The workshop was held on 17-18 December 1993 at ETH Zurich. A list of participants is available.

**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
- extensible

**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.

**Syntax**- 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.

**Semantics**- 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.

**Attributes**- basic attributes do not belong in the standard, but rather in packages (eg. a package of typesetting attributes).

**Types**the proposal from WMS had too many Maple-specific types. The following base types were suggested:- numbers (integer, floating point (including complex))
- symbols
- sets
- arrays

**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.

**Functions**- 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.

- prepare the OpenMath mailing list (openmath@maplesoft.on.ca).
- 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.

This page is part of the OpenMath Web archive, and is no longer kept up to date.