
Ron Avitzur investigated various techniques towards the efficient
generation and visualization of implicitly defined surfaces. The Graphing
Calculator was altered to serve as a testbed for various
experiments. Techniques which were considered and partially
implemented include intervalarithmetic and Chains of Recurrences
based computations of implicit objects, as well as raytracing methods
for the display and animation of precomputed objects
(see Fig.2.1). A short
bibliography about relevant literature was collected.
Figure 2.1: Two precomputed implicit surfaces
displayed by the Graphing Calculator

Ron Avitzur, Olaf Bachmann, and Norbert Kajler investigated the concept
of ``intelligent plotting''. Techniques were explored which take
advantage of the numerical and symbolic capabilities available from
some mathematical engine in order to transparently improve correctness
and completeness of 2D and 3D plotting, increase efficiency, and
achieve better usability (see Fig.2.2).
A paper was written on the subject and
submitted to ISSAC'95.
A preprint is available in the RIACA technical report series.

Olaf Bachmann extended the theoretical concepts of the Chains of
Recurrences method in order to expedite the evaluation of
trigonometric functions and functions of two variables over linearly
sampled points. A general Maxima/Common Lisp implementation which
works over any valid Maxima domains, but is especially effective for
floating point numbers, was written and tested.
: Automatic labeling of extrema,
zeros, and intersections

Olaf Bachmann developed an interface between Maxima and IZIC
which uses the ``Chains of Recurrences'' method
to compute curves and surfaces (see Fig.2.3).
This method results in dramatic speedups with respect to traditional
evaluation of a function within a rectangular grid.
A technical report is available in the RIACA report series.
: two surfaces computed with
Maple and Maxima and displayed using IZIC

Michael Mc Gettrick and Marcel Roelofs worked on a graphical interface for
Dynkin diagrams (which are used in the classification of semisimple
Lie algebras) and interaction mechanism for representations of
semisimple Lie algebras through these diagrams. This resulted in a
prototype implementation.

Norbert Kajler improved the IZIC visualization package
(see Fig.2.3)
in collaboration
with Robert Fournier and Bernard Mourrain (both from INRIA SophiaAntipolis).
Major improvements were achieved concerning memory management and
interfacing with the Maple system.
Several new features, like
automatic animation of objects, bounding boxes, axis, and various
demonstrations were added and the documentation improved.
The design and implementation of IZIC is described in an article to appear
in the Journal of Symbolic Computation.
A preprint is available in the RIACA report series.
A new version (IZIC 1.0) was made available via anonymous FTP.
An introductory paper for IZIC users was published in
the CAN Newsletter.

Norbert Kajler pursued his collaboration with Simon Gray and Paul S. Wang
(from Kent State University)
in the framework of the MULTI project.
The goal of the MULTI project is the development of a distributed
architecture allowing a neat integration
of numeric and symbolic computation software, together
with visualization packages, and related graphical frontends.
Work done in 1994 includes major improvements in the design of the MULTI
protocol (MP) and the implementation of the MPC and MPLisp libraries.
Norbert Kajler visited Kent State University for 10 days in April 1994.

Norbert Kajler and Neil Soiffer completed a survey on user interfaces
for computer algebra. The survey covers the period 196393 and
includes over 130 references.
It will be published in 1995 in the Journal of Symbolic Computation.
A preprint is available in the RIACA report series.

Jari Multisilta worked on the design and development of hypertext and
multimedia authoring and reading systems for Mathematics,
in collaboration with the ACELA project.
Experiments were conducted using Mosaic, MetaCard, and MathLink.

Nadine Rouillon worked with Marc van Leeuwen (from CWI) on the
visualization of combinatorial objects.
Experiments where conducted using the CalIco package developed
by Nadine Rouillon and others in University of Bordeaux I, France,
and using experimental packages developed at CWI for the
visualization of certain kinds of bijections between skew diagrams
that are known as pictures (see Fig.2.4).
: Bijections between skew diagrams

Eugene Zima investigated the implementation of the ``Chains of
Recurrences'' method within the Maple and Mathematica computer algebra
systems.
Eugene Zima collaborated also with Hans van Hulzen
(from University of Twente)
on mixed numericsymbolic approaches to problem solving using
Chains of Recurrences.