Systems related to Number Theory

KASH

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 abbreviation of

Computational
Algebraic
Number
Theory

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 architectures:

• 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:

• 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.

• 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 shell.),
• 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 available. To install KASH obtain the file suitable for your archcitecture from the ftp server ftp.math.tu-berlin.de in the directory /pub/algebra/Kant/Kash/Binaries

A documentation of KASH can be found at /pub/algebra/Kant/Kash/Doc and 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 language etc.). 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

• 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