Systems related to Number Theory
version KANT V4, 12/94
AT the end of 1994 the first release of KASH, the KAnt V4 SHell, takes place.
KANT V4 has been developed at the Technische Universität Berlin
under the project leadership of Prof. Dr. M. Pohst. Its name is the
with a slight hint of its german origin. As the name indicates, KANT
is a software package for mathematicians interested in Algebraic Number
Theory. For those KANT is a tool for sophisticated computations in number
For the first time you are now able to use the powerful KANT V4 functions
within a shell and you don't need to know anything at all about
programming in C. To make your life easier we provide binaries of the
shell. At the moment we are supporting the following
If you are using a machine, which is not one of the above, please
send the developers an e-mail (email@example.com)
- HP 7000 : UP-UX 9.01
- IBM RS6000 : AIX 3.2.5
- SUN SPARC : SunOS 4.1.3
- PC (80486) : Linux 1.1.59 (kernel) --> January 95
The main features of the current release are:
Since the developers just started to implement this shell, a large number of
functions in the KANT V4 library is not available in the shell at the
moment. Therefore new releases of KASH will be available from time to time.
The next release is scheduled for February. This release will include
the following features:
- Computation of maximal orders in number fields,
- unconditional computation of class groups of number fields
(no GRH is used),
- unconditional computation of fundamental units in arbitrary orders
(no GRH is used),
- computation of prime ideal decompositions of integral ideals
in number fields,
- arithmetic of ideals in number fields,
- arithmetic in relative extensions of number fields,
- normal forms of modules in relative extensions,
- norm equation solver for absolute and relative extensions.
At the moment only a few functions (about 70) have been implemented
in the shell, but the developers will increase their number steadily,
so please mail
- PVM support for many parts of KANT (This is already part of the library,
but we didn't find the time to place the necessary functions in the
- Thue equation solver,
- integral basis in relative extensions,
- computation of all subfields of a number field,
- more functions from the KANT V4 library.
- all your suggestions and comments
- bug reports
KANT and KASH are protected by copyright restrictions, but are free
To install KASH obtain the file suitable for your archcitecture from
the ftp server
in the directory
A documentation of KASH can be found at
documentation of the KANT V4 library (not complete) can be found at
/pub/algebra/Kant/V4/Doc. The documentation is a (gzip-fomatted) PostScript file.
The shell combines the KANT V4 library functions with the comfortable
user interface of GAP's release 3.3 (GAP is a software package
developped by Prof. Neubüser at the RWTH Aachen, F.R.G.).
Because we took GAP, stripped out or replaced most of its functions
and then added KANT V4 functions, we refer to the GAP manual for the
general usage of the shell (i.e. syntax of input and programming
But you should be aware of the fact that most of the special
GAP functions (i.e. functions for groups etc.) won't work anymore!
The developers would like to thank
See also: KANT.
- Prof. J. Cannon at the University of Sydney, for the opportunity
of using the MAGMA C - kernel for the development of KANT V4,
the algorithmic part of KASH.
special thanks to Wieb Bosma, Allan Steele and Steve Collins for
their help. It would have been impossible to develop this software
without their help.
- Prof. Dr. J. Neubüser at the RWTH Aachen, F.R.G.,
for his permission to use and modify large parts of the GAP source code.
Especially, we would like to thank M. Schönert, who mainly created
GAP, for his kind support and help.
Special Purpose Systems
Last updated: November 15, 1994