Binomial.TXT  Version 1.00   3 December 1998
============

This program runs on the TI-89 and computes terms of the binomial expansion
of (a + x)^n.

I wrote the first version of this program almost 20 years ago for one of the
early Casio programmable calculators, the FX702P.  A few years ago I rewrote
it for the TI-85, and later the TI-86, but all these incarnations of the
program were purely numerical and were intended to show how changing the
values of the variables a, x and n affected the convergence or divergence of
the expansion.

Upon transferring and adapting the program to the TI-89 I was very pleased to
see that, as well as accomplishing this task, it will produce an algebraic
expansion when deprived of numerical values for "a" and "x"!  i.e. when
prompted for values for "a" and "x", you may enter any combination of numbers
and letters, such as "3a", or "-4p", or "2x/5" for "a" and/or "x", which the
program will then expand correctly according to the binomial theorem.  I
therefore feel that this program enhances the abilities of the TI-89 in that
it will now expand an algebraic (a + x)^n for non-integer values of n.:-)


Installation
============

Send the program to your TI-89 and store it in any convenient folder.  The
first time it runs it will create a folder called BINDATA in which it will
temporarily store values, so it would be wise to check that such a folder
doesn't already exist on your machine.


Running the program
===================

Execute  binomial()  from the command line, which brings up an identifying
screen in which you are asked to press Enter to continue.

Doing so presents you with five choices which you may select by either moving
the highlight with the up/down cursor keys, or by typing the corresponding
number.

The display format is changed to "Auto" and "Float 6" by the program, but
whatever mode your calculator was in beforehand is restored when the program
terminates.  If "Float 6" is not suitable for your particular purposes you
may edit the program easily, although you should not run it in "Fix anything"
as this disrupts the indirection used for saving the terms and totals.


1:  Compute (a+x)^n
===================

This takes you to the main entry screen where you input values for a, x, n
and the number of terms of the expansion that you require.  You may input
numerical values, or alphabetic variables such as "2a", or "-x/3" for "a"
and/or "x", while the value for the exponent "n" may be any real number,
either decimal, fraction or integer, positive or negative.  The value for the
number of terms must, of course, be a positive integer.

After entering the values above the program gives you Term 1, then Term 2 and
the running total as far as Term 2, then Term 3 and the accumulated running
total as far as Term 3, and so on until all the requested terms have been
calculated and displayed.

The program then returns to the list of five choices.


2:  Exit
========

Selecting this option exits the program cleanly leaving all the terms and
totals available within the BINDATA folder for further use.  They may be
brought to the command line for inspection and/or evaluation with the |
"with" operator.

After you have finished examining (and admiring) the terms and totals you may
like to re-run the program and choose option 5: Tidy up, which will delete
all the variables in the BINDATA folder that have been created by this
program.


3:  View Terms
==============

Selecting this option scrolls the values of the individual terms five at a
time, requiring Enter to be keyed to proceed to the next group of five terms. 
This option is only really of use for a numerical expansion.  Try it with an
algebraic expansion and you will see why...!


4:  View Totals
===============

Selecting this option scrolls the running totals after 1, then 2, then 3
terms, etc., in screenfulls of five at a time.  Again, this option is only
really of use with a numerical expansion.


5:  Tidy up
===========

Selecting this option, either after computing the series, viewing terms or
totals, or even after exiting the program to examine the terms or totals and
re-running it again, will delete all the variables in the BINDATA folder that
have been created by this program.

In order to delete all the terms and totals properly a variable "nt" is
created in the BINDATA folder, so don't delete this; if you do the Tidy up
routine will not delete all the terms and totals properly.  This isn't a
disaster as you can delete them manually, and the "nt" variable will be
recreated the next time the program runs.




I hope you find this program useful.  Please do not hesitate to contact me by
email---especially if you find any bugs!

Enjoy!

Richard Smith

richard@risctex.demon.co.uk


