Workshop on environments for computational mathematics

I . Introductio n Since the 1950s, many researchers have worked to realiz e the vision of natural and powerful computer systems fo r interactive mathematical work . Nowadays this vision can b e expressed as the goal of an integrated system for symbolic , numerical, graphical and documentational mathematica l work . Recently the development of personal computers (wit h high resolution screens, window systems and mice), high speed networks, electronic mail and electronic publishing , have created a technological base that is more than adequat e for the realization of such systems . However, the growth o f separate mathematical typesetting, multimedia electroni c mail, numerical computation and computer algebra communities, each with its own conventions, threatens to prevent these systems from being built . To be specific, little thought has been given to unifyin g the different expression representations currently used in th e different communities . This must take place if there is to b e interchange of mathematical expressions among document , display and computation systems . Also, tools that are wante d in several communities, e .g . WYSIWYG mathematica l expression editors, are being built independently by each , with little awareness of the duplication of effort that thereb y occurs . Worst of all, the ample opportunities for cross fertilization among the different communities are not being exploited . For example, some computer algebra system s explicitly associate a type with a mathematical expression (e .g . 3X3 matrix of polynomials with complex numbe r coefficients), which could enable automated math proofreaders, analogous to spelling checkers . The goal of the Workshop on Environments fo r Computational Mathematics was to open a dialogue amon g representatives of the computer algebra, numerica l computation, multimedia electronic mail and mathematica l typesetting communities . In July 1986, during the Computer s and Mathematics Conference at Stanford University, a subset of this year's participants met at Xerox PARC to discuss use r interfaces for computer algebra systems . This group agreed to hold future meetings, of which the present workshop is th e first . Alan Katz's recent essay, "Issues in Defining a n Equations Representation Standard," RFC1003, Arp a Network Information Center, March 1987 (reprinted in th e ACM SIGSAM Bulletin, May 1987, pp . 19-24), influenced th e discussion at the workshop, especially since it discusses interchange of mathematical expressions . This report does not aim to be a transcript of th e workshop, but rather tries to extract the major points upon which (in the editor's view) rough consensus was reached . I t