home
***
CD-ROM
|
disk
|
FTP
|
other
***
search
/
DP Tool Club 12
/
CD_ASCQ_12_0294.iso
/
maj
/
966
/
mathplot.doc
< prev
next >
Wrap
Text File
|
1994-01-28
|
67KB
|
1,629 lines
M A T H P L O T
Mathematical Function Plotting Program
A "shareware" program
Phillip H. Sherrod
Member, Association of Shareware Professionals (ASP)
Mathplot allows you to specify mathematical functions using
ordinary algebraic expressions and immediately plot them.
Four types of functions may be specified: cartesian
(Y=f(X)); parametric cartesian (Y=f(T) and X=f(T)); polar
(Radius=f(Angle)); and parametric polar (Radius=f(T) and
Angle=f(T)). Up to four functions may be plotted
simultaneously. Scaling is automatic. Options are
available to control axis display and labeling as well as
grid lines. Hard copy output can be generated to HP
LaserJet printers as well as screen display. Mathplot is
an ideal tool for engineers, scientists, math and science
teachers, and anyone else who needs to quickly visualize
mathematical functions.
Table of Contents
1. Using Mathplot . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Installing Mathplot . . . . . . . . . . . . . . . . . . . . 1
1.3 Getting Started . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Demonstration Command File . . . . . . . . . . . . . . . . 4
1.5 Command Editor . . . . . . . . . . . . . . . . . . . . . . 4
1.5.1 Function Keys . . . . . . . . . . . . . . . . . . . . . 4
1.5.2 Control Characters . . . . . . . . . . . . . . . . . . 4
1.6 Function Specification . . . . . . . . . . . . . . . . . . 4
1.6.1 Arithmetic Operators . . . . . . . . . . . . . . . . . 5
1.6.2 Numeric Constants . . . . . . . . . . . . . . . . . . . 5
1.6.3 Symbolic Constants . . . . . . . . . . . . . . . . . . 5
1.6.4 Parameter values . . . . . . . . . . . . . . . . . . . 5
1.7 Built in Functions . . . . . . . . . . . . . . . . . . . . 6
1.8 Function Types . . . . . . . . . . . . . . . . . . . . . . 8
1.8.1 Cartesian Functions . . . . . . . . . . . . . . . . . . 8
1.8.2 Parametric Cartesian Functions . . . . . . . . . . . . 9
1.8.3 Polar Functions . . . . . . . . . . . . . . . . . . . . 9
1.8.4 Parametric Polar Functions . . . . . . . . . . . . . . 9
1.9 Plotting Simultaneous Functions . . . . . . . . . . . . . . 10
2. Mathplot Commands . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Start up Command File . . . . . . . . . . . . . . . . . . . 11
2.2 Initialization file . . . . . . . . . . . . . . . . . . . . 11
2.3 Command Arguments . . . . . . . . . . . . . . . . . . . . . 12
2.4 Alphabetical List of Commands . . . . . . . . . . . . . . . 12
2.4.1 AXES . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.2 CALCULATE . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.3 CAXES . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.4 CFn . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.5 CGRID . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.6 COLORBORDER . . . . . . . . . . . . . . . . . . . . . . 13
2.4.7 COLOREDIT . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.8 COLORHEAD . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.9 COLORHELP . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.10 COLORHELPHEAD . . . . . . . . . . . . . . . . . . . . 13
2.4.11 COLORMESSAGE . . . . . . . . . . . . . . . . . . . . . 13
2.4.12 COMMONSCALE . . . . . . . . . . . . . . . . . . . . . 13
2.4.13 CTITLE . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.14 DATA . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.15 DISPLAY . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.16 DO . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.17 DOMAIN . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.18 EXIT . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.19 GRID . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.20 HELP . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.21 LABEL . . . . . . . . . . . . . . . . . . . . . . . . 15
i
Contents ii
2.4.22 LIST . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.23 NUMPOINTS . . . . . . . . . . . . . . . . . . . . . . 15
2.4.24 ORIGIN . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.25 Pn . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.26 PAUSE . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.27 PDEVICE . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.28 PRESOLUTION . . . . . . . . . . . . . . . . . . . . . 16
2.4.29 WIDTH . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.30 PLOT . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.31 PRINT . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.32 RESET . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.33 SAVE . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.34 TITLE . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.35 WAXES . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.36 WFn . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.37 WGRID . . . . . . . . . . . . . . . . . . . . . . . . 17
3. Advanced Applications . . . . . . . . . . . . . . . . . . . . 18
3.1 Root Finding . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Multiple Domains . . . . . . . . . . . . . . . . . . . . . 18
3.3 Interesting Functions . . . . . . . . . . . . . . . . . . . 19
3.4 "Artistic" Plots . . . . . . . . . . . . . . . . . . . . . 20
4. Use and Distribution of Mathplot . . . . . . . . . . . . . . . 21
4.1 Copyright Notice . . . . . . . . . . . . . . . . . . . . . 22
4.2 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . 22
5. Other Software . . . . . . . . . . . . . . . . . . . . . . . . 23
5.1 Nonlin . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 TSX-32 Operating System . . . . . . . . . . . . . . . . . . 24
6. Software Order Form . . . . . . . . . . . . . . . . . . . . . 25
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 1
Using Mathplot
1.1 Introduction
Mathplot is a program for IBM-PC computers which allows interactive
entry and plotting of mathematical functions. Some of the features
of Mathplot are listed below:
. Direct entry of complicated mathematical functions using normal
algebraic expressions with embedded operators and functions.
. An assortment of built-in functions including trigonometric,
square root, log, Gamma, Bessel, elliptic integrals, normal
probability distribution, etc.
. The ability to plot four types of functions: cartesian
(Y=f(X)); parametric cartesian (Y=f(T) and X=f(T)); polar
(Radius=f(Angle)); and parametric polar (Radius=f(T) and
Angle=f(T)).
. The ability to simultaneously plot up to four functions.
. Automatic scaling and axis labeling.
. The ability to save function specifications in command files
which then can be easily executed.
. The ability to accept X-Y data points from an external file.
. A command editor allows easy recall and editing of commands.
. Printed copies of plots may be produced on HP LaserJet
printers.
1.2 Installing Mathplot
The Mathplot system consists of the following files:
1
Chapter 1. Using Mathplot 2
MATHPLOT.EXE -- The executable program.
MATHPLOT.FON -- Font file used for title and axis labels.
MATHPLOT.LJF -- Font file for HP LaserJet printer.
MATHPLOT.FUN -- Example functions
MATHPLOT.DOC -- Documentation file.
REGISTER.DOC -- Software registration form.
To install Mathplot, copy the files into the directory of your
choice. If you do not plan to generated hard copy output for a
LaserJet printer, you may delete the MATHPLOT.LJF file. If the
MATHPLOT.FON and MATHPLOT.LJF files are not in your current
directory, you must place a command of the following form in your
AUTOEXEC.BAT file to tell Mathplot where to look for its font
files:
SET MATHPLOT=directory
Where "directory" is the name of the device and directory where the
files are located. For example, if the files are located in a
directory named MATHPLOT on the C disk, the following command could
be used:
SET MATHPLOT=C:\MATHPLOT
1.3 Getting Started
Mathplot is exceptionally easy to use. Although there are a fair
number of commands to control options, you only need to know a
couple of commands to begin using it.
Start the program by entering the command:
MATHPLOT
Mathplot will display a title screen; press Enter to proceed to
command mode. The main Mathplot screen is divided into three
sections. The top window explains the function keys. The bottom
window is used to display status and error messages. The middle
window is used by the command editor to display commands that you
enter.
Several of the common Mathplot operations can be performed either
by pressing a function key or by typing a command. These commands
are described below:
Function key Command Action
------------ ------- -----------------------------------
ESC EXIT Exit from Mathplot to DOS
F1 PLOT Plot the current functions
F2 Print current functions on LaserJet
F3 HELP Display help menu
F4 RESET Erase functions and reset Mathplot
F5 Run an example
Chapter 1. Using Mathplot 3
The F5 key executes built-in example plots. Each time you press F5
a different example is displayed. I suggest you use this feature
to display a few plots in order to get a feeling for how Mathplot
works and what types of commands are used to produce plots. Press
any key to continue with execution after you finish looking at a
plot. Note that after each example is completed the commands that
produced it are displayed on your screen. By examining a few sets
of example commands you should be able to get a pretty good idea
about how to use Mathplot.
Once you have used F5 to display some plots, it is time to try
entering your own commands. Begin by specifying a simple function
to be plotted. I suggest you enter the command:
Y=SIN(X)
You may use either upper or lower case letters when you type a
command. Press Enter when you are finished typing the line. Next,
press F1 to command Mathplot to evaluate this function and plot the
results.
You should see a sine wave displayed on your screen. Press Enter
to return to the command editor. Now let's make the function
slightly more complicated by entering the command:
Y=SIN(X)+SIN(3*X)/3
This replaces the previous function definition. Press F1 to see
this function plotted. If you make a mistake when typing a
command, use the arrow and editing keys such as Backspace and
Delete to correct your mistake, then press Enter to reexecute the
command.
So far, the function has been evaluated over the interval (0,2*pi),
which is the initial default domain. Use the following command to
change the domain to (-2*pi,2*pi):
DOMAIN -2*PI,2*PI
Also, use the following command to turn on grid line display:
GRID ON
Press F1 to display the plot.
As a final exercise, use the following command to define a second
function to be displayed simultaneously with the first one:
Y2=SIN(X)
And, again press F1 to display them. You should see a simple sine
wave (the Y2 function) superimposed on the previous function (the Y
function). Press ESC to exit Mathplot and return to DOS.
Chapter 1. Using Mathplot 4
1.4 Demonstration Command File
The Mathplot distribution includes a command file named
MATHPLOT.FUN containing a number of interesting example plots. You
can execute this command file by using the Mathplot "DO" command,
or by specifying the command file on the invocation line. The
following DOS command starts the Mathplot program and instructs it
to execute the commands stored in the file MATHPLOT.FUN:
MATHPLOT MATHPLOT.FUN
1.5 Command Editor
The middle window of the main Mathplot screen is used by the
command editor to accept and display commands you type. In
addition to typing commands, you can also use the arrow keys and
other editing functions to recall, edit, and reexecute commands.
If you enter a command that has an error, a message will appear in
the bottom window. You can use the up-arrow key to move the cursor
up to the previous line, edit it, and then reexecute it by pressing
Enter. Each time you press Enter, the line in which the cursor is
positioned is executed. Using the arrow keys to move up and down
does not execute commands.
1.5.1 Function Keys
The following function keys can be used with the command editor:
Delete -- Delete the character under the cursor.
Home -- Move to the left end of the line.
End -- Move to the right end of the line.
Page up -- Move up to the previous page of commands.
Page down -- Move down to the next page of commands.
Insert -- Switch between insert and over type mode.
1.5.2 Control Characters
The following control characters can be used with the command
editor:
Enter -- Execute the command line the cursor is on.
Backspace -- Delete the character to the left of the cursor.
Control-U -- Delete characters to the left of the cursor.
Control-D -- Delete all characters in the current line.
1.6 Function Specification
Much of the power of Mathplot comes from its ability to evaluate
complicated functions entered in ordinary algebraic form. This
section explains the arithmetic operators and built in functions
that are used to define a function.
Chapter 1. Using Mathplot 5
1.6.1 Arithmetic Operators
The following arithmetic operators may be used in expressions:
+ addition
- subtraction or unary minus
* multiplication
/ division
** or ^ exponentiation
Exponentiation has the highest precedence, followed by
multiplication and division, and then addition and subtraction.
Parentheses may be used to group terms.
As a convenience, Mathplot allows you to omit the multiplication
operator between a numeric constant and a following variable or
function. For example, the expressions "2pi", and "2 pi" are
equivalent to "2*pi". Similarly, "5X" is equivalent to "5*X".
However, if you specify a number before the letter "E", it will be
taken as the exponential form of a number (see below) rather than
the number times the constant E (base of natural logarithms).
1.6.2 Numeric Constants
Numeric constants may be written in their natural form (1, 0, 1.5,
.0003, etc.) or in exponential form, n.nnnEppp, where n.nnn is the
base value and ppp is the power of ten by which the base is
multiplied. For example, the number 1.5E4 is equivalent to 15000.
All numbers are treated as "floating point" values, regardless of
whether a decimal point is specified or not.
1.6.3 Symbolic Constants
There are two numeric constants that may be specified using
symbolic names. The symbolic name "PI" is equivalent to the value
of pi, 3.14159... Similarly, the symbolic constant "E" is
equivalent to the base of natural logarithms, 2.7182818...
1.6.4 Parameter values
Mathplot allows you to use parameters named P0, P1, ..., P9 in
function definitions. You can then assign values to the parameters
and replot the function without having to retype the function to
change a value. To assign a value to a parameter, type the
parameter name as a command followed by the value to be assigned.
For example, the following command assigns the value 0.67 to the
parameter P0:
P0 0.67
Note that parameters are like constants during the evaluation and
plotting of a function (i.e., their values do not change). But you
can assign new values to parameters between plot generations. For
example, consider the following commands which define a function
Chapter 1. Using Mathplot 6
and then plot it twice with two different values of the P0
parameter:
Y = EXP(-P0*X) * COS(X)
P0 0.6
PLOT
P0 0.8
PLOT
This function represents the response of a damped oscillator with
the P0 coefficient controlling the damping factor. By changing the
value of the P0 parameter you can examine different forms of the
function without having to retype the function.
1.7 Built in Functions
The following functions are built into Mathplot and may be used in
expressions:
ABS(x) -- Absolute value of x.
ACOS(x) -- Arc cosine of x. Angles are measured in radians.
ASIN(x) -- Arc sine of x. Angles are measured in radians.
ATAN(x) -- Arc tangent of x. Angles are measured in radians.
BETAI(x,a,b) -- Incomplete beta function: Ix(a,b). The incomplete
beta function can be used to compute a variety of statistical
functions. For example, the probability of Student's t with
`df' degrees of freedom can be computed with
BETAI(df/(df+t^2),.5*df,.5). The probability of the F
statistic with df1 and df2 degrees of freedom can be computed
with
2*BETAI(df2/(df2+df1*f),.5*df2,.5*df1).
COS(x) -- Cosine of x. Angles are measured in radians.
COSH(x) -- Hyperbolic cosine of x.
COT(x) -- Cotangent of x. (COT(x) = 1/TAN(x)).
CSC(X) -- Cosecant of x. (CSC(x) = 1/SIN(x)).
DEG(x) -- Converts an angle, x, measured in radians to the
equivalent number of degrees.
EI1(alpha,phi) -- Elliptic integral of the first kind. Computes
the integral from 0 to phi radians of the function
d.phi/sqrt(1-k**2*sin(phi)**2), where k = sin(alpha). alpha
and phi must be in the range 0 to pi/2.
Chapter 1. Using Mathplot 7
EI2(alpha,phi) -- Elliptic integral of the second kind. Computes
the integral from 0 to phi radians of the function
sqrt(1-k**2*sin(phi)**2)*d.phi, where k = sin(alpha). alpha
and phi must be in the range 0 to pi/2.
EIC1(alpha) -- Complete elliptic integral of the first kind.
Computes the integral from 0 to pi/2 radians of the function
d.phi/sqrt(1-k**2*sin(phi)**2), where k = sin(alpha). alpha
must be in the range 0 to (less than) pi/2.
EIC2(alpha) -- Complete elliptic integral of the second kind.
Computes the integral from 0 to pi/2 radians of the function
sqrt(1-k**2*sin(phi)**2)*d.phi, where k = sin(alpha). alpha
must be in the range 0 to pi/2.
ERF(x) -- Standard error function of x.
EXP(x) -- e (base of natural logarithms) raised to the x power.
FAC(x) -- x factorial (x!). Note, the FAC function is computed
using the GAMMA function (FAC(x)=GAMMA(x+1)) so non-integer
argument values may be computed.
GAMMA(x) -- Gamma function. Note, GAMMA(x+1) = x! (x factorial).
GAMMAI(x) -- Reciprocal of GAMMA function (GAMMAI(x) = 1/GAMMA(x)).
GAMMALN(x) -- Log (base e) of the GAMMA function.
HAV(x) -- Haversine of x. (HAV(x) = (1-COS(x))/2).
J0(x) -- Bessel function of the first kind, order zero.
J1(x) -- Bessel function of the first kind, order one.
JN(n,x) -- Bessel function of the first kind, order n.
LOG(x) -- Natural logarithm of x.
LOG10(x) -- Base 10 logarithm of x.
MAX(x1,x2) -- Maximum value of x1 or x2.
MIN(x1,x2) -- Minimum value of x1 or x2.
NORMAL(x) -- Normal probability distribution of x. X is in units
of standard deviations from the mean. See also the description
of the NPD function. NORMAL(x) = NPD(x,0,1).
NPD(x,mean,std) -- Normal probability distribution of x with
specified mean and standard deviation. X is in units of
standard deviations from the mean.
Chapter 1. Using Mathplot 8
PAREA(x) -- Area under the normal probability distribution curve
from -infinity to x. (i.e., integral from -infinity to x of
NORMAL(x)).
PULSE(a,x,b) -- Pulse function. If the value of x is less than a
or greater than b, the value of the function is 0. If x is
greater than or equal to a and less than or equal to b, the
value of the function is 1. In other words, it is 1 for the
domain (a,b) and zero elsewhere. If you need a function that
is zero in the domain (a,b) and 1 elsewhere, use the expression
(1-PULSE(a,x,b)).
RAD(x) -- Converts an angle measured in degrees to the equivalent
number of radians.
SEC(x) -- Secant of x. (SEC(x) = 1/COS(x)).
SIN(x) -- Sine of x. Angles are measured in radians.
SINH(x) -- Hyperbolic sine of x.
SQRT(x) -- Square root of x.
STEP(a,x) -- Step function. If x is less than a, the value of the
function is 0. If x is greater than or equal to a, the value
of the function is 1. If you need a function which is 1 up to
a certain value and then 0 beyond that value, use the
expression STEP(x,a).
T(n,x) -- Chebyshev polynomial of order n.
TAN(x) -- Tangent of x. Angles are measured in radians.
TANH(x) -- Hyperbolic tangent of x.
Y0(x) -- Bessel function of the second kind, order zero.
Y1(x) -- Bessel function of the second kind, order one.
YN(n,x) -- Bessel function of the second kind, order n.
1.8 Function Types
Mathplot allows four different types of functions to be plotted:
cartesian, parametric cartesian, polar, and parametric polar. Each
of the function types is described below:
1.8.1 Cartesian Functions
A cartesian function has the form Y=f(X), where X is the
independent variable that is plotted along the horizontal axis and
Y is the dependent variable plotted on the vertical axis. The
value specified with the DOMAIN command controls the interval of X
Chapter 1. Using Mathplot 9
values over which the function is evaluated. Some examples of this
type of function are listed below:
Y=SIN(X)
Y=2*X**2-3*X+5
Y=SIN(X)/EXP(X)
Y=1/SQRT(2*(X+1))
1.8.2 Parametric Cartesian Functions
Parametric functions use a third variable, which we will call T, as
the independent variable. Both X and Y are dependent variables
defined as functions of T. The value of the T variable is not
directly displayed on the plot but is used only in the functions
that define the values of the X and Y variables that are plotted.
For example, the following commands define X and Y as functions of
T:
X=COS(T)
Y=SIN(T)
When parametric functions are defined, the DOMAIN statement
specifies the interval over which the T variable is computed. If
the two functions of X and Y specified above are plotted over the
domain (0,2*PI), the result is a circle with radius 1 centered
around the origin.
1.8.3 Polar Functions
A polar function specifies the distance (or radius) of a point from
the origin as a function of the angle swept around the origin. The
angle (A) is the independent variable and the radius (R) is the
dependent variable. The DOMAIN statement specifies the interval of
values that the angle is to be evaluated over. The angle begins on
the positive X axis; positive angles are measured counterclockwise
around the origin. Angles are measured in radians; the RAD and DEG
functions can be used to convert between degrees and radians. The
simplest polar function is
R=1
which specifies that for all angles the radius is 1. If this
function is plotted over the domain (0,2*pi) the result is a circle
of radius 1 centered around the origin. Another simple polar
function is
R=A
which defines a spiral with the radius increasing with the angle.
1.8.4 Parametric Polar Functions
A parametric polar function defines the radius (R) and angle (A) as
functions of the parametric variable, T. The DOMAIN statement
defines the interval of T values over which the function is
Chapter 1. Using Mathplot 10
evaluated. The following is an example of a parametric polar
function definition:
R=COS(T)
A=SIN(T)
Over the domain (0,2*pi), this produces a figure-eight pattern.
1.9 Plotting Simultaneous Functions
Up to four functions may be plotted at the same time. When
defining multiple functions, add a single-digit suffix to the
dependent variable name for the function. For example, the
following commands define four functions to be plotted
simultaneously:
Y1=SIN(X)
Y2=COS(X)
Y3=SIN(2*X)
Y4=COS(2*X)
If no number is specified, the default value is 1. Thus, the
following two function definitions are equivalent:
Y=2*X**2
Y1=2*X**2
You can remove a function definition by defining another function
for the same dependent variable or by specifying the dependent
variable without a function. For example, the following command
removes the definition for Y2:
Y2
When a function of a type (cartesian, polar, etc.) different from
the current type is defined, all of the currently defined functions
are removed.
Chapter 2
Mathplot Commands
The commands described in this section are used to control
Mathplot. When Mathplot is waiting for a command, the cursor is
positioned in the middle window of the screen.
If you need to type a command that is longer than a single line,
you may continue a command by typing a minus sign as the last
character on the line to be continued. Note that a minus sign as
the last character on a line is interpreted by Mathplot as a
continuation marker. It is NOT used as a minus sign in the
expression.
Commands may be abbreviated to the first three letters of their
keyword. Commands may be typed using upper or lower case letters.
You may place comments on commands by preceding the comment by an
exclamation point. For example, the following commands have
comments:
! Define square wave function
Y=SIN(X)+SIN(3*X)/3 ! Approximate square wave
DOMAIN 0,2*PI ! One cycle of the function
2.1 Start up Command File
The DOS command to start Mathplot is:
MATHPLOT [filename]
where "filename" is an optional parameter specifying the name of a
file containing commands to be executed by Mathplot as soon as it
is started. This start up command file may contain one or more
complete sets of statements to define functions and plot them. The
default file extension is ".FUN". See also the descriptions of the
DO and SAVE commands for additional information about command
files.
2.2 Initialization file
Each time Mathplot is started it attempts to open a file named
MATHPLOT.INI. If this file exists, all commands in it are
executed. You may create such a file to contain initialization
11
Chapter 2. Mathplot Commands 12
commands to set default values. For example, if you normally like
to have grid lines turned on, create a file named MATHPLOT.INI
containing the command "GRID ON". Mathplot looks for this file
first in the current directory and if it does not find it there it
checks to see if a MATHPLOT environment variable has been defined
to specify a directory. The initialization file is executed before
any file specified on the command that starts Mathplot.
2.3 Command Arguments
Many of the commands accept numeric arguments. In the descriptions
below, the notation "cexpr" is shown wherever a numeric argument
may be specified. These numeric arguments may consist of numbers,
symbolic constants, and expressions using operators and built in
functions. For example, the following is a valid DOMAIN command:
DOMAIN -2*PI,PI*SQRT(2)
The argument expressions may NOT contain variables such as X, Y, R,
A, or T, or parameters such as P0 or P1.
Arguments shown in brackets are optional. Braces around a set of
options indicate that you must choose one of the options in the
set.
2.4 Alphabetical List of Commands
2.4.1 AXES
AXES {ON | OFF} (default=ON) -- Specifies whether to display axes.
Use the LABELS command to control whether axis labels are
displayed.
2.4.2 CALCULATE
CALCULATE cexpr -- Evaluate the specified expression, which must
contain only numbers, operators, and built in functions, and
display the result in the bottom window.
2.4.3 CAXES
CAXES cexpr (default=3) -- Specify the color to be used for the
axis lines and labels.
2.4.4 CFn
CFn cexpr (default=2,1,4,3) -- Define the color to be used when
plotting function 'n'. For example, the command "CF1 3" specifies
that color 3 is to be used when plotting function 1.
Chapter 2. Mathplot Commands 13
2.4.5 CGRID
CGRID cexpr (default=8) -- Specify the color to be used for grid
lines.
2.4.6 COLORBORDER
COLORBORDER color1 [ON color2] (default=WHITE) -- Specify the color
of the border lines. The 'color1' and 'color2' parameters must be
one of the following keywords: WHITE, BLACK, BLUE, GREEN, RED,
CYAN, MAGENTA, BROWN. The 'color1' parameter specifies the
foreground color (i.e., the color of the characters). If the "ON
color2" phrase is used 'color2' is the background color. If the
"ON color2" phrase is omitted, "ON BLACK" is used by default. For
example, to get white characters on a blue background, specify:
COLORBORDER WHITE ON BLUE
This command (and the other COLORxxx) commands can be placed in the
MATHPLOT.INI initialization file to cause your selected colors to
be initialized automatically each time Mathplot is started.
2.4.7 COLOREDIT
COLOREDIT color1 [ON color2] (default=WHITE) -- Specify the color
of the center portion of the screen where commands are typed and
displayed.
2.4.8 COLORHEAD
COLORHEAD color1 [ON color2] (default=CYAN) -- Specify the color of
the text in the heading portion of the screen (i.e., "ESC=Exit
F1=Plot", etc.).
2.4.9 COLORHELP
COLORHELP color1 [ON color2] (default=WHITE) -- Specify the color
of the help screen text.
2.4.10 COLORHELPHEAD
COLORHELPHEAD color1 [ON color2] (default=MAGENTA) -- Specify the
color of the heading of the help display screen.
2.4.11 COLORMESSAGE
COLORMESSAGE color1 [ON color2] (default=GREEN) -- Specify the
color of information and error messages displayed in the lower
portion of the screen.
2.4.12 COMMONSCALE
COMMONSCALE {ON | OFF} (default=OFF) -- If this option is turned
on, the X and Y directions are forced to have the same scale. If
this option is off, the X and Y ranges are scaled independently,
Chapter 2. Mathplot Commands 14
which may cause figures to be distorted - for example, a circle may
display as an ellipse. However, turning this option on may result
in one of the dimensions using only a small portion of the screen
if the X and Y ranges are very different. This option is always on
for polar function plots.
2.4.13 CTITLE
CTITLE cexpr (default=7) -- Specify the color to use for the title
line.
2.4.14 DATA
DATA filename -- Causes X and Y data values to be read from an
external file rather than being computed from function definitions.
After the data has been read, use the PLOT command to display it.
Any function definition following this command will clear the
external data values and revert to function mode. Each X,Y data
pair must be specified as a separate line in the file with a space
separating the X value from the Y value. The default extension for
the file is ".DAT".
2.4.15 DISPLAY
DISPLAY string -- Display the string in the bottom window of the
screen. The string is displayed for 3 seconds. This command may
be placed in command file to cause information to be printed while
the command file is being processed.
2.4.16 DO
DO filename -- Execute the Mathplot commands stored in an external
file. This allows you to specify a complete plot request,
including functions and options, and then execute it without having
to retype the commands. An external file may itself contain a DO
command and this nesting may be performed to a depth of 10 files.
The default file extension is ".FUN". Use the LIST command to
control whether the commands in the file are displayed in the edit
window. See also the description of the SAVE command.
2.4.17 DOMAIN
DOMAIN cexpr1,cexpr2 (default=0,2*pi) -- Define the domain of the
independent variable over which the functions are evaluated and
plotted. This command may be abbreviated to "DOM".
2.4.18 EXIT
EXIT -- Stop Mathplot and return to DOS. Pressing ESC will also
cause Mathplot to exit.
Chapter 2. Mathplot Commands 15
2.4.19 GRID
GRID {ON | OFF} (default=OFF) -- Specify whether grid lines are to
be displayed.
2.4.20 HELP
HELP -- Display the help menu. You can also do this by pressing
F3.
2.4.21 LABEL
LABEL {ON | OFF} (default=ON) -- Specify whether axis labels are to
be displayed.
2.4.22 LIST
LIST {ON | OFF} (default=OFF) -- Specify whether commands executed
from an external file by subsequent use of the DO command are to be
listed as they are executed.
2.4.23 NUMPOINTS
NUMPOINTS cexpr (default=100) -- Specify the number of points at
which the functions are to be evaluated over the domain.
Specifying a larger number of points results in a smoother plot but
increases the computation time. The maximum number of points that
may be computed is 2000. This command may be abbreviated to the
single letter 'N'.
2.4.24 ORIGIN
ORIGIN {ON | OFF} (default=OFF) -- Specify whether the origin (0,0)
is to be forced to be included in the plot. If this option is off
and the range of values does not span 0, then the origin may not be
displayed. Turning this option on allows the range of the function
relative to the origin to be observed, but may result in a small
scale factor if the range is far from the origin.
2.4.25 Pn
Pn cexpr -- Specify a value for parameter Pn where 'n' is in the
range 0 to 9. Mathplot allows you to use up to ten parameter
values in function specifications. The parameters are named P0,
P1, ..., P9. You can assign a new value to a parameter and replot
the function without having to retype the function.
2.4.26 PAUSE
PAUSE [cexpr] (default=0) -- This command may be placed in a
command file to cause execution to pause until a key is pressed or
the specified number of seconds elapse. If cexpr is omitted or has
the value 0, execution pauses for an indefinite time until a key is
pressed.
Chapter 2. Mathplot Commands 16
2.4.27 PDEVICE
PDEVICE device (default=PRN) -- Allows you to specify the device or
file to which printer output is written when printing is turned on
by use of the PRINT ON command. The default device is "PRN" but
you may specify another device such as LPT2 or COM. You may also
direct output to a disk file that you can printer later using the
DOS PRINT or COPY commands.
2.4.28 PRESOLUTION
PRESOLUTION value (default=150) -- Specifies whether plots sent to
HP LaserJet printers should use 150 or 300 dot-per-inch resolution.
The value parameter must be 150 or 300. The default value is 150
causes the plots to use most of the horizontal width of an 8.5x11
inch page. These plots are suitable for direct transfer to
overhead transparencies. Specifying 300 for the resolution
produces smaller plots that are suitable for inclusion in printed
documents.
2.4.29 WIDTH
WIDTH value (optional) -- Specify the width, in inches, of printed
plots. Due to memory space considerations, the maximum width is
limited to about 7.9 inches for 150 DPI resolution and 4.5 inches
for 300 DPI resolution. If you have limited memory space, you may
have to reduce the width to be able to produce printed plots. This
statement is ignored unless you request that a plot be printed.
2.4.30 PLOT
PLOT [cexpr] (default=0) -- Evaluate the currently defined
functions and plot them. If an optional value (cexpr) is
specified, the function is displayed for the specified number of
seconds or until a key is pressed. If the optional value is
omitted or is zero, the plot is displayed for an indefinite time
until a key is pressed. The use of the optional value is most
useful when the PLOT command occurs in a command file producing a
"slide show" of functions. You can also plot the function(s) by
pressing F1.
2.4.31 PRINT
PRINT {ON | OFF} (default=OFF) -- Turns printer output on or off.
When turned on, any plot displayed on the screen is also written to
the printer (or file as directed by the PDEVICE command). To
produce a printed copy of the currently defined function(s) press
F2.
2.4.32 RESET
RESET -- Reset all parameters and options to their initial values
and remove all function definitions. You can also perform this
function by pressing F4.
Chapter 2. Mathplot Commands 17
2.4.33 SAVE
SAVE filename -- Write the current function definitions and the
values of all options and parameters to the specified file. The DO
command can then be used at a later time to redisplay the function.
The default file extension is ".FUN".
2.4.34 TITLE
TITLE string -- Define a title line to be displayed at the top of
the plot.
2.4.35 WAXES
WAXES cexpr (default=3) -- Specify the width (in dots) of the axis
lines for printed output. This parameter does not affect the
screen display.
2.4.36 WFn
WFn cexpr (default=3) -- Specify the width (in dots) of the line
used to draw the plot of function 'n'. This only affects hard copy
output.
2.4.37 WGRID
WGRID cexpr (default=1) -- Specify the width (in dots) of the grid
lines. This only affects hard copy output.
Chapter 3
Advanced Applications
3.1 Root Finding
Mathplot can be used to find the roots of equations. To do this,
turn on axis labeling (LABEL ON) and plot the function over the
domain in which a root occurs. Observe the approximate X value at
which the function crosses the X axis and then reset the domain to
closely span the crossing point. Replot the function and obtain a
new X estimate. After several iterations you will be able to
determine the root to several significant digits. For example, use
this technique to find the root of the function:
Y = X^4 - EXP(X)
in the domain (2,9.5).
For a course in Algebra I, Mathplot can be used to demonstrate the
graphical method of solving two simultaneous linear equations by
locating the point of intersection. For an Algebra II course,
Mathplot can be used to locate minimum and maximum points for
quadratic and cubic equations.
3.2 Multiple Domains
Mathplot only allows specification of a single continuous domain of
values. However, by using the multiple function plotting
capability it is sometimes possible to simulate multiple domains.
For example, the function X*Y=5 defines a hyperbola with branches
in both the positive X-Y domain (upper right quadrant) and the
negative X-Y domain (lower left quadrant). The following set of
commands defines two parametric functions to draw each of the
branches:
X1=T
Y1=5/T
X2=-T
Y2=-5/T
DOMAIN 0.5,10
LABEL ON
COMMONSCALE ON
PLOT
18
Chapter 3. Advanced Applications 19
3.3 Interesting Functions
The following specifications plot interesting and attractive
functions:
TITLE Four Leaved Rose
CTITLE 4
R=2*SIN(2*A)
CF1 3
DOMAIN 0,2*PI
NUMPOINTS 150
AXES ON
CAXES 1
PLOT
TITLE Prolate Cycloid
CTITLE 4
Y=1-2*COS(T)
X=T-2*SIN(T)
CF1 2
DOMAIN -4*PI,4*PI
NUMPOINTS 400
CAXES 1
COMMONSCALE ON
PLOT
TITLE Hypocycloid of four cusps (Asteroid)
CTITLE 4
Y=SIN(T)^3
X=COS(T)^3
CF1 2
DOMAIN 0,2*PI
NUMPOINTS 100
AXES ON
CAXES 1
COMMONSCALE ON
PLOT
TITLE Bifolium
CTITLE 4
Y=2*SIN(T)^2*COS(T)^2
X=2*SIN(T)*COS(T)^3
CF1 3
DOMAIN 0,2*PI
NUMPOINTS 100
AXES ON
CAXES 1
COMMONSCALE ON
PLOT
Chapter 3. Advanced Applications 20
TITLE Epicycloid
CTITLE 4
Y=5*SIN(T)-SIN(5*T)
X=5*COS(T)-COS(5*T)
CF1 3
DOMAIN 0,2*PI
NUMPOINTS 150
AXES ON
CAXES 1
COMMONSCALE ON
PLOT
3.4 "Artistic" Plots
When Mathplot plots a function, it evaluates the function at the
number of points specified by the last NUMPOINTS command and then
connects the points together using straight lines. By specifying
very large domain values for polar or parametric functions, the
lines connecting the points span large distances and produce
interesting and "artistic" plots. It is best to turn off axis
display (AXES OFF, LABELS OFF) and turn on common scaling
(COMMONSCALE ON) for these plots. Here are some examples to try:
Y=SIN(T)^3
X=COS(T)^3
CF1 2
DOMAIN 0,4000
NUMPOINTS 500
R=2*SIN(2*A)
CF1 3
DOMAIN 0,2000
NUMPOINTS 500
Y=5*SIN(T)-SIN(5*T)
X=5*COS(T)-COS(5*T)
CF1 3
DOMAIN 0,6000
NUMPOINTS 400
Parametric and polar functions seem to produce the best artistic
plots. By varying the NUMPOINTS and DOMAIN values you can usually
produce many different plots from the same functions.
Chapter 4
Use and Distribution of Mathplot
There are two versions of the Mathplot program: shareware and
registered. You are welcome to make copies of the shareware
version of Mathplot and pass them on to friends or post this
program on bulletin boards or distribute it via disk catalog
services, CD ROMS, or other means provided the entire Nonlin
distribution is included in its original, unmodified form. A
distribution fee may be charged for the cost of the diskette,
shipping and handling. Vendors are encouraged to contact the
author to get the most recent version of Nonlin.
As a shareware product, you are granted a no-cost, trial period of
30 days during which you may evaluate Mathplot. If you find
Mathplot to be useful, educational, and/or entertaining, and
continue to use it beyond the 30 day trial period, you are required
to compensate the author by sending the registration form printed
on page 25 (and in REGISTER.DOC) with the appropriate registration
fee to help cover the development and support of Mathplot.
In return for registering, you will be authorized to continue using
Mathplot beyond the trial period and you will receive the
registered version of the program, a bound, typeset manual, and
three months of support via telephone, mail, or e-mail. Your
registration fee will be refunded if you encounter a serious bug
that cannot be corrected.
See also the special offer for Nonlin on page 23.
This program is produced by a member of the Association of
Shareware Professionals (ASP). ASP wants to make sure that the
shareware principle works for you. If you are unable to resolve a
shareware-related problem with an ASP member by contacting the
member directly, ASP may be able to help. The ASP Ombudsman can
help you resolve a dispute or problem with an ASP member, but does
not provide technical support for members' products. Please write
to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442 or send
a CompuServe message via CompuServe Mail to ASP Ombudsman
7007,3536.
21
Chapter 4. Use and Distribution of Mathplot 22
You are welcome to contact the author:
Phillip H. Sherrod
4410 Gerald Place
Nashville, TN 37205-3806 USA
615-292-2881 (evenings)
CompuServe: 76166,2640
Internet: 76166.2640@compuserve.com
4.1 Copyright Notice
Both the Mathplot program and documentation are copyright (c)
1991-1994 by Phillip H. Sherrod. You are not authorized to modify
the program. "Mathplot" is a trademark.
4.2 Disclaimer
This software and documentation are provided on an "as is" basis.
This program may contain "bugs" and inaccuracies, and its results
should not be assumed to be correct unless they are verified by
independent means. Phillip H. Sherrod disclaims all warranties
relating to this software, whether expressed or implied, including
but not limited to any implied warranties of merchantability or
fitness for a particular purpose. Neither Phillip H. Sherrod nor
anyone else who has been involved in the creation, production, or
delivery of this software shall be liable for any indirect,
consequential, or incidental damages arising out of the use or
inability to use such software, even if Phillip H. Sherrod has
been advised of the possibility of such damages or claims. The
person using the software bears all risk as to the quality and
performance of the software.
This agreement shall be governed by the laws of the State of
Tennessee and shall inure to the benefit of Phillip H. Sherrod and
any successors, administrators, heirs and assigns. Any action or
proceeding brought by either party against the other arising out of
or related to this agreement shall be brought only in a state or
federal court of competent jurisdiction located in Davidson County,
Tennessee. The parties hereby consent to in personam jurisdiction
of said courts.
Chapter 5
Other Software
5.1 Nonlin
If you like Mathplot, you should check out Nonlin -- the nonlinear
regression analysis program by the same author. And, if you
register your use of Mathplot and order Nonlin at the same time,
you can get both for the special price of $60.
What is regression analysis? Regression analysis is a mathematical
technique for determining the best values of parameters to fit an
equation to a set of data points. For example, you might want to
develop an equation of the form
price = p0 + p1*age + p2*miles
to predict the price of a used car based on its age and the number
of miles driven. With Nonlin you can collect data from car ads and
then perform the analysis using the following set of commands:
VARIABLES PRICE,AGE,MILES
PARAMETERS P0,P1,P2
FUNCTION PRICE = P0 + P1*AGE + P2*MILES
DATA
Nonlin will analyze the data and determine the best values of the
parameters P0, P1, and P2 to fit the data values.
Ordinary linear regression programs can only determine parameter
values for linear (straight line) equations. Nonlin, on the other
hand, can handle multivariate, linear, polynomial, and general
nonlinear equations. For example, using Nonlin you can easily
determine the best values for the parameters Offset, Amplitude, and
Frequency for an equation of the form:
Y = Offset + Amplitude * sin(Frequency * X)
Nonlin uses the same expression evaluator as Mathplot so you can
model complicated equations using the full set of operators and
library functions available in Mathplot.
Nonlin comes with a 45 page manual that explains regression
analysis and gives many examples. Nonlin is in use at many
universities and research labs around the world.
23
Chapter 5. Other Software 24
5.2 TSX-32 Operating System
If you have a need for a multi-user, multi-tasking operating
system, you should look into TSX-32. TSX-32 is a full-featured,
high performance, multi-user operating system for the 386 and 486
that provides both 32-bit and 16-bit program support. With
facilities such as multitasking and multisessions, networking,
virtual memory, X-Windows, background batch queues, data caching,
file access control, real-time, and dial-in support, TSX-32
provides a solid environment for a wide range of applications.
A two user, shareware version of TSX-32 called TSX-Lite is also
available.
TSX-32 is not a limited, 16-bit, multi-DOS add-on. Rather, it is a
complete 32-bit operating system which makes full use of the
hardware's potential, including protected mode execution, virtual
memory, and demand paging. TSX-32 sites range from small systems
with 2-3 terminals to large installations with more than 64
terminals on a single 386.
In addition to supporting most popular 16-bit DOS programs, TSX-32
also provides a 32-bit "flat" address space with both Phar Lap and
DPMI compatible modes of execution.
Since the DOS file structure is standard for TSX-32, you can
directly read and write DOS disks. And, you can run DOS part of
the time and TSX-32 the rest of the time on the same computer.
TSX-32 allows each user to control up to 10 sessions. Programs can
also "fork" subtasks for multi-threaded applications. The patented
Adaptive Scheduling Algorithm provides consistently good response
time under varying conditions.
The TSX-32 network option provides industry standard TCP/IP
networking through Ethernet and serial lines. Programs can access
files on remote machines as easily as on their own machine. The
SET HOST command allows a user on one machine to log onto another
computer in the network. FTP, Telnet, and NFS are available for
interoperability with other systems.
System requirements: 386 or 486 system, 4MB memory, 12MB of free
disk space (Stacker and DoubleSpace are not supported).
TSX-32 is the best and most powerful operating system available for
the 386 and 486. For additional information contact:
S&H Computer Systems, Inc.
1027 17th Avenue South
Nashville, TN 37212 USA
615-327-3670 (voice)
615-321-5929 (fax)
CompuServe: 71333,27
Internet: 71333.27@compuserve.com
=================================================================
Software Order Form
=================================================================
Name ______________________________________________________
Address ___________________________________________________
City _______________________ State _______ Zip ___________
Country ____________________ Telephone ___________________
Internet address (optional) _______________________________
Mathplot version you currently have _______________________
Bulletin board where you found Mathplot ___________________
Comments __________________________________________________
Check the box below which indicates your order type:
___ I wish to register Mathplot ($20).
___ I wish to order Nonlin ($45).
___ I wish to register Mathplot and order Nonlin ($60).
Add $5 to any amount shown above if the software is being shipped
out of the United States. I cannot accept checks from non-US
banks. Visa, MasterCard and American Express credit card charges
are accepted but a check, money order, or cash is preferred. If
you wish to use a credit card specify the billing name, address,
card number, and expiration date.
In return for registering, you will receive the registered version
of the program, a laser-printed, bound copy of the manual, and
three months of telephone or CompuServe support. Your registration
fee will be refunded if you find a serious bug that cannot be
corrected.
Distribution disk choice (check one):
3.50" HD (1.4 MB) ______
5.25" HD (1.2 MB) ______
5.25" DD (360 KB) ______
Send this form with the amount indicated to the author:
Phillip H. Sherrod
4410 Gerald Place
Nashville, TN 37205-3806 USA
615-292-2881 (evenings)
CompuServe: 76166,2640
Internet: 76166.2640@compuserve.com
Index 26
Abbreviating commands, 11 DEG function, 6
ABS function, 6 Device for output, 16
ACOS function, 6 Disclaimer, 22
Arc cosine, 6 DISPLAY command, 14
Arc sine, 6 DO command, 14
Arc tangent, 6 DOMAIN command, 14
Artistic plots, 20 Domains
ASIN function, 6 multiple, 18
ASP, 21 Edit area color, 13
Asteroid, 19 EI1 function, 6
ATAN function, 6 EI2 function, 7
AXES command, 12 EIC1 function, 7
Bessel function, 7, 8 EIC2 function, 7
Beta function, 6 Elliptic integral, 6, 7
BETAI function, 6 Epicycloid, 20
Bifolium, 19 ERF function, 7
Border color, 13 Error color, 13
Build-in functions, 6 EXIT command, 14
Calculate command, 12 EXP function, 7
Cartesian functions, 8 Exponential, 7
CAXES command, 12 Exponentiation operator, 5
CFn command, 12 External command file, 14
CGRID command, 13 External data file, 14
Chebyshev polynomial, 8 FAC function, 7
Color Factorial, 7
of axes, 12 Four leaved rose, 19
of border, 13 GAMMA function, 7
of edit area, 13 GAMMALN function, 7
of errors, 13 GAMMI function, 7
of function, 12 Grid color, 13
of grid, 13 GRID command, 15
of heading, 13 HAV function, 7
of help, 13 Haversine, 7
of messages, 13 Heading color, 13
of title, 14 Help color, 13
COLORBORDER command, 13 HELP command, 15
COLOREDIT command, 13 Hyperbolic cosine, 6
COLORHEAD command, 13 Hyperbolic sine, 8
COLORHELP command, 13 Hyperbolic tangent, 8
COLORHELPHEAD command, 13 Hypocycloid, 19
COLORMESSAGE command, 13 Initialization file, 11
Comments, 11 Interesting functions, 19
COMMONSCALE command, 13 Inverse gamma, 7
Continuing lines, 11 J0 function, 7
Copyright notice, 22 J1 function, 7
COS function, 6 JN function, 7
Cosecant function, 6 LABEL command, 15
COSH function, 6 LIST command, 15
COT function, 6 LOG function, 7
Cotangent function, 6 Log gamma, 7
CSC function, 6 LOG10 function, 7
CTITLE command, 14 Long lines, 11
Curve fitting, 23 MATHPLOT.INI, 11
Cycloid, 19 MAX function, 7
DATA command, 14 Message color, 13
Index 27
MIN function, 7 WGRID command, 17
Multiple domains, 18 WIDTH command, 16
Nonlin, 23 Y0 function, 8
Nonlinear regression, 23 Y1 function, 8
NORMAL function, 7 YN function, 8
NPD function, 7
Numeric constants, 5
NUMPOINTS command, 15
Operator precedence, 5
Order form, 25
ORIGIN command, 15
Parameter values, 5, 15
Parametric functions, 9
PAREA function, 7
PAUSE command, 15
PDEVICE command, 16
PI constant, 5
PLOT command, 16
Pn command, 15
Polar functions, 9
Precedence of operators, 5
PRESOLUTION command, 16
PRINT command, 16
Printer resolution, 16
Probability distribution, 7
Prolate cycloid, 19
PULSE function, 8
RAD function, 8
REGISTER.DOC, 21
Registration form, 25
Regression analysis, 23
RESET command, 16
Resolution of printer, 16
Root finding, 18
Rose figure, 19
SAVE command, 17
Scaling, 13
SEC function, 8
Secant, 8
SIN function, 8
SINH function, 8
SQRT function, 8
Standard error function, 7
Start up file, 11
STEP function, 8
Symbolic constants., 5
T function, 8
TAN function, 8
TANH function, 8
Title color, 14
TITLE command, 17
Trademark notice, 22
TSX-32, 24
WAXES command, 17
WFn command, 17
