
                             KASH 3


The release 3 of KASH, the KAnt V4 SHell is available now.  KANT is a
software package for mathematicians interested in algebraic number theory.
For those KANT is a tool for sophisticated computations in number fields,
in global function fields, and in local fields.

KANT V4 is developed by a research group at the Technische Universitaet
Berlin.  Its name is the abbreviation of

     Computational
     Algebraic
     Number
     Theory

with a slight hint to its german origin. 

Many parts of KASH have been redesigned since the release of KASH 2.5.
We must apologize to our old KASH users that code written for KASH 2.x
will not run under KASH3 without modifications.  There will continue to be 
bugfixes and at least one more version of KASH 2.x which will be released in
late 2005 or early 2006.

The main new features of KASH3 are

o  modular type system,
o  integrated help system with inline help and a reference manual in html
   format,
o  overloading of functions,
o  local fields (unramified extensions, ramified extensions, polynomial
   factorization),
o  access to the QaoS databases of numberfields and transitive groups,
o  new generic function names.

KASH is freely available from:

  http://www.math.tu-berlin.de/~kant/download.html


/******* INSTALLATION ** INSTALLATION ** INSTALLATION ************/

To make your life easier we provide binaries of the shell. At the
moment we are supporting the following architectures:

o  Linux on x86
o  Mac OS X on PPC 
o  MS Windows 2000/XP on x86

For the above architectures you have to download the corresponding file:

  KASH3-Linux-YYYY-MM-DD.tar.bz2
  KASH3-Darwin-YYYY-MM-DD.tar.bz2
  KASH3-Windows-YYYY-MM-DD.zip

Under Linux and OS X you can unpack it with

  tar xvjf KASH3-Linux-YYYY-MM-DD.tar.bz2 
or
  tar xvjf KASH3-Darwin-YYYY-MM-DD.tar.bz2 

Now change to the new directory KASH3-Linux-YYYY-MM-DD 
(respectively KASH3-Darwin-YYYY-MM-DD) and start KASH3 with

./kash3

Under Windows Winzip can be used to unpack the zip archive.  Open the 
directory KASH3-Windows-YYYY-MM-DD and start kash by double clicking 
kash3.exe.


/***** DOCUMENTATION *********************************************/

An introduction to KASH3 as well as the reference manual can be accessed 
through the inline help (type '?<return>' at the kash% prompt) or viewed 
using a web browser (open index.html in the html directory).  The pdf 
directory contains the introduction to KASH3 and a manual to the programming 
language of KASH3.


/**** QaoS *******************************************************/

If you want to use the QaoS databses of number fields and transitive groups 
you must have cURL installed.  you can get cURL at:

http://curl.haxx.se/


/**** KASH 3 ** KASH 3 ** KASH 3 ** KASH 3 ** KASH 3 ** KASH 3 ***/

The main features of the current release are the following:

Computations in number fields

o  arithmetic of algebraic numbers,
o  computation of maximal orders in number fields,
o  modular computation of resultants,
o  unconditional and conditional (GRH) computation of class groups
   of number fields,
o  unconditional and conditional (GRH) computation of fundamental
   units in arbitrary orders,
o  S-unit computation,
o  computation of all subfields of a number field,
o  determination of Galois groups of number fields up to degree 15,
o  ray class groups, 
o  automorphisms of normal and abelian fields,


Ideals in number fields

o  arithmetic of fractional ideals in number fields,
o  computation of prime ideal decompositions of fractional ideals
   in number fields,
o  (ray) class group representation of an ideal (discrete 
   logarithm for ray class groups),
o  computation of the multiplicative group of residue rings of maximal 
   orders modulo ideals and infinite primes, 
o  Chinese remainder for ideals and infinite places,


Relative extensions of number fields

o  computation of maximal orders (relative Round 2),
o  arithmetic of algebraic numbers,
o  signature of polynomials,
o  normal forms of modules in relative extensions,
o  arithmetic of relative ideals,
o  computation of a 2-element-representation for relative ideals,
o  Kummer extensions of prime degree, relative field discriminant and
   integral basis,

Computations in class field theory

o  Hilbert and ray class fields of imaginary quadratic fields by
   complex multiplication,
o  Hilbert class fields of totally real number fields via the 
   computation of Stark units by Stark's conjecture,
o  computation of discriminants and conductors of ray class fields,
o  computation of ray class fields, subgroups of ray class
   groups supported via Kummer theory
o  Artin map and automorphisms of ray class fields,

Galois groups

o  computation of Galois groups of polynomials over Q
   up to degree 21 and their representation as permutation
   groups on the roots,
o  symbolic computation of Galois groups of polynomials over Q,
   number fields and Q(x) up to degree 7

Lattices

o  lattices and enumeration of lattice points,
o  lattices and lattice reduction for lattices over number fields,

Diophantine equations

o  Thue equation solver,
o  unit equations and exceptional units,
o  index form equations,
o  integral points on Mordell curves,
o  norm equation solver for absolute and relative extensions,

Algebraic function fields over finite fields, Q or number fields

o  absolute and relative extensions of algebraic function fields,
o  arithmetic of algebraic functions,
o  genus computation,
o  places, divisors and Riemann-Roch spaces,
o  dimension of exact constant field,
o  computation of maximal orders in function fields,
o  arithmetic of fractional ideals of orders of function fields,
o  computation of prime ideal decompositions of fractional ideals,
o  basis reduction for orders, fundamental unit computation in global
   function fields,
o  determination of places of degree one in global function fields,
o  S-units for global function fields
o  differentials, differential spaces, differentiations
o  Cartier operator for global function fields
o  Hasse-Witt invariant of a global function field
o  L-polynomial computation for global function fields
o  gap numbers, Weierstrass places

Local rings and fields 

o  unramified extensions of local fields
o  ramified extension of local fields
o  factorization of polynomials over local fields,

Qaos Database Support

o  access functions to the Qaos databases of number fields and 
   transitive groups  


/****** SUPPORT ** SUPPORT ** SUPPORT ** SUPPORT ** SUPPORT ** SUPPORT *******/

Please mail all your questions, suggestions, comments and bug reports
concerning KASH to

   kant@math.tu-berlin.de


/******** ACKNOWLEDGMENTS ** ACKNOWLEDGMENTS ** ACKNOWLEDGMENTS *************/

We would like to thank

o   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 and Allan Steel for their help.
    It would have been impossible to develop this software without
    their help.

o   Prof. Dr. J. Neub\"user 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. Sch\"onert, who mainly created
    GAP, for his kind support and help.

o   Prof. Dr. J. Neub\"user 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. Sch\"onert, who mainly created
    GAP, for his kind support and help.

o   Dr. A. Weber at Cornell University, USA, for his work on the database.

o   Dr. M. Klebel at Augsburg for his work on class fields
    of imaginary quadratic number fields.

o   Dr. A. Hulpke at Colorado State for his support for the Galois package.

