Comparative CAS Reviews and Philosophy
1801 Quincy, SE
Albuquerque, New Mexico
Tel: 1-(505) 243-2800
Right now, a large number of computer algebra systems, both general purpose and
special purpose, are available. Some of these systems are commercial while
many others are partially or fully in the public domain. As more and more
systems become available, it becomes important to have some idea about the
strengths and weaknesses provided by each system, both mathematically and
inherent in the system's philosophy of use. The point of view of the user will
vary depending on the application, and so a statistician may have different
considerations than say a physicist which may in turn be different from that of
a mathematician or an educator. Each type of user has certain goals and wants
to know how a particular system will aid in his or her quest to achieve them.
- User Friendly Reviews of Computer Algebra Systems
Nicolas Robidoux (email@example.com)
So far, comparative reviews of computer algebra systems have, for the most
part, consisted of lists of implemented packages with a sampling of related
bugs. Organizing this information into a coherent whole must begin with an
explicit model of the users and what they do with and expect from the
systems. "Scores" must be accompanied by a description of the attributes
of the yardstick user: her skill level, her model and use of the computer
algebra system (oracle, table book, compute engine, high level programming
language, teaching aid, driver for numerical or graphics libraries...), her
willingness to hand hold and check answers (for some users, a wrong answer
which can easily be found to be wrong may be quite acceptable, unlike one
which is quite difficult to "back plug"), the size of typical problems...
Some "yardstick users" and their attributes will be presented.
- A Review of Symbolic Solvers
Laurent Bernardin (firstname.lastname@example.org)
Solving equations and systems of equations symbolically is a key feature of
every computer algebra system. This review examines the capabilities of the
six best known general purpose systems to date in the area of general
algebraic and transcendental equation solving. Areas explicitly not
covered by this review are differential equations and numeric or polynomial
system solving as special purpose systems exist for these kinds of
- Factorized Gröbner Bases and Polynomial Systems
Hans-Gert Gräbe (email@example.com)
Solving complicated polynomial systems with special purpose CASs (as
proposed in L. Bernardin's abstract) is often only of restricted benefit
due to the complicated output structure. Especially for systems with
infinitely many solutions, algorithms near to a prime decompositions must
be involved instead to obtain more insight into the structure of the set of
solutions. A central tool for such a purpose is the Gröbner algorithm
with factorization. No special purpose systems offer both facilities (yet)
on a satisfactory level. In my report, I will present both a comparison of
the Gröbner factorizer capabilities of the big general purpose CASs
(as far as these capabilities are accessible) and a survey about the output
quality of this algorithm compared to a full prime decomposition.
- A review of the ODE solvers of Axiom, Derive, Macsyma, Maple,
Mathematica, MuPAD and Reduce
Frank Postel (firstname.lastname@example.org) and Paul Zimmermann
Using a wide set of more than 50 different kinds of ordinary differential
equations and systems, we try to give an idea of the capabilities of Axiom,
Derive, Macsyma, Maple, Mathematica, MuPAD and Reduce in solving
differential equations. In our conclusion we firstly want to give the user
an answer to the question "What system should I use?" and secondly to point
out to developers of computer algebra systems the advantages and/or
drawbacks of their ODE solver, to help to improve it.
- Multiple-valued Complex Functions and Computer Algebra
Helmer Aslaksen (email@example.com)
I will discuss some elementary, but not very well-known facts about
multiple-valued complex functions, and see how computer algebra systems
deal with these problems.
- Computer Algebra Systems: Pitfalls, Pratfalls and also Elegance
Michael Wester (firstname.lastname@example.org)
General purpose computer algebra systems have many wonderful abilities.
But how easy are they really to use in practice? Can the answers they
produce be trusted? In this talk, I will give some examples of both the
good and the bad (selected from a collection of now more than 400 problems)
with an occasional philosophical digression.
- Computer Algebra and Problem Solving Environments
Stanly Steinberg (email@example.com)
Problem Solving Environments provide a promising new approach for solving
modeling problems that occur in engineering and science. Such environments
will provide easy access to integrated symbolic and numeric computing and
this will greatly enhance the tools available to modelers. However, this
will place new demands on computer algebra systems.
- Commercial vs Free Computer Algebra Systems
Paul Zimmermann (Paul.Zimmermann@loria.fr)
Today, the two or three leading computer algebra systems are commercial.
However, in some other fields, some leading products are free systems, for
example gcc for compilers, gnu-emacs for editors, TeX for (scientific) text
processing. In this talk, we will try to figure out the reasons (if any)
why the situation is different for computer algebra systems, and try to
guess what the future market of symbolic computation will be.
- Discussion of Issues Raised and Not Raised