An application of symbolic computation in the physical sciences

ABSTRACT

An example of a problem in the physical sciences is discussed where application of various symbolic computation facilities available in many algebraic computing systems leads to a significant expansion of the range problems that can be solved. Since most interesting problems in the physical sciences eventually require the numerical solution of systems of equations, of various types, we will introduce an example and describe an approach to a solution, beginning at the development of relevant differential equations, using, for example REDUCE, and leading eventually to the generation of highly efficient and stable numerical code for the solution, using, in our case, the C language. The use of SCOPE and GENTRAN, as well as series packages in REDUCE will be discussed.In many areas of interest, a considerable amount of work has to be performed to arrive at the symbolic equations to solve, and this is particularly true in General Relativity and related gravitation theories. Some packages, such as REDTEN [1], for calculation in this field will be discussed.

REFERENCES

• 1: J. Harper and C. Dyer, The REDTEN User's Manual, 1986, 1994.
• 2: C. Dyer, F. Marleau, E. Shaver, submitted to Phys. Rev. D.
• 3: R. Schopf, in REDUCE 3.~ Miscillaneous Documentation.
• 4: A. Barnes, J. Padget, in REDUCE 3.~ Mzscillaneous Documentation.
• 5: B. Gates, M. Dewar, in REDUCE 3.~ Miscillaneous Documentation.
• 6: J. van Hulzen, in REDUCE 3.~ Miscillaneous Documentatzon.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.5 Testing and Debugging
          Subjects: Debugging aids

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms
      I.1.3 Languages and Systems

          Nouns: REDUCE

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Physics

General Terms:
Algorithms, Languages, Reliability, Verification