This version of Bracmat is the oldest C-version I have. 
It is from 1988 and written for the Acorn Archimedes. However, it can also
be compiled using Turbo C 2.01 under DOS, which I have just done. 
This source code has an error if compiled under DOS: there is one closing 
accolade too many near line 1500. I had to remove this before I could compile
the source code. The source file REKEN in the Archimedes folder is almost a 
day older and does not have the erroneous accolade. Apparently I used a day 
introducing hacks to make the code compile with a 16-bit compiler. 
(The Archimedes, which was the first commercially available machine with an 
ARM processor - Acorn Risc Machine! - was of course 32-bit. Well, almost.)
While converting a switch that switched on 32-bit integers to a lengthy 
if ... else if ... else if ... construction, I introduced the erroneous
accolade.

In 1987 I bought an Archimedes computer with two 3.5" disk drives and no hard
disk. I used a DOS-emulator to run the Turbo C compiler.

Today, in a DOS-box in Windows XP SP3 I issued the following command line to 
reconstruct the executable file

tcc -Iinclude -Llib -ml reken.c


The program is called "REKEN", the Dutch word for "compute". The language used
in comments and during execution of the program is Dutch. Shortly after this 
version, the program was renamed "Bacmat" and then "Bracmat".

The three files DET, PRIME and NNFAC are bracmat program files.
To run DET do the following:

start the program REKEN by just typing REKEN at the command prompt. Then type:
    get$DET
    det$mat

The answer is the string

    r^#4*cos$theta^2*sin$theta^4*-1+r^#4*cos$theta^4*sin$theta^2*-1

which is the determinat of the matrix

    1,0  ,0                          ,0                      ,
    0,r^2,0                          ,0                      ,
    0,0  ,r^2*sin$theta^2*cos$theta^2,r*sin$theta^2*cos$theta,
    0,0  ,r*sin$theta^2*cos$theta    ,cos$theta^2*-1

If you want to try something else, do a taylor expansion. If you
want to know the expansion of 1/(1+x) to the 3rd power of x, type:

    taylor$((x+1)^-1,x,3)
    
The program answers with

    x*-1+x^#2+x^#3*-1+1
    
In current versions of Bracmat this function is called tay:

    tay$((x+1)^-1,x,3)
    
which gives

    1+-1*x+x^2+-1*x^3
   

Leave the REKEN program by typing a period.

The other two programs: PRIME and NNFAC don't work. Not under DOS, that is.

****

The predecessor of the REKEN program is a program written in Basic on a Amstrad
CPC464 computer. The Basic program has only mathematical operators and no
control structures at all. The idea was to let mathematical expressions flow
to a state of mathematical equilibrium, e.g. combining likes, differentiating
and sorting according to a canonical order. See ver-0.001


Bart Jongejan, 23 October 2009