Ivo Dntsch | Phone: (++44) 1232 - 368 976
School of Information and | Fax: (++44) 1232 - 366 803
Software Engineering | E-mail: I.Duentsch@ulst.ac.uk
University of Ulster | http://www.infj.ulst.ac.uk/~cccz23/
Newtownabbey, BT37 0QB
N. Ireland
March 16, 1995
Help: In the course of my move to Belfast I have lost the file
containing the registered users. Please, register again, if you
want to be informed of new versions.
___________________________________________________________
Changes in version 202b, Jan 13, 1992
1. Several bugs have been removed.
2. The array of the first thousand primes is now part
of the data area.
3. Some improvements have been made to the Pollard-Brent
algorithm:
a. It is now possible to set the starting value, the
shift, and the period when the gcd is taken.
b. The shift is increased when the algorithm is not
successful.
4. The corresponding changes have been made to NUMTYPE.PAS
NUMBERS.CFG, LFACTOR.OBJ, LPRIME.OBJ.
Caution: These routines will not work with 202A, neither
will these routines of 202A work with 202B.
5. Registration procedure has changed; the program now may
be freely used for educational purposes, under the
condition that the use is registered with the author
(Jun 13, 1992).
Fixed January 20, 1992:
The ESC key in the Arithmetic procedure of NUMBERS was not
returned correctly.
Fixed January 21, 1992:
The n-th residue test was not working correctly for an even
modulus. Changed routine to only test for quadratic residue.
Removed option to set the number of primes to use.
Updated the manual.
Changed January 23, 1992
Include compiled readme and manual.
Changes in version 202c (June 10, 1992)
Removed an inconvenience in ESC routine while factoring.
Removed an error in the input routine for long numbers.
Added support for trapping rings during the computation
of aliquot chains.
Streamlined computation of aliquot chains.
Fixed June 28, 1992: File I/O error in saving aliquot chains
Updated the manual files, July 02, 1992
Fixed July 06, 1992: A bug in the division routine which in rare
circumstances might cause the program to go into an infinite loop.
Changes in version 202d, March 16, 1995
Jan Pedersen discovered and fixed a bug in the factoring routine
which on very rare occasions caused the program to go into an
infinite loop.
Changed address information
Re-wrote manual in TeX
Changed version number
___________________________________________________________
Welcome to the NUMBERS calculator. It is designed to facilitate
the computation of number theoretic functions for positive
integers of up to 150 decimal digits on almost any PC.
My main objective in writing NUMBERS was to allow students in
a course in elementary number theory to do nontrivial examples
and pursue investigative projects, and it has served quite well
in this respect.
The NUMBERS package is not in the public domain. It may be
freely used for educational purposes and I recommend that
you register its use with me. Registered users will be notified
of new versions and will receive some support. To register, just
send me an e-mail message.
I should appreciate any reports on the suitability of the system
for the teaching and learning of number theory; bug reports are
also welcome, that is, if there are any bugs.
The documentation can be found in NUMBERS.DOC, a PostScript
version in NUMBERS.PS, and an on-line manual in manual.exe
(Thanks to DRC).
Disclaimer:
Extensive care has been taken to assure that the program runs
properly; however, I disclaim all reliability to the user for
any direct, indirect or consequential loss arising from the use
of, or inability to use, this program.
No warranty is given that the program will work under all
circumstances, or that it does what it claims it does.
The NUMBERS package contains the following files:
1. The Calculator
numbers.exe ;the calculator
numbers.hlp ;calculator help
2. Documentation
numbers.dvi ;documentation, dvi
numbers.ps ;documentation, postscript
read.me ;introduction
3. Turbo Pascal Interface
numtype.pas ;type definitions and link commands
primes.inc ;table of first 1000 primes
4. Object Files
cmpre.obj ;compare two long numbers
ladd.obj ;add, subtract
lcoprime.obj ;decide if n,m are coprime
ldiv.obj ;divide
lfactor.obj ;factor a number
lgcd.obj ;find greatest common divisor of n and m
llcm.obj ;find lowest common multiple of n and m
lmp.obj ;power to a modulus
lmult.obj ;multiply
lphi.obj ;Euler's Phi function
lprime.obj ;decide if n is prime,related procedures
numtostr.obj ;convert long number to string
lroot.obj ;integral square root
sigma.obj ;sum of divisors
strtonum.obj ;convert string to longnum