MINION: an environment to organize mathematical problem solving

ABSTRACT

Existing computer algebra systems relieve us of having to perform tedious mathematical computations manually, thus enabling us to gain insight on the abstract problems at hand. Often these systems suggest alternate solution techniques directly. However, existing systems do little to help us manage the interactive computing environment as the scale of the problem grows: when the number of mathematical objects being studied increases, the complexity for a user to manage those objects in his environment seems to grow disproportionately. We need tools to relieve us of tedious organizational overhead every bit as much as we need the mathematical tools themselves. In response to this need, we are constructing a management assistant that works in conjunction with existing symbolic computation systems. Called Minion, it allows users to express simple plans for solving large problems in the interactive environment, and then guides the user's interaction according to that plan. Key features of this assistant are that plans are easy to construct (whether statically or during the problem solving session); the assistant helps a user visualize progress towards solving the global problem; and individual steps within a plan can be executed by arbitrary software tools, whether symbolic-, numeric- or logic-based in their implementation. Our prototype of Minion is made possible by the Polylith software interconnection system [Purt85, Purt88]. Previously we showed how Polylith's general software tool-bus based organization could help overcome the so-called 'symbolic-numeric gap' [Purt86]. Our current work with Minion takes advantage of that interconnection technology in order to focus on the management problems inherent within large scale, mathematical problem solving efforts. This paper briefly portrays the organizational problem that must be treated, and motivates the need for structure management tools in mathematical problem solving environments. We detail features of our Minion prototype that meet these needs. After a brief update on the status of our existing Polylith system, we describe how Minion is implemented using our interconnection resource.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Parallel algorithms

General Terms:
Algorithms, Theory