From fieker@math.tu-berlin.de Wed Jun 18 20:46:01 1997 Date: Wed, 18 Jun 1997 16:06:58 -0400 From: Claus Fieker To: NMBRTHRY@LISTSERV.NODAK.EDU Subject: Kash 1.8 KASH 1.8 (version KANT V4, 6/97) This is release 1.8 of KASH, the KAnt V4 SHell. KANT V4 is developed by a research group at the Technische Universit\"at Berlin under the project leadership of Prof. Dr. M.E. Pohst. Its name is the abbreviation of Computational Algebraic Number Theory 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 fields. With KASH you are able to use the powerful KANT V4 functions within a shell and you do not need to know anything at all about programming in C. KASH is freely available by ftp from ftp.math.tu-berlin.de where it sits in the subdirectory /pub/algebra/Kant/Kash or ftp://ftp.math.tu-berlin.de/pub/algebra/Kant/Kash /***** NEW FEATURES ** NEW FEATURES ** NEW FEATURES ** NEW FEATURES **********/ o computation of the multiplicative group of residue rings of maximal orders modulo infinite places o computation of discriminants of ray class fields o Chinese remaindering for infinite places o direct computation of the maximal order of an relative extension via the relative Round 2 algorithm o absolute Round 4 algorithm o lattices and lattice reduction for lattices over number fields o dramatically improved subfield computation o computation of automorphisms of absolute-normal and absolute-abelian extensions o computation of Galois groups of integral polynomials up to degree 12 o genus computation for function fields over finite fields o ideal arithmetic including factorization for function fields over finite fields o new interface to the Postgres database for algebraic number fields o index form equations o integral points on Mordell-curves /******* INSTALLATION ** INSTALLATION ** INSTALLATION ** INSTALLATION ********/ To make your life easier we provide binaries of the shell. At the moment we are supporting the following architectures: o HP 7000 : HP-UX 9.01 o IBM RS6000 : AIX 3.2.5 o SUN SPARC : SunOS 4.1.3 o SUN SOLARIS2: SunOS 5.5 o SGI MIPS : Irix 6.2 o PC (80486) : Linux 2.0.0 (elf) For all of the above versions you'll have to get (at least) TWO files, Kash_1.8.***.tar.gz (for the binary) and Kash_1.8.common.tar.gz (containing the library, documentation, ...) Kash_1.8.galois.tar.gz (only if you're interested in large Galois-groups) o PC (80486) : IBM OS/2 3.0 Warp (release in the next 2 days) o PC (80486) : MS DOS 5.0 (release in the next 2 days) o PC (80486) : MS Windows 3.1 (release in the next 2 days) o PC (80486) : MS Windows 95 (release in the next 2 days) All files needed for the DOS/ OS/2/ Windos version are located in a subdirectory Kash_1.8.OS2_DOS_Windows Here you'll find installation guides for this version. /**** KASH 1.8 ** KASH 1.8 ** KASH 1.8 ** KASH 1.8 ** KASH 1.8 ** KASH 1.8 ***/ The main features of the current release are: - computations in number fields o arithmetic of algebraic numbers, o computation of maximal orders in number fields, 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 norm equation solver, o computation of all subfields of a number field, o ray class groups and residue rings computation, o ray class fields of imaginary quadratic fields, o automorphisms of normal and abelian extensions, o computation of Galois groups of integral polynomials up to degree 12, - 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, - relative extensions of number fields o computation of maximal orders (relative Round 2), o arithmetic of algebraic numbers, o normal forms of modules in relative extensions, o arithmetic of relative ideals, o norm equation solver for relative extensions, o Kummer extensions of prime degree, relative field discriminant and integral basis, - class field theory o Hilbert and ray class fields of imaginary quadratic fields, o Hilbert class fields of algebraic number fields o computation of discriminants of ray class fields - lattices o lattices and enumeration of lattice points, o lattices and lattice reduction for lattices over number fields, - specials o a Thue equation solver, o factorization of polynomials over number fields, o basic linear algebra over number fields, - function fields over finite fields o arithmetic of algebraic functions, o computation of maximal orders in function fields, o basis reduction, fundamental unit computation, o genus computation, o arithmetic of fractional ideals of orders of function fields, o computation of prime ideal decompositions of fractional ideals, - environment o PVM access in the programming language of KASH, o PVM support for many parts of KANT, o Help system (TeX based online help), o support of internal structures for programmers, o examples for the programming language, o database for number theoretic data, o 600 pages of documentation. /****** 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 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.