
                    +---------------------------------+
                    |                                 |
                    |   CALC PROGRAM TUTORIAL FILE    |
                    |                                 |
                    +---------------------------------+


The purpose of this file is to provide a tutorial lesson on most of the basic
features of the program called CALC.  While it is possible to learn how to
use the program by reading all the built-in help screens, if you are a
first-time user, we suggest you read this tutorial while first running the
program, and then later you can digest all the information contained in the
help functions within the program.  You can import this file, CALC.TXT, into
any word processor and then print it so you can read the hard copy output
while you run the program.

To begin the tutorial you must have the compiled binary on-line help file
called CALC.HLP, and you must have the program file CALC.EXE.  We assume these
two files are in the current directory on the currently selected disk drive.


PRELIMINARIES
=============


USING A MOUSE
-------------

The CALC program has been designed to be used with a mouse.  It provides
a standard windows interface.  If you are already familiar with either
Microsoft Windows or with a Macintosh interface, then we assume you know
how to work pull-down menus, and how to differentiate selecting things
with a mouse versus dragging things with a mouse.  We assume you know how
to work radio buttons, list boxes, and pushbuttons, and how to manipulate
the objects commonly found in dialog boxes.  CALC operates in a text mode on
IBM-compatible computers.


USING THE PROGRAM WITHOUT A MOUSE
---------------------------------

If you do not have a mouse, you can still access all the features of the
program.  A mouse is recommended because its use makes things faster, but
for those times when you do not have a mouse you can accomplish everything
with a keyboard, at the cost of making a few more keystrokes.


KEYBOARD CONVENTIONS FOR BOTH MOUSE AND NON-MOUSE USERS
-------------------------------------------------------

As part of this tutorial we need to give directions on which keys to press on
your keyboard.  We will enclose in angle brackets single keystrokes that you
should type.  For example, if we ask you to type the first three letters
of the alphabet we will show <A> <B> <C>.  If we ask you to press the control
key, the alternate key, the backspace key, the space bar, the tab key, or the
enter (or return) key, we will show <CTRL>, <ALT>, <BACKSPACE>, <SPACEBAR>,
<TAB>, or <ENTER>.

Each enclosure in angle brackets should refer to exactly one keystroke or one
character.  Some characters like <+> or <*> can be entered in two different
ways on some keyboards, one way uses the <SHIFT> key, the other way does not.
In general, we would only show the single character in angle brackets and we
leave it up to you to decide whether or not the <SHIFT> is needed to enter the
character.  Function keys will be denoted by <Fn> where n is the corresponding
number.  In most situations pressing <F1> brings up the context sensitive help
system.

These keyboard conventions should make clear exactly how many and which keys
you press.  If it is necessary to press two keys simultaneously we will show
a connecting plus sign between the keystrokes.  This is done primarily with
the Control key <CTRL>, and the Alternate key <ALT>.  For example, when we
show <ALT>+<X> it means you should press both the Alternate key and key X at
the same time.  <ALT>+<X> is used to exit the program.

At other times we may need to refer to a keystroke without intending that you
actually press the keys.  If we mention the  ALT+X  command, but it is not
enclosed with angle brackets, then you should not press the keys.  You only
press the keys when the angle brackets surround the command.


DISPLAY STRINGS
---------------

We also need to indicate the contents of text strings you might see on the
display screen.  Such text parts will always be displayed in double quotes in
this tutorial file.  You will not see the double quotes on the screen, and the
screen may contain other text parts that we do not show in this file.  The
double quotes are simply a convenient way to indicate parts of what you may
see on the display.


ADVICE FOR NOVICES AND EXPERTS
------------------------------

This tutorial file assumes you have the mathematical background required to
understand the features that will be demonstrated.  You may find some sections
more applicable to novices than experts, or vice versa, depending on your
background and experience.  If you encounter an example that is beyond your
understanding, you can either skip that example, or you can press the keys and
view the results, even though you may not fully comprehend the output.  This
tutorial does not discuss techniques on how to best use or apply the available
features.  It only serves to demonstrate the basic features and capabilities
which you can learn to apply to solve problems that are of interest to you.


GETTING STARTED
===============

To begin running the CALC program type the command:

                          <C> <A> <L> <C> <ENTER>


The entire screen can be considered to be divided into three distinct sections.
The very top line on the screen is what is called the Menu Bar.  The very
last line is called the Status Line.  The area of the screen between the Menu
Bar and the Status Line is called the Desktop, and it is within the Desktop
that your numbers will be displayed.  Each number is displayed in a separate
window that is surrounded by a border or what will be called the window frame.
The default configuration has 8 windows labeled as Stack T, Stack Z, Stack Y,
Stack X, Last X, Memory, Clipboard, and Status.  These windows are a working
model of a Hewlett-Packard calculator with a 4-level stack.  With a few
exceptions this model operates exactly as a normal Reverse Polish logic
calculator.  Each window can hold a number except the Status window.  The
purpose of the Status window is to display messages which report on the status
or mode of the calculator.


THE MAIN MENU BAR AND SELECTING SUBMENU ITEMS
=============================================

Commands are always selected from items on the Menu Bar.  If you have a mouse
then you exercise each pull-down menu by clicking or selecting the text of the
menu titles.  If you do not have mouse you can use the ALT key together with
the highlighted letter of each menu item.  For example, pressing  Alt+M  will
cause the Mode menu item to display its list of contents.  Pressing  Alt+C
will show the items under the Calculate menu.

To further select an item under any menu (what is called a submenu item), use
the down arrow or up arrow keys to move the highlighting to the item you wish
to select and then press the ENTER key to execute the corresponding command.


KEYBOARD ACCELERATORS
=====================
A few of the menu items are labeled with keys that are called keyboard
accelerators.  When you press one of these keys the command is immediately
executed without going through the pull down menu.  For example, pressing
the key  +  causes the addition function to be executed.  Other examples
are the -, * and / keys for subtracting, multiplying, and dividing numbers.



INDICATORS FOR MENU COMMANDS
============================

Most of the commands of the CALC program are derived from menu items.  To
indicate the selection of a command in this tutorial file that is associated
with one or more menu commands we will show the menu titles in all upper case
letters.  Submenu commands will be preceded by their parent menu titles, with
a vertical line | separating the items.  For example,

                          OPTIONS | DECIMALS & FRACTIONS

refers to the main menu command OPTIONS and then the further submenu command
under OPTIONS that is titled DECIMALS & FRACTIONS.

Most commands use two levels of depth within the menus.  In any case, each
capitalized title represents a menu command that you should select.  We will
not show the keystrokes if you have only a keyboard.  In this tutorial file
we prefer to show the command names which are meaningful for both mouse and
keyboard users.  After a little use you will recognize the menu names and the
submenu items and you will feel more comfortable with the command organization
and the logical grouping of the menus and commands.


THE STATUS LINE
===============

The Status Line at the bottom of the screen is used to give you hints or
messages about the actions you are performing.  The hints are context
sensitive.  Usually the left side of the Status Line shows the two commands
ALT+X EXIT  and  F1 Help.  If you have a mouse, you can click the mouse over
the text of these commands without using the keyboard.


THE ACTIVE WINDOW
=================

Although the Desktop contains several windows, only one will show a double-
line frame.  This window is called the active window.  The other windows will
be drawn with frame borders that show single thin lines.  The active window
border is also highlighted; the other window borders will appear more plain.
The initially highlighted window is labeled as Stack X.


COMPUTING 10!
==============

The first example we give will show how to use the program to compute the
value of 10 factorial, denoted by 10!.

Press                               <ENTER>

and a dialog box will appear into which you are to type the number 10.


DIALOG BOXES AND THEIR CONTROLS
===============================

Most dialog boxes have two special buttons marked OK and CANCEL.  If you have
only a keyboard then you should know that the ENTER key normally selects the
OK pushbutton and the ESC key selects the CANCEL pushbutton.  If a dialog box
also has a Help pushbutton then you can press function key F1 to execute that
pushbutton.

You should also note that when a dialog box contains several controls, you can
use the Tab key to move the focus from one control to the next.  Most controls
are labeled with a text title that contains a highlighted letter.  Pressing
the Alt key simultaneously with that letter will move the focus directly to
that control.  If the control is a pushbutton you can further press the space
bar to execute the button.


The focus should already be in the input line which shows the number

                             "0.00000000000000000"

so press
                                <1> <0> <ENTER>

After pressing ENTER (this pushes the OK button) the dialog box will disappear
and you should see the Stack X window now holds the number 10.


                            "10.00000000000000000"


The factorial command is under the Calculate menu and then under the
Probabilistic submenu which is the 7th item down.  With a mouse you can
issue the command

                           CALCULATE | PROBABILISTIC

which causes the drop-down menu under Probabilistic menu to appear.  In fact,
the right pointing triangle after the word  Probabilistic >  means that menu
command will make a further submenu appear.  Then further select the command

                                 FACTORIAL X!

The program will sound a short beep.

The Stack X window will change and show

                      "3628800.00000000000000000"


ALTERNATIVE DISPLAY FORMATS
===========================

Select the command
                      OPTIONS | DECIMALS & FRACTIONS

When the dialog box appears change the number of displayed decimal places
from the default value of 17 to the new value of 5 by pressing

                               <5> <ENTER>

Now the number in the Stack X window should appear as

                           "3628800.00000"

In fact, all numbers in all the windows should now be displayed with 5
decimal places.  The Status window should show "Decimal Places = 5".


CONTROLLING THE SPEAKER
=======================

The program normally beeps after it finishes any calculation.  If this
beeping of the speaker bothers you, you can turn the speaker permanently
off by selecting the command

                          OPTIONS | SPEAKER...

which brings up a dialog box.

This dialog box allows you to control the use of the speaker.

Press                              <ESC>

to close the Speaker Control Dialog Box.


GETTING HELP
============

Select the command
                      OPTIONS | DECIMALS & FRACTIONS

When the dialog box appears press
                                     <F1>

and you can read about the display options.

When you get to the bottom of the help window you can use the down arrow key
to scroll the window contents.  Or, with a mouse you can employ the scroll bar
down arrow to scroll the window.  The scrolling stops when there is no more
information below the bottom window edge.  Read all the information.

With a mouse you can click the close box in the upper left window title frame,
or with a keyboard press
                                     <ESC>

to quit Help.

Press                                <ESC>

again to remove the dialog box.

Later, if you want to read all of the on-line help, you can start with the
first item in the index and then select each Next Topic until you return to
where you started.


WINDOW MANAGEMENT
=================

We would next like to demonstrate how to move and resize the active window.
Note the shape and color of the Stack X window frame.  Then select the
command

                         WINDOW | MOVE/RESIZE WINDOW

(With a keyboard <Ctrl>+<F5>)

The window frame should change and if you now use the four arrow keys on
the keyboard you should be able to move the window anywhere, up or down or
left or right on the desktop.  The Status Line indicates the use of the
arrow and shift keys.

Now move the window so it is nearly in the center of the entire desktop and
then start holding down and continue to hold a <SHIFT> key while you press the
arrow keys.

You should now see the window size is being changed.  The right arrow key
makes the window wider, the down arrow key makes it taller.  The left and up
arrow keys have the opposite effects and make the window smaller.  If you let
up on the SHIFT key and continue to press the arrow keys the window position
changes.

To quit the moving and resizing press

                                    <ENTER>

The window frame should now be a highlighted double line.

If you have a mouse, you can move the window position by grabbing and
dragging the the top of the title frame.  You can reshape the window by
grabbing and then dragging the lower right window frame corner.


MORE WINDOW MANAGEMENT
======================

At this point we have 8 windows on the desktop.  Give the command

                           WINDOW | TILE ALL WINDOWS

and you should see the 8 windows that cover the entire desktop like tiles
cover a floor.

Now select the command

                           WINDOW | CASCADE ALL WINDOWS

and you should see the 8 windows stacked one on top of the other, but in a
in a cascaded form.  You could now press key F6 several times to select each
window in turn.

Now select the command

                           WINDOW | INITIAL CONFIGURATION

and this time all 8 windows will be returned to their initial configuration.


COMPUTING COMBINATIONS
======================

Next we will compute the number of combinations of 20 elements selected 5
at a time.  This is a number which appears in the 20th row of Pascal's
Triangle.  This number may be denoted by C(20,5).


Press                               <ENTER>

to edit the number in the Stack X window.


Type in                             <2> <0>

and then press                      <ENTER>

to close the dialog box.


Next press                        <SPACEBAR>

to copy the number 20 into the Stack Y window.  Both the Stack Y and Stack X
windows should now contain the number 20.  Next press

                                    <ENTER>

to again edit the Stack X window number.

Then type in                          <5>

and press                           <ENTER>


Now you should have 20 in Stack Y and 5 in Stack X.  Select the command

              CALCULATE | PROBABILISTIC | COMBINATIONS C(Y,X)


The answer should appear in the Stack X window.

                                "15504.00000"


PRIME FACTORING A REAL INTEGER
==============================

The Stack X window should still show  "15504.00000".  Give the command

                CALCULATE | NUMBER THEORETIC | PRIME FACTOR X

An information box should appear which shows the result:

                                 "2^4*3*17*19"

Two raised to the fourth power times three times seventeen times nineteen.

Press                          <ESC> or <ENTER>

to make the information box disappear.

Next we are going to compute the inverse tangent value of 1, but we first need
to change the angle mode to Radians.

Select the command        OPTIONS | DECIMALS & FRACTIONS

and set the angle mode to Radians.  You can do this with a keyboard by typing

                                  <ALT>+<R>

With a mouse you can just click anywhere on the text "Radians Mode".

Press                               <ENTER>

to return to the calculator.  Note the Status window shows "(Radians)".


Press                               <ENTER>

to edit X and type in            <1> <ENTER>


The Stack X window should now hold "1.00000".


Now give the command    CALCULATE | TRIGONOMETRIC | ARCTANGENT

The answer should be Pi divided by 4, but the decimal value may not be
recognizable.
                                  "0.78540"

At any time you can show the decimal in X as a fractional multiple of Pi by
giving the command

                    CALCULATE | NUMBER THEORETIC | (M/N)*PI

An information box appears showing the value in X could be interpreted as
one-fourth of Pi.  Press
                                     <ESC>

to make the information box disappear.


COMPUTING WITH COMPLEX NUMBERS
==============================

Now give the command

                             MODE | COMPLEX NUMBERS

Note the Status window shows you are in Complex Number mode and the number
of decimal display places defaults to 10.

We are going to compute the complex-valued logarithm of the complex number i.

Press                               <ENTER>

and then                         <i> <ENTER>

You should see the Stack X window displays

                       "0.0000000000 + 1.0000000000*i"

which means the real part is zero and the coefficient on i is one.  Give the
command
                       CALCULATE | LOGARITHMIC | LN(X)

The result should show

                       "0.0000000000 + 1.57079632680*i"

Give the command      CALCULATE | NUMBER THEORETIC | (M/N)*PI

An information box appears showing the complex number in X could be
interpreted as zero plus one-half of Pi times i.  Press

                                     <ESC>

to make the information box disappear.


Next select the command

                     CALCULATE | CONSTANTS | PI CONSTANT

and you should see stack X now holds the value of Pi as the real part of the
complex number that is in stack X.

                         "3.1415926536 + 0.00000000000*i"

Next give the command to add the two complex numbers that are in stack Y and
stack X.

                            CALCULATE | Y+X ADD +

You should see the result:

                       "3.1415926536 + 1.57079632680*i"

Next we will show this complex number in polar form.  Select the command

                    CALCULATE | COMPLEX | POLAR FORM OF X...

and you should see

                    "Stack X = 3.1415926536 + 1.5705963268*i

                     Radius = 3.5124073655
                     Angle (radians) = 0.4636476090
                     Angle (m/n*Pi)  = (9/61)*Pi
                     Angle (degrees) = 26.5650511771"


The angle is shown in the three forms that are most commonly used.  The angle
is given in radians twice, the first time is pure radians and the second time
it is given as a fractional multiple of Pi.  The angle is also given in terms
of degrees.  Note that the angle is normalized to always lie between the
limits of Pi and -Pi (in radians) or between 180 and -180 in terms of degrees.



COMPUTING WITH FRACTIONS
========================

Give the command                MODE | FRACTIONS

Note the contents of the Status window.  We will add the two mixed numbers
5 2/3  plus  6 5/8.

Press            <ENTER> <5> <SPACEBAR> <2> </> <3> <ENTER>

You should see                       "17/3
                                      = 5 2/3"

in the Stack X window.

Press                             <SPACEBAR>

to copy this fraction in Stack Y.

Press            <ENTER> <6> <SPACEBAR> <5> </> <8> <ENTER>

You should see                       "53/8
                                      = 6 5/8"

in the Stack X window.

Now press                             <+>

to add the two fractions.  The answer should appear in Stack X as

                                  "295/24
                                   = 12 7/24"

Mixed numbers only appear in the second line when the whole number part is
nonzero and the Mixed Number display mode is set.


COMPUTING WITH BINARY INTEGERS
==============================

Give the command             MODE | BINARY INTEGERS

and a dialog box will appear which shows all the options associated with
this mode.  Press
                                    <ENTER>

to accept the default values.

Reading the status window shows we are in the binary display mode.  Each
number will displayed as 16 bits which appear in groups of 4 digits.

Press                               <ENTER>

to edit the number in X.  Type a series of alternating 1's and 0's in the
input line.

                            1010 1010 1010 1010

Press                               <ENTER>

The spaces in the above binary integer are optional but they may help you
group the digits.

Now give the command
                          OPTIONS | BINARY INTEGERS

When the dialog box appears press
                                   <ALT>+<X>

to change to Hexadecimal display mode.  Press

                                    <ENTER>

to leave the dialog box.


This does not change the integer value that is in the Stack X window, but it
does change the way the value gets displayed.  Now you should see 4 hex
digits grouped in two pairs of two.

                                    "AA AA"

Press                              <SPACEBAR>

to copy this number into Stack Y.  Then press

                         <ENTER> <1> <2> <3> <4> <ENTER>

to place a new number in X which should then appear as  "12 34".

Now press                             <+>

to add these the two values in Y and X.  The answer should appear as

                                    "BC DE"

which is still in hexadecimal display format.

                                                                                         
COMPUTING WITH POLYNOMIALS
==========================

Give the command                  MODE | POLYNOMIALS

to change to a mode for working on polynomials.

Press                               <ENTER>

to start editing a new polynomial in X.  A new dialog box will appear that is
used to edit polynomials.  One thing special about this dialog box is that the
OK pushbutton is not controlled by the ENTER key.  The ENTER key controls the
pushbutton marked "Update Edited Coeff." while ALT+O controls the OK button.

We are going to enter the 3rd degree polynomial  6*X^3 - 23*X^2 - 39*X + 140.
The first thing we do is exercise the pushbutton for increasing the degree of
the polynomial.  Press

                                     <ALT>+<I>

three times and you should see the current degree changes to 3 and there
should be 4 zeros in the variable coefficient list box on the left.  The edit
line should show that the current power of X being edited is the 3rd power.
Press
                                    <6> <ENTER>

to enter the leading coefficient as 6 and to update the coefficient list on
the left.  The next power of X is automatically selected for editing in the
input line.  So press

                                 <-> <2> <3> <ENTER>

to enter and update the coefficient on the X-squared term.  Note the vertical
list of coefficients in the list box on the left holds the highest power
coefficients at the top.  The next power of X is automatically selected for
editing.  This starts the linear term.  Press

                                 <-> <3> <9> <ENTER>

Finally enter the last constant by pressing

                                 <1> <4> <0> <ENTER>

All the coefficients have now been entered and updated so press

                                    <ALT>+<O>

to press the OK pushbutton.

The polynomial now appears in the Stack X window.  The degree of the
polynomial appears on the first line, but since the window is not tall
enough you probably don't see all of the polynomial.

Press                                <F5>

to zoom the Stack X window so it fills the desktop area.  Now you can see
that all of the polynomial displayed in a vertical format.  Press

                                     <F5>

again to zoom the window back to its default size.

Next we are going to factor this polynomial.  Give the command

                CALCULATE | NUMBER THEORETIC | PRIME FACTOR X

and an information box should show

                             "(X-4)(2X+5)(3X-7)"

which is the complete factorization of the above polynomial.

Press                                 <ESC>

to get back to the polynomial mode.  Then give the command

                               MODE | REAL NUMBERS

to return to the normal real number mode.


ANALYZING REPEATING DECIMALS
============================

Give the command

                CALCULATE | NUMBER THEORETIC | REPEATING DECIMALS

to bring up a dialog box for analyzing fractions as repeating decimals.

Press                           <3> </> <1> <3>

to enter the fraction 3/13 and then press

                                  <ALT>+<D>

to calculate the repeating pattern.  You should see about the first 200
digits in the repeating pattern.  The periodic length should be 6.  Press

                                    <ENTER>

to make the information box go away, but you should still see the repeating
decimal dialog box.  We will leave the fraction as  3/13  but we are going to
change the number base to 16.  Press

                                  <ALT>+<B>

and you should see the base change to 16.

Press                             <ALT>+<D>

to calculate a new repeating pattern for hexadecimal format.  You should see
hexadecimal digits in the repeating pattern which now shows the periodic
length is 3.  Press
                                    <ENTER>

to make the information box disappear.  This time we will change the number
base to 2.  Press

                                  <ALT>+<B>

and you should see the base change to 2.

Press                             <ALT>+<D>

to calculate a new repeating pattern for binary format.  You should see only
0 and 1 binary digits with a repeating length of 12.  Press

                                     <ESC>

twice to return to the normal calculating mode.


CONVERTING A DECIMAL TO A CONTINUED FRACTION
============================================

Give the command
                      OPTIONS | DECIMALS & FRACTIONS

When the dialog box appears press
                                     <ALT>+<A>

to edit the value which determines the accuracy of decimal to fraction
calculations and then type in the number 0.0000000001 and press  <ENTER>.

Then give the command

          CALCULATE | NUMBER THEORETIC | DECIMAL -> CONTINUED FRACTION

to bring up a new dialog box.  Enter a 10-digit decimal approximation for Pi
by typing

                    <3> <.> <1> <4> <1> <5> <9> <2> <6> <5> <4>

Press
                                  <ALT>+<F>

to calculate the convergents of the continued fraction that approximates this
decimal.  You should see the following series of 4 columns of numbers.

         "Term       Convergent Fraction      Decimal Value
      Original Decimal = 3.14159265400000000
      1   3          3/1                      3.00000000000000000
      2   7          22/7                     3.14285714285714286
      3   15         333/106                  3.14150943396226415
      4   1          355/113                  3.14159292035398230
      5   293        104384/33215             3.14159265392142104"

The left-most column simply counts the terms which appear in the second
column.  The third column contains the continued fraction convergents that
are formed by accumulating more terms.  The right-most column is just the
decimal form of the fractions in the third column when they are divided to
make decimals.  The higher the term the better the fractions approximate
the original decimal.

Press                                <ESC>

twice to return to the normal calculating mode.


ACCUMULATING THE TERMS OF A SIMPLE CONTINUED FRACTION
=====================================================

Give the command

            CALCULATE | NUMBER THEORETIC | SIMPLE CONTINUED FRACTION

A new dialog box will appear into which you can type the terms of a simple
continued fraction, separated by spaces.  Key in a sequence of 20 1's
separated by spaces.

                  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


Then press                       <ALT>+<V>

to compute the accumulated convergents.  You should see the following
amazing sequence of numbers.


         "Term       Convergent Fraction      Decimal Value
      1   1          1/1                      1.00000000000000000
      2   1          2/1                      2.00000000000000000
      3   1          3/2                      1.50000000000000000
      4   1          5/3                      1.66666666666666666
      5   1          8/5                      1.60000000000000000
      6   1          13/8                     1.62500000000000000
      7   1          21/13                    1.61538461538461538
      8   1          34/21                    1.61904761904761905
      9   1          55/34                    1.61764705882352941
      10  1          89/55                    1.61818181818181818
      11  1          144/89                   1.61797752808988764
      12  1          233/144                  1.61805555555555556
      13  1          377/233                  1.61802575107296137
      14  1          610/377                  1.61803713527851459
      15  1          987/610                  1.61803278688524590
      16  1          1597/987                 1.61803444782168186
      17  1          2584/1597                1.61803381340012523
      18  1          4181/2584                1.61803405572755418
      19  1          6765/4181                1.61803396316670653
      20  1          10946/6765               1.61803399852180340"



Actually, only the first 13 lines may show in the list box, but you can press
the down arrow key or with a mouse use the vertical scroll bar to scroll the
remaining lines into view.

What is so amazing about these numbers?  Well, the third column of numbers
are the numbers from the Fibonacci sequence and the fourth column of numbers
are decimals that converge to the Golden Ratio!

Press                                <ESC>

twice to return to the normal calculator mode.


INTERRUPTING LONG CALCULATIONS
==============================

When factoring a large polynomial you may find it takes more time than you
are willing to wait.  You can abort the factoring process by pressing the keys

                                  CTRL+BREAK

at any time in the middle of the calculation.  The program will then stop
with an error message indicating it was interrupted.  Once interrupted, you
cannot continue where you left off.  The stack will be left in an
intermediate state.


ENTERING CONSTANTS IN REAL NUMBERS MODE AND POLYNOMIALS MODE
============================================================
When in Real Numbers Mode and editing the stack X element you can actually
type in any expression that evaluates to a real constant.  For example, if
you want to compute the sine of the square root of 2 you can type in the
expression  SIN(SQRT(2))  and the program will automatically compute the
value of this expression as a constant and enter that constant for you.  You
do not have to simply enter 2 and then go through the menus twice to evaluate
the square root and then evaluate the sine.  You can perform most calculations
by editing and typing in your functions within the input line.

Function expressions may be of unlimited complexity in terms of nesting.
Under Help see the index topic Scientific Functions.  You can also take
advantage of this feature when editing polynomial coefficients in Polynomials
Mode.  Note that the values of trigonometric functions depend on the current
setting of the angle mode which may be in either degrees or radians.


CONCLUSION
==========

This concludes the CALC program tutorial.  If you haven't done so already,
you can now read the help information.  Most of the basic features have been
covered here, but you will gain more insight by reading all the help
information available to you.  If after all this you still have questions,
you can contact the author at the address given below.


To quit the CALC program press

                                   <ALT>+<X>


The CALC program is periodically updated to make improvements, add new
features, (and sometimes to correct bugs!).  You may also wish to contact the
author to check if you have the latest version of the program.  The author
also invites your comments about how you liked the program and will consider
any suggestions you may wish to offer for making the program even more useful.



OTHER PROGRAMS
==============

If you enjoy using the CALC program you may be interested to know there
is a whole suite of mathematical programs made by the author of CALC.
These programs are intended to help motivate an interest in mathematics and
computer science.  Some of the titles of these programs and a brief
description of each is given below.


 1. MATRIX - a program that teaches row operations with matrices.  Features
    include fraction mode, decimal mode, solves linear systems, inverses,
    determinants, sets of basis vectors, eigenvectors and eigenvalues,
    Gram-Schmidt orthogonalization, and the simplex algorithm.


 2. YFUNX - a program for graphing and analyzing functions in rectangular
    form, Y=F(X).  Includes coordinate trace and tangent/normal line modes,
    zooming in and out, scalable axes, graph parameter variable. Numerical
    integration features standard algorithms plus Gaussian Quadrature and the
    Romberg algorithm.  Animation features include plane areas, plane arc
    length, 3D volumes (disks & cylindrical shells) and 3D surface areas.
    Newton's method and the method of successive bisections are for solving
    F(X)=0.  Automatically finds maximum/minimum extrema.  All algorithms
    may be demonstrated in either graphics or text modes.


 3. POLAR - a program for graphing and analyzing functions in polar form,
    R=F(@) or R^2=F(@).  Similar to YFUNX, includes coordinate trace and
    tangent/normal line modes, zooming in and out, scalable axes, and a graph
    parameter variable.  Numerical integration for polar areas and arc length.
    Automatically finds maximum/minimum extrema over any section of a curve.


 4. PARAM - a program for graphing and analyzing functions in parametric form,
    X=F(T) and Y=G(T).  Similar to YFUNX, includes coordinate trace and
    tangent/normal line modes, zooming in and out, scalable axes, and a graph
    parameter variable.  Numerical integration calculates plane areas and arc
    length.  Automatically finds maximum/minimum extrema over any section of
    a curve.


 5. POLPM - a program for graphing and analyzing functions in polar
    coordinates, but that have been parametrized, say R=F(T) and @=G(T).
    Similar to the POLAR and PARAM programs, this program includes coordinate
    trace and tangent/normal line modes, zooming in and out, scalable axes,
    and a graph parameter variable.  Numerical integration for plane areas
    and arc length.  Automatically finds maximum/minimum extrema over any
    section of a curve.


 6. DIFEQ - a program related to 1st order differential equations.  Includes
    graphing the direction field and solves initial value problems using
    Euler methods and a 4th order Runge-Kutta method.  Includes coordinate
    trace mode, zooming in and out, and scalable axes.  Algorithms may be
    demonstrated in either graphics or text modes.


 7. CURVE3D - a program for making 3D graphs of curves given in the parametric
    form X=f(t), Y=g(t), and Z=h(t).  The resulting curve may be viewed from
    any position, and the drawing is a true-perspective 3D picture.


 8. SURF3D - a program to graph 3-dimensional surfaces of the form Z=F(X,Y).
    The resulting surface may be viewed from any position, and the drawing is
    a true-perspective 3D picture.  The surface may be displayed using lines
    of constant x, or constant y, or a fishnet.  Included is a hidden line
    algorithm for more realistic pictures.


 9. CFIT - a program which performs curve fits to data.  Includes linear
    regression for linear, exponential, logarithmic, and power functions.
    Graphs scatter diagrams and the fitted function curves and performs
    a statistical analysis, including an automatic best fit selection.  Data
    may be saved to or read from disk files.


10. GALTON - simulates coin tossing experiments related to probabilities and
    demonstrates graphically how the binomial distribution is related to the
    standard normal Gaussian bell-shaped curve.  Also compares stack counts
    with the numbers generated in Pascal's Triangle.  Either coins or
    ping-pong balls may be used in simulated experiments.  Variable number of
    rows of pegs, variable number of objects, variable left-right probability
    for generating skewed distributions.  Includes a single-step mode under
    full user control.


11. BUFFON - simulates needle dropping experiments related to probabilities
    used to approximate the number Pi.  Needles are randomly dropped on a
    grid of equally spaced parallel lines.  The length of each needle is 1/2
    that of the distance between the lines.  After dropping a large number
    of needles a count is made of the needles which cross a line.  Most
    needles do not touch or cross any line, but the ratio of the total
    number of needles dropped divided by the number of needles which cross
    a line approximates Pi.


12. PROPC - a symbolic logic program that calculates truth tables, analyzes
    tautologies, parses infix formulas and displays their Polish notation
    form, and generates Karnaugh maps from either tables or formulas.


13. RPNDEMO - a program which simulates how a calculator with RPN logic works.
    This program includes its own language and is similar in power to the
    HP-41 calculator.  Programs may be animated to show the internal workings
    of the machine.  Can also be used to teach assembly language concepts.


14. CALC - a reverse Polish logic calculator that operates on 5 data types.
    Included are real and complex numbers, fractions, binary integers and
    polynomials.  Special features include factoring integers and
    polynomials, analyzing repeating decimals and working with continued
    fractions.


15. LOAN - a finance program that handles the two standard cases of compound
    interest.  Uses the 5 standard financial variables n i PV PMT FV found
    on most financial calculators.  Can determine payment schedules for
    loans and annuities and can print amortization schedules for loans and
    interest earning schedules for lump sums and periodic payments.


16. FCARD - simple flash card type of program that can be used to memorize
    any simple series of facts, with one item per line of text.  Items can
    be presented in a random order with timing if desired.


17. THANOI - a game known as the Towers of Hanoi.  The game solution uses
    a recursive algorithm and the purpose of the program is to demonstrate
    the validity and simplicity of a recursive solution to a complex problem
    that would otherwise overwhelm a normal human being.


18. TRIANGLE - a simple program which solves triangle problems in which one
    is given 3 facts about a triangle and must solve for all the remaining
    parts.  Handles all 19 cases of triangle inputs and includes the Law of
    Cosines and the ambiguous case of the Law of Sines.  Can automatically
    determine when two valid triangle solutions exist.  Draws all triangle
    solutions to scale on a graphics screen and computes the perimeter and
    and the area in addition to finding and labeling all the sides and angles.


19. EXPMCON - a utility type of program that works with the above MATRIX
    program and the commercial scientific word processor called EXP.  This
    program converts MATRIX files from an ASCII format to the EXP format.


20. BMPLOT - a utility program that makes high resolution monochrome bitmap
    function plots, identical to the kinds of graphs made by the programs
    YFUNX, POLAR, PARAM, and POLPM.  The bitmaps may be read into other
    programs such as paint or drawing or desktop publishing programs which
    can be used to add labels and titles.  The monochrome bitmaps may be of
    any size or resolution so the output is compatible with virtually every
    printer and/or graphics environment.  The file formats supported include
    PCX, TIFF, and BMP.  The HP-GL/2 plotter language is an optional output
    to either a file or any HP-compatible plotter or PCL 5 LaserJet compatible
    printer.


21. XPRES - a program which computes integers with up to 20,000 digits per
    integer.  This RPN calculator is useful for computing exact values of
    factorials, permutations, combinations, and powers of integers.  For
    example, you can compute the exact value of numbers like 1000! or the
    exact value of 2 raised to the 5,000th power.  Integers may be saved to
    or read from ASCII text disk files.


22. TURING - a program which simulates the operation of a Turing Machine
    which is an abstract model of a primitive digital computer.  In fact,
    the model is fundamental to all digital (logical) computations.  Such a
    machine was conceived by the British mathematician Alan Turing in 1935,
    long before digital computers became established.  Turing also worked on
    machines to break codes used by the German Enigma spy machine in World
    War II.  Three sample demonstration programs are included.


23. PTRIPLE - a program which generates and tests Pythagorean Triples.
    Three numbers, say a, b, c are a Pythagorean Triple if a^2 + b^2 = c^2.
    If the GCF among a, b,and c is 1 the triple is called primitive.  Every
    non-primitive triple is a multiple of a primtive triple.  This program
    works with both general and primitive triples and can make ranges of
    tables of triples in ASCII text files.


For more information about any of these programs you may contact the author.

   John Kennedy                 Voice Phone/Messages any time of day or
   Mathematics Department       night: (310) 450-5150  Extension 9721.
   Santa Monica College
   1900 Pico Blvd.              Internet E-Mail: jkennedy@netcon.smc.edu
   Santa Monica, CA  90405
   U.S.A.
