Text/Math}
to verify that your insertion point is in a valid position.

\strut

\subsection{\ Evaluating Expressions\label{Evaluating Expressions}}

To enter a mathematics expression for a computation, begin a new line with
the mathematics expression or type the expression immediately to the right
of text or a text space. If you enter mathematics immediately to the right
of other mathematics, the expressions will be combined in ways you may not
intend. A safe way to begin is to press \textsc{enter} and start on a new
line.

\begin{enumerate}
\item[1.]  Click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{text.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
16.0625pt;original-height 16.0625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Text.wmf';file-properties "XNPEU";}} (or press 
\textsc{ctrl +m}) to toggle to mathematics mode, so that the \textsf{%
Text/Math} button looks like \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{%
math.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 0.3009in;height 0.3009in;depth
0.0701in;original-width 20.3125pt;original-height 18.8125pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'Math.wmf';file-properties "XNPEU";}}.

\item[2.]  Type $3+8$.

\item[3.]  Leaving the insertion point in the expression $3+8$, do one of
the following:

\begin{itemize}
\item  from the \textsf{Maple\ }menu, choose\textsf{\ Evaluate}

- or -

\item  click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{evaluate.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Evaluate.wmf';file-properties "XNPEU";}}

- or -\medskip 

\item  press \textsc{ctrl +e}.
\end{itemize}
\end{enumerate}

\strut

This sequence prompts \textsl{Scientific Notebook} to insert $=11$ to the
right of the $3+8$, resulting in the equation $3+8=11$.

By following the \emph{same} procedure, you can carry out the following
operations and perform a vast variety of other mathematical computations.

\strut

\begin{quotation}
\emph{Note}\textbf{\quad }The contents of the gray boxes display the
mathematical expressions you enter, together with the results of the
indicated operation. In general, throughout this document, the mathematical
contents of gray boxes display both the input for an action and the results.
In the case of plots, the input is displayed in the gray box and the results
are displayed immediately following the gray box.\ 
\end{quotation}

\begin{quote}
$\blacktriangleright $ Add
\end{quote}

\begin{quotation}
$235+813=1048\vspace{6pt}$

$49.3+2.87=52.17\vspace{6pt}$

$\dfrac{2}{3}+\dfrac{1}{7}=\,\dfrac{17}{21}\vspace{6pt}$

$\left( x+3\right) +\left( x-y\right) =\,2x+3-y$
\end{quotation}

\begin{quote}
$\blacktriangleright $ Subtract
\end{quote}

\begin{quotation}
$96-27=\,69\vspace{6pt}$

$\left( 2x^{2}-5\right) -\left( 3x+4\right) =\,2x^{2}-9-3x\vspace{6pt}$

$49.3-2.87=\,46.43\vspace{6pt}$

$\dfrac{2}{3}-\dfrac{8}{7}=\,-\dfrac{10}{21}\vspace{6pt}$
\end{quotation}

\begin{quote}
$\blacktriangleright $ Multiply
\end{quote}

\begin{quotation}
$82\times 37=\,3034\vspace{4pt}$

$\left( 936\right) \left( -14\right) =\,-13104\vspace{4pt}$

$14.2*83.5=\,1185.7\vspace{4pt}$

$\dfrac{2}{3}\;\dfrac{8}{7}=\,\dfrac{16}{21}$
\end{quotation}

\begin{quote}
$\blacktriangleright $ Divide
\end{quote}

\begin{quotation}
$82\div 37=\,\dfrac{82}{37}\vspace{4pt}$

$36/14=\,\dfrac{18}{7}\vspace{4pt}$

$\dfrac{14.2}{83.5}=\,.1700598802\vspace{4pt}$

$\dfrac{-\frac{2}{3}}{\frac{8}{7}}=\,-\dfrac{7}{12}\vspace{6pt}$
\end{quotation}

\strut

\begin{quotation}
\emph{Important}\textbf{\quad }Except that it be mathematically correct,
there are \emph{no rules} about the form for entering a mathematical
expression.\strut
\end{quotation}

\strut

For example, the expressions 
\[
\frac{\frac{2}{3}}{\frac{8}{7}}\ \qquad \frac{2}{3}\div \frac{8}{7}\ \qquad 
\frac{2}{3}/\frac{8}{7}\qquad \left( 2/3\right) /\left( 8/7\right) 
\]
are equally acceptable ways of entering a quotient of fractions. Also, 
\[
\left( 936\right) \left( 14\right) \ \quad 936\cdot 14\ \quad 936\times 14\
\quad \left( 936\right) \ast 14\ \quad 936\left[ 14\right] 
\]
and many other variations are acceptable for the same product. Certain
constants are recognized in their usual forms---such as $\pi $, $i$, and $e$%
---as long as the context is appropriate. On the other hand, they are
recognized as arbitrary constants, variables, or indices when appropriate to
the context. \textsl{Scientific Notebook} provides a completely natural way
for you to enter and perform mathematical computations.

\strut

\subsection{\ Interpreting Expressions\label{Interpreting expressions}}

If your mathematical notation is ambiguous, it may still be accepted.
However, the way it is interpreted may or may not be what you intended. To
be safe, remove an ambiguity by placing additional parentheses in the
expression.

\begin{quote}
$\blacktriangleright $ To see \textsl{Scientific Notebook}'s interpretation
of a mathematical expression
\end{quote}

\begin{enumerate}
\item[1.]  Leave the insertion point in the expression.

\item[2.]  Press \textsc{ctrl}, and while holding it down, type \textsc{?}.
\end{enumerate}

\begin{quote}
$\blacktriangleright $ \textsc{ctrl + ?}
\end{quote}

\begin{quotation}
$1/3x+4=\,\dfrac{1}{3x}+4$\qquad

$1/\left( 3x+4\right) =\,\dfrac{1}{3x+4}$\qquad

$\left( 1/3\right) x+4=\,\frac{1}{3}x+4$
\end{quotation}

\strut

\begin{quotation}
\emph{Note}\textbf{\quad }The number of digits in answers to numerical
problems depends on settings that you can change in the \textsf{Maple
Settings} menu discussed at the end of this chapter. The examples in this
document may differ in this respect from the answers you get with your
system, and different examples in this document use different settings.
\end{quotation}

\strut

\subsection{\ The Compute Menu and Toolbar\label{Maple menu}}

Click \textsf{Maple} at the top of the screen and a drop-down menu will
appear with a number of computing choices, beginning with \textsf{Evaluate}, 
\textsf{Evaluate Numerically,} \textsf{Simplify}, \textsf{Combine}, \textsf{%
Factor}, and \textsf{Expand}.

\strut

\begin{quotation}
\emph{Important}\textbf{\ }Throughout this document, whenever computing
choices are specified, the preceding \textsf{Maple} is implied. For example,
when you see \textsf{Evaluate}, perform \textsf{Maple + Evaluate}.
\end{quotation}

\strut

The \textsf{Compute Toolbar} contains some of the most often used choices
from the compute menu.

\FRAME{dtbpF}{3.3416in}{1.254in}{0pt}{}{}{computebar.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
3.3416in;height 1.254in;depth 0pt;original-width 204.0625pt;original-height
85.5625pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Computebar.wmf';file-properties "XNPEU";}}

\strut

\subsection{\label{Selecting an expression}\ Selecting Mathematical
Expressions}

When you perform a mathematical operation, \textsl{Scientific Notebook}
automatically selects a mathematical expression for the operation, depending
on the position of the insertion point and the operation involved. We will
refer to these automatic selections as \textsl{Scientific Notebook}
selections. You can also force other selections by selecting mathematics
with the mouse. We will refer to the latter as \emph{user selections}.

\subsubsection{Understanding Scientific Notebook Selections\label{Selections}
}

When you place the insertion point in a mathematical expression and choose
an operation from the \textsf{Maple} menu, the mathematics that \textsl{%
Scientific Notebook} automatically selects depends primarily on the
operation you choose. It also depends on the location of the mathematics,
such as in-line, in a matrix, or in a display. The following two
possibilities occur for mathematical objects that are typed in-line.

\begin{itemize}
\item  \textsl{Scientific Notebook} selects the entire mathematical object,
such as an equation or inequality.

\item  \textsl{Scientific Notebook} selects that part of the mathematics
containing the insertion point that is enclosed between a combination of
text and the class of symbols---such as $=$, $<$, or $\leq $---known as 
\emph{binary relations}.
\end{itemize}

Click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{binrels.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Binrels.wmf';file-properties "XNPEU";}} on the
symbol panel to see the full panel of binary relations. The following
examples illustrate situations where these two types of selections occur.

\paragraph{Operations that Select an Expression}

The majority of operations select an expression enclosed between text and
binary operations. Place the insertion point anywhere in the \emph{left}
side of the equation $2x+3x=1+4$ except to the left of the $2$, and choose%
\textsf{\ Evaluate.}

\begin{quote}
$\blacktriangleright $ \textsf{Evaluate}
\end{quote}

\begin{quotation}
$2x+3x=\,5x=1+4$
\end{quotation}

The expression $=5x$ is inserted immediately after the expression $2x+3x$.
This time, \textsl{Scientific Notebook\/} selected only the left side of the
equation for evaluation. Since the result of the evaluation was equal to the
original expression, the result was placed next to the expression, preceded
by an equals sign. The insertion point is placed at the right end of the
result so that you can select another operation to apply to the result
without moving the insertion point.

Other commands, including \textsf{Evaluate Numerically}, \textsf{Simplify}, 
\textsf{Combine}, \textsf{Factor,} and\ \textsf{Expand,} make similar
selections under similar conditions.

\paragraph{Operations that Select an Equation or Inequality}

Place the insertion point anywhere within the equation $2x+3x=1$ and from
the \textsf{Solve} submenu, choose \textsf{Exact}\label{Solve, exact}.

$\blacktriangleright $ \textsf{Solve + Exact}

\begin{quotation}
$2x+3x=1$, Solution is : $\left\{ x=\frac{1}{5}\right\} $
\end{quotation}

In this case, \textsl{Scientific Notebook\/} selected the entire
mathematical object---that is, the equation. The solution is not equal to
the selection, so \textsl{Scientific Notebook} does not make it part of the
original equation.

\begin{quote}
$\blacktriangleright $ \textsf{Solve + Exact}
\end{quote}

\begin{quotation}
$3x+5\leq 5x-3$, Solution is : $4\leq x$
\end{quotation}

The other choices on the \textsf{Solve} submenu and the operation \textsf{%
Check Equality} also select the entire mathematical object.

If the mathematics is not appropriate for the operation, no action is taken.
For example, applying \textsf{Check Equality} or one of the \textsf{Solve}
commands to $x=y=z$ causes a syntax error, because of the pair of equals
signs. (You see an error message, hear a beep, or see no action, depending
on whether \textsf{Error level} is set at 2 or higher, at 1, or at 0.) You
can change this setting in the \textsf{\hyperref{Maple Settings}{}{}{Maple
error levels}} dialog.

\paragraph{Selections Inside Displays and Matrices}

You can use a \emph{matrix} \label{Matrices}to arrange mathematical
expressions in a rectangular array. To create a matrix, choose \textsf{Matrix%
} from the \textsf{Insert} menu or click \FRAME{itbpF}{0.3009in}{0.3009in}{%
0.0701in}{}{}{matrix.wmf}{\special{language "Scientific Word";type
"GRAPHIC";display "PICT";valid_file "F";width 0.3009in;height 0.3009in;depth
0.0701in;original-width 17.8125pt;original-height 16.9375pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'Matrix.wmf';file-properties "XNPEU";}}, set the number of rows and columns,
and choose \textsf{OK}. You can then type a number or any mathematical
expression in each of the input boxes of the matrix.

Operations may behave somewhat differently when mathematics is entered in a
display or in a matrix. If you place the insertion point inside a display or
matrix, \textsl{Scientific Notebook} selects the entire array of entries for
any operation. Some operations apply to a matrix, and others to the entries
of a matrix or contents of a display. If the operation is not appropriate
for either a matrix or its entries or for all the contents of a display, you
may receive a report of a syntax error.

When you click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{evaluate.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Evaluate.wmf';file-properties "XNPEU";}} or
apply \textsf{Evaluate} with the insertion point in the left side of the
displayed equation 
\[
2x+3x=\,3+\,5 
\]
you get the result $=\,5x=8$ in line outside the display, rather than the
result $2x+3x=\,5x=3+5$, which would appear if the equation had been placed
in line. Inside a display or matrix, \textsl{Scientific Notebook} selects
all the mathematics, and it generally returns the result outside the display.

When you click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{evaluate.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Evaluate.wmf';file-properties "XNPEU";}} or
apply \textsf{Evaluate} to a matrix of expressions, \textsl{Scientific
Notebook} evaluates all the expressions in the array. \textsf{Evaluate
Numerically, Simplify, Factor}, and choices from the \textsf{Combine}
submenu behave similarly.

\begin{quote}
$\blacktriangleright $ \textsf{Evaluate }(or\textsf{\ Simplify})
\end{quote}

\begin{quotation}
$\left( 
\begin{array}{cc}
x+x & 5+3 \\ 
5/2 & 6^{2}
\end{array}
\right) =\,\left( 
\begin{array}{cc}
2x & 8 \\ 
\frac{5}{2} & 36
\end{array}
\right) $
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsf{Evaluate Numerically}
\end{quote}

\begin{quotation}
$\left( 
\begin{array}{cc}
x+x & 5+3 \\ 
5/2 & 6^{2}
\end{array}
\right) =\,\left( 
\begin{array}{cc}
2.0x & 8.0 \\ 
2.5 & 36.0
\end{array}
\right) $
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsf{Factor}
\end{quote}

\begin{quotation}
$\left( 
\begin{array}{cc}
x+x & 5+3 \\ 
5/2 & 6^{2}
\end{array}
\right) =\left( 
\begin{array}{cc}
2x & 2^{3} \\ 
\frac{5}{2} & 2^{2}3^{2}
\end{array}
\right) $
\end{quotation}

On the other hand, applying one of these commands to the array

\[
\left( 
\begin{array}{cc}
x+x=1+2 & 2+3 \\ 
5/2 & 6^{2}
\end{array}
\right) 
\]
gives a syntax error, since an equation is not a valid entry for these
commands.\bigskip

\subsubsection{Understanding User Selections\label{User selection}}

You can restrict the computation to a selection you have made and so
override \textsl{Scientific Notebook\/}'s automatic choice. (Recall that you
can \emph{select} a piece of mathematics by holding down the left mouse
button while moving the mouse; your \emph{selection} is the information that
appears on the screen in reversed colors.)

There are two options for applying operations to your selection---one
displays the result of the operation but leaves the selection intact, and
the other replaces the selection with the result of the operation. Following
are two examples illustrating the behavior of the system for each of these
two options.\ 

\begin{quote}
$\blacktriangleright $ To operate on a selection
\end{quote}

\begin{itemize}
\item  Use the mouse or press \textsc{shift+arrow} to select $2+3$ in the
expression $2+3-x$. From the \textsf{Maple} menu, choose \textsf{Evaluate}. 
\textsl{Scientific Notebook} puts the answer to the right of the expression,
following a colon (:).
\end{itemize}

\begin{quotation}
$2+3-x$ : $5$
\end{quotation}

\begin{itemize}
\item  \label{Expand}Use the mouse or press \textsc{shift+arrow} to select $%
(x+y)^{3}$ within the expression $\left( x+y\right) ^{3}(7x-13y)^{3}+\sin
^{2}x$. From the \textsf{Maple} menu, choose\textsf{\ Expand}. \textsl{%
Scientific Notebook\/} puts the answer to the right of the whole expression,
following a colon (:).
\end{itemize}

\begin{quotation}
$\left( x+y\right) ^{3}(7x-13y)^{3}+\sin ^{2}x$ : $%
x^{3}+3x^{2}y+3xy^{2}+y^{3}$
\end{quotation}

In general, \textsl{Scientific Notebook\/} assumes that the result of
applying an operation to a \emph{user selection} is not equal to the entire
original expression, so it places the result at the end of the mathematics,
separated by something in text (in this case, a colon). You can then use the
word-processing capabilities of \textsl{Scientific Notebook\/} to put the
result where you want it in your document.

You can replace\label{Replacing a selection} part of an expression with the
result of a computation on that part.

\begin{quote}
$\blacktriangleright $ To replace a selection
\end{quote}

\begin{itemize}
\item  To replace $394876+205583$ by its value, select the entire
expression, hold down \textsc{ctrl }, and click \FRAME{itbpF}{0.3009in}{%
0.3009in}{0.0701in}{}{}{evaluate.wmf}{\special{language "Scientific
Word";type "GRAPHIC";display "PICT";valid_file "F";width 0.3009in;height
0.3009in;depth 0.0701in;original-width 17.8125pt;original-height
16.9375pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Evaluate.wmf';file-properties "XNPEU";}} or choose \textsf{Evaluate}. Your
selection $394876+205583$ is \emph{replaced} by its value
\end{itemize}

\begin{quotation}
$600459$
\end{quotation}

\begin{itemize}
\item  To replace $\left( x-2y\right) ^{2}$ in the expression $\allowbreak
\left( x-2y\right) ^{2}\left( 7x-13y\right) \left( x^{2}+1\right) $ with its
expansion, select $\left( x-2y\right) ^{2}$, hold down the \textsc{ctrl }
key, and click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{cxpand.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Cxpand.wmf';file-properties "XNPEU";}} or choose%
\textsf{\ Expand}. Your selection, $\left( x-2y\right) ^{2}$, is replaced by
its expansion. The expansion has no parentheses around it, but since it
remains selected, you can click \FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{%
}{}{parens.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 0.3009in;height 0.3009in;depth
0.0701in;original-width 17.8125pt;original-height 16.9375pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'Parens.wmf';file-properties "XNPEU";}} to add the needed parentheses.
\end{itemize}

\begin{quotation}
$(x^{2}-4xy+4y^{2})(7x-13y)(x^{2}+1)$
\end{quotation}

You can return the expression\label{Computing in place} to a factored form
by selecting $\left( x^{2}-4xy+4y^{2}\right) $, holding down the \textsc{%
ctrl } key, and choosing\textsf{\ Factor}.

\begin{itemize}
\item  To factor in place the subexpression $-b+b^{2}$ inside the expression 
$a-b+b^{2}$, first insert a $+$ before the $-b$ to get $a+-b+b^{2}$, then
select the expression $-b+b^{2}$, and while holding down the \textsc{ctrl }
key, apply \textsf{Factor}.
\end{itemize}

\begin{quotation}
$a+b\left( -1+b\right) $
\end{quotation}

\strut

\begin{quotation}
\emph{Important}\textbf{\quad }This ``computing in place''--- that is,
holding down the \textsc{ctrl } key as you choose an operation from the 
\textsf{Maple} menu---is a key feature of \textsl{Scientific Notebook}. It
provides a convenient way for you to manipulate expressions into the forms
you desire.
\end{quotation}

\strut

\subsection{\ Stopping a Computation \label{Stopping a computation}}

Most computations are done more or less instantaneously, but some may take
several minutes to complete, and some may take a longer time. So it is
convenient to be able to make \textsl{Scientific Notebook} stop computing
and return control to you.

\begin{quote}
$\blacktriangleright $ To stop a computation
\end{quote}

\begin{itemize}
\item  Click the stop sign \FRAME{itbpF}{0.3105in}{0.3009in}{0.0701in}{}{}{%
abort.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 0.3105in;height 0.3009in;depth
0.0701in;original-width 20.3125pt;original-height 18.8125pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'abort.wmf';file-properties "XNPEU";}}on the \textsf{Stop} toolbar.

- or -\medskip

\item  Press \textsc{ctrl + break}.\medskip
\end{itemize}

Try it out by applying \textsf{Factor} to $2^{91}+3$. \textsl{Scientific
Notebook} will factor this expression in several minutes, but you can stop
the computation if you wish.

\subsection{\ Computing in Place\label{Computing in place (2)}}

With the help of the \textsc{ctrl}\textsf{\ }key, you can perform any
computation in place, that is you can replace an expression directly with
the results of that computation. Select the expression you wish to replace
with the mouse, and while holding down the \textsc{ctrl}\textsf{\ }key,
choose the desired operation from the Maple menu. The response that replaces
the original expression will remain selected, making it convenient to add
parentheses around the new expression when needed simply by clicking the
parentheses button.

\begin{quote}
$\blacktriangleright $ \textsc{ctrl} + \textsf{Evaluate}
\end{quote}

\begin{quotation}
$2/3$ is replaced by $\allowbreak \frac{2}{3}$

$146+529-19+6$ is replaced by $\allowbreak 662$
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsc{ctrl} + \textsf{Expand}
\end{quote}

\begin{quotation}
$2345/567$ is replaced by $4\frac{11}{81}$

$\left( a+b\right) ^{3}$ is replaced by $a^{3}+3a^{2}b+3ab^{2}+b^{3}$
\end{quotation}

This feature, combined with copy and paste, allows you to ``fill in the
steps'' in demonstrating a computation.

\ 

\begin{example}
To illustrate the associative law for addition, first make two copies of the
sum. 
\[
\left( 5+8\right) +7=\left( 5+8\right) +7 
\]
Then in the second copy, select the sum $5+8$ with the mouse and, while
pressing \textsc{ctrl}, choose \textsf{Evaluate}. The result will be the
equality 
\[
\left( 5+8\right) +7=\left( 13\right) +7 
\]
Then carry out similar steps with the other association. 
\[
5+\left( 8+7\right) =5+\left( 15\right) 
\]
Now apply \textsf{Evaluate} to each of the sums. 
\begin{eqnarray*}
\left( 13\right) +7 &=&20 \\
5+\left( 15\right) &=&20
\end{eqnarray*}
\bigskip
\end{example}

\subsection{\ Maple Error Levels \label{Maple error levels}}

From the \textsf{Maple} menu, choose \textsf{Settings} and click the \textsf{%
General} tab. This page contains an \textsf{Error Level} box. The error
levels range from 1 to 8. Typically, you will have the error level set for
0, 1, or 2.

Here are the meanings of the various error levels:

\begin{center}
\begin{tabular}{ll}
\textbf{Level} & \textbf{Meaning} \\ \hline
0 & No messages under any circumstances \\ 
1 & Beep if there is an error \\ 
2 & Display errors in a dialog box \\ 
3 & Display memory use in status area \\ 
4 & Show all Maple commands sent in the \\ 
& status area \\ 
5 & 3 and 4 \\ 
6 & Show memory use in dialog boxes \\ 
7 & Show all Maple commands sent in \\ 
& dialog boxes \\ 
8 & 6 and 7
\end{tabular}
\end{center}

There are eight memory-use numbers displayed. A typical display looks like
this:

\begin{center}
1001684, 288768, 126.417, 0, 250000, 132847, 140124, 4
\end{center}

The numbers have the following meaning:

\begin{center}
\begin{tabular}{ll}
\textbf{Number} & \textbf{Meaning} \\ 
1 & Total number of words requested of the \\ 
& storage allocator \\ 
2 & Total number of words currently allocated \\ 
3 & Number of CPU seconds used \\ 
4 & Words increment for `words used' messages \\ 
5 & Words increment for automatic garbage \\ 
& collection \\ 
6 & Number of words returned in last garbage \\ 
& collection \\ 
7 & Number of words available after last \\ 
& garbage collection \\ 
8 & Number of times that garbage collection \\ 
& was executed
\end{tabular}
\end{center}

Each word takes four bytes. Multiply the word numbers by four to get the
number of bytes involved.

\strut

\subsection{\ Related topics}

\begin{itemize}
\item  \hyperref{Addition and Subtraction}{}{}{DM2-1.tex#Addition}

\item  \hyperref{Multiplication and Division}{}{}{DM2-1.tex#Multiplication}

\item  \hyperref{Polynomials and Rational Expressions}{}{}{%
DM3-1.tex#Polynomials}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{0.5275in}{0.3399in}{0.0519in}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.5275in;height 0.3399in;depth 0.0519in;original-width
36.875pt;original-height 22.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'index.wmf';file-properties "XNPEU";}}}{}{}{%
DMIndex.tex#Math Index}\quad {\small Index entries: \hyperref{Computing in
place}{}{}{DMIndex.tex#Computing in place}, \hyperref{Error level}{}{}{%
DMIndex.tex#Error level}, \hyperref{Evaluate}{}{}{DMIndex.tex#Evaluate}, 
\hyperref{Expand}{}{}{DMIndex.tex#Expand}, \hyperref{Interpreting expressions%
}{}{}{DMIndex.tex#Interpreting expressions}, \hyperref{Maple settings}{}{}{%
DMIndex.tex#Maple settings}, \hyperref{Maple menu}{}{}{DMIndex.tex#Maple
menu commands}, \hyperref{Matrices}{}{}{DMIndex.tex#Matrices}, \hyperref{%
Selecting mathematical expressions}{}{}{DMIndex.tex#Selecting mathematical
expressions}, \hyperref{Solve}{}{}{DMIndex.tex#Solve}, \hyperref{Stopping a
computation}{}{}{DMIndex.tex#Stopping a computation}}

\end{document}
