Education Sampler 1992 [NeXTSTEP]/Education_1992_Sampler.iso/Mathematics/form1.1/README

Text File | 1992-08-27 | 6KB | 103 lines

A:  FORM was written by Jos Vermaseren ([e-mail])
B:  Astronomy, Chemistry, Engineering, Math, Physics
C:  FORM is a symbolic manipulation program. It is almost, but not
quite, entirely unlike Mathematica. In a sense it is complimentary
to Mathematica or Maple. Its main properties are:

1:  It runs in batch (i.e. not interactively). You prepare your
program like you would prepare a C, FORTRAN, PASCAL, etc. program,
using your favorite text editor.
2:  It is optimized for very big expressions and speed. There are
many programs nowadays that will let you do 'small' things, but
many people eventually encounter the limitations of these programs.
(Definition of big: > 10^5 terms).
3:  Of course FORM is not the miracle program that can do everything
all the others can do and much more. The tradeoff is that it is just
a symbolic manipulation program. You have to spoonfeed much of the
mathematical knowledge, and it doesn't do windows (no pictures). But
what it does, it does fast. Very fast.
4:  There is a very flexible substitution mechanism with some high
level wildcarding.
5:  It knows several types of objects: regular symbols, vectors,
indices, functions and some more. It knows some of the proterties of
these objects, allowing fast processing. It does not have to guess.
(The language is strong typing: you have to declare everything).
6:  There are many facilities to build in knowledge.
(For very big problems general knowledge is rarely sufficient anyway.
Such problems can usually be solved only by considering the particular
special cases.)
7:  Version 1 is FREE. The manual comes as a .dvi file with it.
(Version 2 is not free. Information about it can be obtained by sending
an e-mail to [e-mail]  CAN stands for Computer Algebra Nederland
which runs an expertise center for computer algebra and serves also
as a distributer for many algebra programs. So you may want to ask about
more general info if you have a job to do)
8:  Originally FORM was made for massive formula manipulation in physics,
but it turns out that many of its features are useful in mathematics,
chemistry and engineering. For example its dealing with non commuting
objects is far easier and more intuitive that with the regular algebra
programs.
9:  The size of the free diskspace determines the size of the expressions
you can manipulate. There is very little slowdown due to disk accesses,
because this is not done with the use of virtual memory. The program
does its own memory management, knowing what it will need and when it
will need it.
10: FORM runs very well on the NeXT. The NeXT is the computer on which its
future versions are being developed. (It runs rather well on other UNIX
systems too of course. There are sometimes peculiar problems with VMS,
MS-DOS, IBM 3090 systems and their ilk, although most have been solved)


Strategic advise:
It happens frequently that people start setting up a problem with one
of the computer algebra programs. Then they enlarge the scope of the
program and run into the limitations of the algebra program. At that
point they will waste much time, because they have made a big investment
in the program, so they do not want to switch to another program.
If your problem has a chance of becoming big by the standards of your
algebra program, you should have a look at whether you can (admittely
often at the cost of somewhat more programming time) do the problem
with FORM. In the end you will be able to deal with far bigger cases.

D:  I use FORM for computations in perturbations expansions in field
theory. This involves dealing with vectors, vector products, tensors,
Dirac algebra. It may involve some horrible integrals that have to be
broken down step by step till there are only a few integrals left that
can be done by hand. (None of these integrals are in the tables or in
any other algebra program). Other people here use it for similar
computations. Together with a mathematician we used it to attack an
enormous system of nonlinear equations (all arithmetic modulus 1831)
showing how they could be solved. It has also been used for solving
some problems involving non commuting variables.
At other institutes it is used for a variety of computations. Some are
similar to the above, and some I don't even know about.
E:  The enclosed version of FORM was made with NeXTstep 2.1, but this
should have no effect.
F:  The best is to put the file form in /local/bin. This way it can
be invoked by typing
'form [options] filename'
in the console or a terminal window.
Reading the manual can be done with the TeX previewer. Alternatively one
may want to print the manual. Unfortunately the pages are in A5 format
which can be rather wasteful. Hence there is a conversion program to
read the postscript file and shuffle the pages a little bit.
First make the postscript file with the command
'dvips manual -t landscape -o'
Then translate the conversion program with
'cc -o 2A5onA4 -O 2A5onA4.c'
and finally run the conversion with
'2A5onA4 manual.ps manual1.ps'
After that you can print the file with
'lpr manual1.ps'
If you have a different papersize you may want to change some of the numbers
in the c sources of the conversion program. I do not have American paper
here, hence it is rather hard for me to experiment with it. The file
folder.dvi is meant for such experiments.
The file talk.tex contains the written version of a talk I have given
about FORM some time ago. It gives a little bit of an idea of what FORM
can do.
G:  The license for using FORM 1.1 is free. You are not allowed to
disassemble it or modify it in any way. You are allowed to pass it on
to others provided you let them know about these conditions and they
agree to these conditions.