Preliminary Report on OpenMath Workshop 1
Thanks to Stefan Vorkoetter for supplying these notes.
The workshop was held on 17-18 December 1993 at ETH Zurich.
A list of participants is available.
A workshop to formulate a character based standard for the exchange
of mathematical formulas and other mathematical objects between
Notes on the presentations
For any presentations accompanied by paper(s), we omit detail here
and refer the reader to the paper(s).
Gaston Gonnet gave an introduction to OpenMath, and outlined some of
the requirements that such a protocol must have in order to function
in arbitrary environments. Some of these requirements are:
- text (character) based
- can be sent by electronic mail
- a limit on line length
Chris Howlett outlined Waterloo Maple Software's plans for OpenMath:
- committed to implementing a client/server math architecture
for Maple during 1994
- need a standard such as OpenMath to ensure utility and
acceptance; input from and agreement of a large group is essential
Stefan Vorkoetter described the current OpenMath proposal, as put
forward by Waterloo Maple Software. During the ensuing discussion,
some weaknesses and Maple-specific aspects were discovered:
- choice of data structures too Maple-biased
- how to decide which operators/functions to include
Heikki Apiola described ESC, an Environment for Scientific
Computation, which combines various mathematical tools.
Wolfgang Weck described his concept of a math protocol, based on
modular decomposition and type extension:
"A Module Library for Computer Algebra", Dominik Gruntz, Wolfgang Weck (submitted to ISSAC 94).
Marc Gaetano described the ASAP protocol:
"Designing a protocol for exchanging mathematical objects", S. Dalmas, M. Gaetano, A. Sausse
"The ASAP Protocol: a description", S. Dalmas, M. Gaetano, A. Sausse
"A C library for ASAP", S. Dalmas, A. Sausse
Carlo Traverso described POSSO:
"The POSSO External Data Representation", J. Abbott, C. Traverso
Norbert Kajler spoke on building a computer algebra environment. He
described the SAFIR project and CAS/PI:
"Building a Computer Algebra Environment by Composition of Collaborative Tools", Norbert Kajler
Mika Seppala gave a brief historical review of EuroMath.
- general agreement (expression trees in LISP-like notation).
- modifying the proposed standard seemed to be acceptable.
- it was agreed that the sequences defined by SGML standard
would be adopted for special characters.
- there is still the issue of which escape character to use.
- it was agreed that the basic proposal should support all the
functions in Abramowitz and Stegun, Chapters 1 to 3.
- the standard should allow for the definition of packages of
functions as extensions.
- basic attributes do not belong in the standard, but rather in
packages (eg. a package of typesetting attributes).
the proposal from WMS had too many Maple-specific types. The
following base types were suggested:
- numbers (integer, floating point (including complex))
- Sub-, super-, and other-scripts
- there was intense discussion about what method should be used
to represent these.
- eventually, it was generally agreed that this was beyond the
scope of the standard, because these are typographical, and
not mathematical, attributes.
- after some discussion, it became clear that it would be both
impossible and undesirable to include all possible functions
in the base proposal.
- there would always be functions that someone considers
important that were left out.
- four extensions were proposed: Polynomial Manipulation, Group Theory, Programming, and Tensors.
- Control Layer: discussion was deferred to future meetings.
Assignment of responsibilities
Waterloo Maple Software: will take care of the following list:
- prepare the OpenMath mailing list (email@example.com).
- prepare this report.
- update the OpenMath proposal based on the discussions at the
workshop. Some things that are to be incorporated are:
- simplified structure level operators.
- a method to determine packages understood.
- in-line OpenMath recognition via <openmath>..<\openmath>.
- adoption of SGML character set extensions.
- an OpenMath to SGML mapping.
- a Maple extension to the standard.
- extensions for number bases.
- clarification of labels and references.
- simplification of concept of symbols.
- complex numbers.
Carlo Traverso: design of an extension for polynomial manipulation.
Someone at CWI: design of an extension for group theory.
Michael Monagan, Marc Gaetano: design of an extension for programming.
Someone called MB: design of an extension for tensors.
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