Preliminary Report on OpenMath Workshop 1

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

Purpose

Notes on the presentations

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.

Discussions

• 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.

Assignment of responsibilities

• 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.