SCICALC Math Utilities Demo
Scicalc 2.0

Bob Zorich
Acro Technology, Inc.
1111 W El Camino Real Suite 331
Sunnyvale, CA 94086

Copyright 1985, 1986 Acro Technology
All Rights Reserved


This file is the description for the Scicalc Math Utilities demo
program. This is a totally rewritten version of the Scicalc Math Demo
Version 1.0, released in August, 1985, and version 1.2, released
February, 1986. The SCICALC Math Utilities Demo program is hereby
released to the Public Domain using the concept of "Shareware". Share
this program with your friends, user's groups, and your favorite BBS.
Please do not modify the program in any way, or try to accept
remuneration for it. After all, MANY hours of work were put into this
work, the authors should get the credit. Treat it the same as you would
expect OTHERS to treat YOUR work. If you feel that this program has
benefited you, then please find it in your heart to send $20.00 to the
above address.

The demo program illustrates the use of, and finds accurate
solutions to over 250 functions. These functions range from unit
conversions to Fast Fourier Transform, Complex Number analysis, matrix
algebra, and a wide variety of others. A complete list of the functions
available is at the end of this file.

NOTICE : To move up one level or to cancel the window you are in
type "0".

This program is set up to run in a completely windowed mode, at
some point in the future, I may make it memory resident. Right now, it
runs only as a stand alone program. This version is also not compiled
for use of the 8087 coprocessor, although a version exists that does use
8087's. I am attemping to reach the widest possible number of users with
this version.

The Scicalc Demo program was developed on an IBM XT, and has been
tested on an IBM AT with Hercules graphics. It requires 192K of free
RAM, of which about 40K is used for window storage, and 40-45K bytes are
for program space. The rest of the space is reserved for heap space,
which is where all matrix manipulations are done. The program also
expects the use of IBM's CGA, although it only uses Text Mode and should
therefore be compatible with almost everything, except the monochrome
adaptor, which may give some trouble.

In general, the routines are error protected, especially against
illegal input. However, there may still be conditions that will cause
the program to dump. There are limitations to what you can do, such as
the size of three dimensional matrices. These limitations will be
described in a minute.

The program is fairly self-explanatory, with all functions called
through menus, and most input routines labelled for what is expected.
There is no direct on-line help, but short of putting in gibberish into
the routines, the program will "lead" you through. The solutions are
sometimes returned as real numbers, sometimes as complex numbers,
sometimes as vectors. Again, it should be relatively clear as to what
is being displayed.

The basic limitations are these:

1- Matrices have limited size capabilities, limited due to the
methods I have used implementing the window routines. The math
routines themselves are only limited by the available memory.
The maximum sizes are about 20 items in a one dimensional
vector, about an 8x8 two dimensional matrix, and about 4x4x3
three dimensional matrix.

2- Second and third level menus may crash if the value entered to
select the menu choice does not exist on the menu. This is not
a serious issue, as long as you are careful with data entry.

3- Needs 192K RAM, Color Graphics Adaptor, one disk drive
(preferably a hard drive), MS-DOS 2.1 or higher. Known to be
incompatible with IBM Monochrome Graphics Board.

4- Non-8087 version limited to real values under abs(1e37). This
can only be noticed in very unusual circumstances, and in
most cases, this number will not be exceeded. Watch out for
intermediate solutions exceeding these limits.

The Math Utilities and all source code of these routines are
available from Acro Technology, Inc. The source codes for the math
routines are written in Turbo Pascal and are built so that all variables
are passed on the command line, and so that only stack and heap space are
used. The actual data segment size on the math routines themseleves is 32
bytes. They are commented, and written in an easy to use modular manner.
All error trapping is already built in, any user extensions to the error
trapping routines are easy to implement. Use of the routines is as easy
as including the modules that you need, and then interfacing the functions
to your programs.

The following is a list of all math functions available within the
Scicalc Math Utilities Package:

NOTICE : To move up one level or to cancel the window you are in
type "0".

Function Evaluations

Solutions to Common Formulas
----------------------------
1- Polynomial Evaluations 2- Quadratic Formula 3- Newton Raphson Roots
4- Derivative Calculation 5- Function Integration 6- Integration by Data
7- Gaussian Elimination 8- Fast Fourier Transform

Statistical Tables

Various Statistical Formulas
----------------------------
1- Geometric Mean of List 2- Arithmetic Mean List 3- Median of a List
4- Variance of a List 5- Standard Deviation 6- Binomial Distribution
7- Poisson Distribution 8- Normal Distribution

General Math Functions

Solutions to Common Formulas
----------------------------
1- Log Base 10 2- Log Any Base 3- Factorial
4- Nth Power of Real 5- Nth Root of Real 6- Permutations
7- Combinations 8- Max Min Locator 9- Find Circle 3 Pts
10- Gaussian Dist Random # 11- Sieve Eratosthenes 12- Great Common Denom

Complex Algebra

Common Complex Number Functions
-------------------------------
1- Real to Complex 2- Complex to Polar 3- Polar to Complex
4- Complex Conjugate 5- Multiply by Scalar 6- Addition
7- Add N Complex 8- Subtraction 9- Multiplication
10- Division 11- Raise to Real 12- Complex Root
13- Complex Exponential 14- Complex Sine 15- Complex Cosine
16- Complex Tangent 17- Complex Square 18- Complex Square Root
19- Complex Natural Log 20- Raise to Complex

Physical Phenomena

General and Relativistic Functions
----------------------------------
1- Angular Momentum 2- Percent C to Met/sec 3- Meter/Sec to Percent C
4- Rel Distortion 5- Lorentz Transform 6- Velocity Addition
7- Velocity Add Prime 8- Time Distortion 9- Mass Distortion
10- Rel Kinetic Energy 11- Rel Total Energy 12- Rel Momentum
13- Radius of Particle Moving in Magnetic Field

Co-ordinate System Transformation
---------------------------------
1- Rectang to Polar 2- Polar to Rectang 3- Spherical to Rectang
4- Rectang to Spher 5- Cylin to Rectang 6- Rectang to Cylind
7- Translate and Rotate 8- Scale Factor

Trigonometric Functions

Extended Trig Functions
-----------------------
1- Degrees to Radians 3- Tangent 5- Secant
2- Radians to Degrees 4- Cosecant 6- Cotangent

Arc Trig Functions
------------------
1- Arc Sine 3- Arc Cotangent 5- Arc Secant
2- Arc Cosine 4- Arc Cosecnt

Hyperbolic Functions
--------------------
1- Hyperbolic Sine 3- Hyperbolic Tangent 5- Hyperbolic Secant
2- Hyperbolic Cosine 4- Hyperbolic Cosecant 6- Hyperbolic Cosecant

Arc Hyperbolic Functions
------------------------
1- Arc Hyperbolic Sine 4- Arc Hyper Tangent 7- Arc Hyp Secant
2- Arc Hyperbolic Cosine 5- Arc Hyper Cotangent 8- Alt Arc Hyper Secant
3- Alt Arc Hyper Cosine 6- Arc Hyper Cosecant

Mensuration Tables

2-d Figures
-----------
1- Circumference of Circle 2- Area of Circle
3- Circumference of Ellipse 4- Area of Ellipse

Cubes
-----
1- Volume of Box 2- Area of Box
3- Diagonal of Box 4- Diagonal of Face

Cylinders
---------
1- Surface Area of Sid of Cylinder 2- Total Surface Area of Cylinder
3- Volume of Cylinder

Cones / Conic Sections
----------------------
1- Volume of general right cone 2- Slant height of side
3- Area of side of cone 4- Total Area of cone
5- Volume of cone 6- Side Area of Frustrum
7- Total Area of Frustrum 8- Volume of Frustrum

Spheres / Spherical Sections
----------------------------
1- Surface Area of Sphere 2- Volume of Sphere
3- Area of one zone of Sphere 4- Volume of one zone of sphere
5- Area of two zones of Sphere 6- Volume of two zones of sphere

Spheroids / Ellipsoidal Solids
------------------------------
1- Surface Area of Lune 2- Eccentricity of Ellipse
3- Sur Area of Oblate Ellipsoid 4- Volume of Oblate Spheroid
5- Sur Area of Prolate Ellipsoid 6- Volume of Prolate Spheroid
7- Surface area of Torus 8- Volume of Torus

Matrix Functions

Matrix Primitives
-----------------
1- Null Vector 2- 2-d Null Matrix 3- 3-d Null Matrix
4- 2-d Unit Matrix 5- Copy Vector 6- Copy 2-d Matrix
7- Copy 3-d Matrix 8- Swap Rows 2-d Mat 9- Swap Columns 2-d Matrix
10- Insert Row 2-d Mat 11- Insert Column 2-d 12- Delete Column
13- Delete Row 14- Send Row to Vector 15- Send Column to Vector
16- Send Diagonal to Vec 17- Send Vector to Row 18- Send Vector to column
19- Send Vector to Diag

Matrix Evaluations
------------------
1- Magnitude of a vector 2- Dot Product 3- Angle Between Vectors
4- Cross Product 5- Add Two Vectors 6- Add N Vectors
7- Add and Subtract Mat 8- Matrix Multiply 9- Transpose Matrix
10- Multiply by Scalar 11- Invert Matrix 12- Multiply by inverse
13- Add Constant to Matrix 14- 3-d Add / Subtract 15- 3-d Matrix Mult
16- 3-d Scalar Multiply

Matrix Functions
----------------
1- Square Vector 2- Square 2-d Matrix 3- Square 3-d Matrix
4- Square Root Vector 5- Square Root 2-d Mat 6- Sqare root 3-d matrix
7- Absolute Value Vector 8- Absolute 2-d Matrix 9- Absolute 3-d Matrix
10- Round Vector 11- Round 2-d Matrix 12- Round 3-d Matrix
13- Truncate Vector 14- Truncate 2-d matrix 15- Truncate 3-d Matrix
16- Natural Log Vector 17- Ln of 2-d matrix 18- Ln of 3-d matrix
19- Exponential vector 20- Exponential 2-d Mat 21- Exponential 3-d Mat

Unit Conversion Functions

Linear
------
1- Cm to Inch 9- Yards to Meters 17- Feet to Fathom
2- Meters to Feet 10- Miles to Km 18- Fathom to Feet
3- Meters to Yards 11- Mile to Feet 19- Light Year to Meter
4- Km to Miles 12- Feet to Mile 20- Meter to Light Year
5- Millimeter to Micron 13- Naut Mile to Mile 21- Light Year to Parsec
6- Micron to Millimeter 14- Mile to Naut Mile 22- Parsec to Light Year
7- Inch to CM 15- Angstrom to Meter
8- Feet to Meters 16- Meter to Angstrom

Spatial
-------
1- Sq Meter to Sq Foot 7- Acres to Sq Foot 13- Cub Inch to Cub Meter
2- Sq Inch to Sq Meter 8- Sq Foot to Acres 14- Cub Meter to Cub Inch
3- Cub Meter to Cub Foot 9- Acre to Hectare 15- Cub Foot to Cub Inch
4- Cub Foot to Cub Meter 10- Hectare to Acre 16- Cub Inch to Cub Foot
5- Sq Foot to Sq Meter 11- Acre to Sq Mile
6- Sq Meter to Sq Foot 12- Sq Mile to Acre

Mass/Density
------------
1- Gram to Ounce 7- Ton to Pound 13- Kg/Cub M to Gm/Cub Cm
2- Kilogram to Pound 8- Pound to Ton 14- Gm/Cub Cm to Kg/Cub M
3- Ounce to Gram 9- KGram/Cub Met to Lb/Cub Foot
4- Pound to Kilogram 10- Lb/Cub Foot to KGram/Cub Met
5- AMU to Gram 11- Gm/Cub Inch to Lb/Cub Cm
6- Gram to Amu 12- Lb/Cub Inch to Gm/Cub Cm

Fluids
------
1- Liter to Gallon 5- Gallon to Cub Inch 9- Fluid Ounce to Gallon
2- Fl Oz to Milliliter 6- Cub Inch to gallon 10- Gallon to Fl. Ounce
3- Millilliter to Fl Oz 7- Liter to Cub Meter
4- Gallon to Liter 8- Cub Meter to Liter

Time
----
1- Year to Day 5- Day to hour 9- Hour to Minute
2- Day to Year 6- Hour to Day 10- Minute to Hour
3- Year to Second 7- Hour to Second
4- Second to Year 8- Second to Hour

Energy
------
1- Joules to BTU 5- Joules to Ft-Lb 9- Dyne to Newton
2- BTU to Joules 6- Ft-Lb to Joules 10- BTU to Calories
3- HP to Kwatts 7- BTU/Min to Watts 11- Calories to BTU
4- Kwatts to HP 8- Newton to Dyne

Velocity
--------
1- MPH to Knots 3- KM/Hr to Mile/Hr 5- Mile/Hr to Feet/Sec
2- Knots to MPH 4- Mile/Hr to KM/Hour 6- Feet/sec to Mile/Hr

Pressure
--------
1- PSI to Atmosphere 4- MmHg to Atmosphere 7- MlBar to Dyne/cm
2- Atmosphere to PSI 5- PSI to Dyne/CM 8- Dyne/Cm to MlBar
3- Atmos to MmHg 6- Dyne/Cm to PSI

Temperature
-----------
1- Celsius to Fahrenheit 3- Kelvin to Fahrenheit 5- Kelvin to Celsius
2- Fahrenheit to Celsius 4- Fahrenheit to Kelvin 6- Celsius to Kelvin

NOTICE : To move up one level or to cancel the window you are in
type "0".