An Efficient Symbolic-Numeric Environment By
Extending Mathematica's Format Rules.

M. SOFRONIOU[1]

[1]Dipartimento di Matematica, Universitá degli Studi di Bologna, Piazza Porta San Donato, 40126 Bologna, Italia. Email: sofronio@dm.unibo.it

Abstract:

• Contents
• Introduction
• Overview
  • Summary of features
  • Initialisation
• Construction
  • Output formats
  • Output as strings
  • Reformatting expressions
  • Localised definitions
  • Renaming functions
  • Package documentation
  • Parameter and option checking
• Implementation
  • The precedence of operators and operator syntax
  • Rules for code translation
  • Conforming to ANSI standards
  • Utilising intrinsic compiled language functions
  • Maintaining appropriate precision
  • Converting powers
  • Array arguments and the negative sign
  • String manipulation
    • String replacement
    • Upper and lower case
    • Controlling line breaking
  • Assignments to expressions
  • FORTRAN compiler limitations
  • Formatting C Expressions
  • Conversion to Maple
  • Other Assign forms
  • Interactive output
• Optimized computational sequences
• Splice and template files
  • Introduction to unstructured communication using Splice
  • Defining a subroutine
  • Combining code
  • A generalised Runge-Kutta subroutine
    • Hamiltonian systems
    • The gravitational n-body problem
    • Creating a template file
    • Optimising the code
    • Extension to non-autonomous Hamiltonian systems
  • A generalised Newton iteration scheme
    • Evaluating the Jacobian matrix analytically
    • Performance issues
    • Stopping criteria
    • Further enhancements
    • Optimization of the function and Jacobian matrix
  • Code optimization using Splice
• Conclusions and further enhancements
• Acknowledgements
• References
• About this document ...