[123] in mathematical software users group
Maple math package
daemon@ATHENA.MIT.EDU (alexp@MIT.EDU)
Fri Dec 24 14:48:14 1993
From: alexp@MIT.EDU
To: msug@MIT.EDU
Date: Fri, 24 Dec 93 14:45:30 EST
From news.cs.brandeis.edu!noc.near.net!MathWorks.Com!europa.eng.gtefsd.com!howland.reston.ans.net!xlink.net!fauern!news.dfn.de!rubb.rz.ruhr-uni-bochum.de!rubb.rz.ruhr-uni-bochum.de!not-for-mail Thu Dec 23 23:33:16 EST 1993
Archive-Name: auto/sci.math.symbolic/Announcement-Maple-package-for-algebraic-geometry
A group of people at the Research Institute for Symbolic Computation
in Linz, Austria, wrote a package in Maple to deal with objects in
algebraic geometry - algebraic sets. You may retrieve it either by ftp
or via mail-server. Here is what you can expect from it:
*************************************************
* CASA *
* *
* COMPUTER ALGEBRA SOFTWARE *
* FOR *
* ALGEBRAIC GEOMETRY *
* *
*************************************************
version 2.1
Introduction
============
CASA is a package written in Maple for facilitating computations in
constructive algebraic geometry. The objects that CASA deals with are
algebraic sets in four different representations.
1. Implicit representation:
An algebraic set is the set of common zeros of a system of polynomial
equations. To give an algebraic set in implicit form means to give
finitely many polynomials.
2. Projected representation:
As a consequence of the primitive element theorem every irreducible
d-dimensional algebraic set in n-dimensional space is, after a suitable
linear transformation of coordinates, birationally projectable onto an
irreducible d-dimensional algebraic set in (d+1)-dimensional space, which
can be specified by a single polynomial in d+1 variables. This can be
generalized to unmixed-dimensional algebraic sets. An algebraic set in
projected form is given by a polynomial and a tuple of rational functions
(specifying the birational mapping).
3. Parametric representation:
Some irreducible algebraic sets can be parametrized by rational
functions. An algebraic set in parametric form is given by a tuple of
rational functions that parametrizes the algebraic set.
4. Representation by places:
All algebraic curves can be parametrized by a set of power series that
are convergent around a point of the curve. An algebraic set is given by
places if for each branch passing through a certain point on the
algebraic set a tuple of power series that parametrizes the algebraic set
around the point is specified.
CASA also works with the polynomial ideals corresponding to these
geometric objects.
The operations available in CASA include:
- ideal theoretic operations +, *, intersection, /
- creating algebraic sets in different representations,
- generating curves of fixed multiplicities at given points,
- intersection, union, and difference of algebraic sets,
- computing tangent cones and tangent spaces,
- computation of the dimension of an algebraic set,
- decomposition into irreducible components,
- transformations of algebraic sets to hypersurfaces,
- computation of the genus of a curve,
- rational parametrization of curves,
- implicitization of parametrically given algebraic sets,
- Puiseux series expansions,
- plotting both explicitly and implicitly given curves and surfaces.
How to get CASA?
================
Currently there are two ways how to obtain the package CASA.
1. By anonymous ftp
-------------------
Host: ftp.risc.uni-linz.ac.at
Directory: pub/CASA
Name: anonymous
Password: <your email address>
Get the file `CASA-README' first to see what might be interesting for you.
*******************
melmac!68> ftp ftp.risc.uni-linz.ac.at
Connected to melmac.risc.uni-linz.ac.at.
220 melmac FTP server (Version 4.33 Wed Jan 20 12:24:01 GMT 1993) ready.
Name (ftp.risc.uni-linz.ac.at:alggeo): anonymous
331 Guest login ok, send ident as password.
Password: alggeo@risc.uni-linz.ac.at
230 Guest login ok, access restrictions apply.
ftp> cd pub/CASA
250 CWD command successful.
ftp> ls
200 PORT command successful.
150 Opening data connection for /bin/ls (193.170.36.100,42807) (0 bytes).
.
..
CASA-2.0.tar.Z
CASA-2.1.tar.Z
CASA-README
CONTENTS
226 Transfer complete.
92 bytes received in 0.03 seconds (2.99 Kbyte/s)
ftp> get casa-2.1.tar.Z
*******************
2. By e-mail
------------
Send email to
listserv@risc.uni-linz.ac.at
with empty Subject: field and the body saying:
get casa CASA-README
Decide what is appropriate for you and then send the text (e.g.):
get casa CASA-2.1.tar.Z
You will obtain a series of email messages with parts of the tar'ed
package. Remove mail headers and concatenate all parts together to,
say, CASA-2.1.tar.Z. Uncompress and untar.
--
Computer Algebra Laboratory
Research Institute for Symbolic Computation
Johannes Kepler Iniversity
A-4040 Linz, Austria
E-mail: alggeo@risc.uni-linz.ac.at
--
--
Michal Mnuk
Research Institute for Symbolic Computation
A-4040 Linz, Austria
Phone: +7236 3231 75
Fax : +7236 3231 30
E-mail: mmnuk@risc.uni-linz.ac.at
