🚀 go-pugleaf

     This posting contains a summary of the e-mail messages that we
received from our initial "Query on the use of software packages in ....".  
Thanks to all those that contributed.  What we were really looking 
for was opinions on what is needed in a link between a symbolic computer
algebra package (e.g. Mathematica etc.) and a numerical library (e.g. NAG, 
IMSL, Numerical Recipes).  Please feel free to e-mail or post any more 
suggestions.


A) THE REQUIREMENTS MATHEMATICIANS, ENGINEERS & SCIENTISTS HAVE OF 
   INTEGRATED (SOFTWARE) SYSTEMS,

[These can be split into two sections, one containing more general comments
and the second relating to specific applications]

(i)

- A good programming interface, reliable and a clean language structure.
- Consistent syntax.
- Not cumbersome.
- Easy to use, transparent interface.
- Ability to save current state.
- Good online help.
- Speed.
- Solve equations algebraically, model systems and graph results.
- A complete toolkit covering basic areas with good robust implementations of 
  known algorithms.
- Make it easy to modify the code to do something slightly different.
- Available on a wide variety of platforms, Macs, PCs, workstations etc. 
  (Some thought that only Unix workstations were necessary).
- A better learning environment.
- Packages constantly being upgraded to include the newest techniques
  (Some disagreed saying this resulted in costly upgrades).
- Good Fortran, C code generation.
- Easy to import own c/f77 code.
- Front-end on a workstation, heavy computation on a supercomputer.
- Correct answers.
- Few bugs.
- Package split into maintainable modules.
- Significant number of other users so that help is available.
- Package uses standard i/o e.g. Postscript.
- User-friendly licensing policy.


(ii)

- A system that would let you specify the partial differential equations to be 
  solved in symbolic form, then specify the rules used for evaluating each 
  derivative, and would then apply the derivative rules to the specified 
  equations and then solve them numerically.
- Probability Integrals.
- Combining a solid mechanics stress/deformation solver with a fluid mechanics 
  flow solver. Then you could solve aeroelasticity ("flutter") problems.


B) WHAT POSSIBLE APPLICATIONS HAVE SUCH SYSTEMS IN MATHEMATICS, ENGINEERING
   & SCIENCE, 


- For cross checking C/f77 coding.
- statistics (general, biomedical, sociometrics, engineering, etc.)
- As an intelligent blackboard
- Complex nonlinear regression 
- Interactive learning environment - computer classroom
- Aircraft and engine control system designs
- Finite Element Analysis
- Computational Fluid Dynamics
- Verification of technical papers.


C) THE PACKAGES AVAILABLE AT THE MOMENT,

Computer algebra packages:
         Mathematica, Maple, Macsyma, Reduce, Axiom.

Integrated symbolic & computational packages:
	 Irena, Intercall, Mathlink, ESC.

Group theory packages:
	 Cayley, GAP & Pari.

Others:
	 MathCAD, S(+), SAS, Glimpse, I-Deas, Spice, MatLab, MatrixX.