[Om3] OpenMath Symbols for Symbolic Computation

[Peter Horn]

Dear OpenMath Community,

within the SCIEnce project (http://www.symbolic-computation.org) we  
heavily use OpenMath to marshal the mathematical objects that we send  
back and forth between our computer-algebra-systems. We encountered a  
couple of problems that are possibly unnoticed in the OM-world so far.

(1) There is no reasonable representation for matrices.
    (We developed a 'matrix1' CD, if you are interested, we'd love to  
moot it.)

(2) arith1.sum, calcucus1.diff etc. all take a function as a parameter.
    There are several quirks with this:
    * First, there ARE no functions in OM. From the examples I found  
that this
      is referring to fns1.lambda-expressions.
    * Handling around these is -- from a computer-algebra point of
      view -- rather cumbersome.
    * In CA, you very frequently use expressions for this purpose and  
specify
      the variable as an additional parameter as in diff(x^2+1, x),  
we'd highly
      prefer this.

(3) prog1 doesn't really make me happy:
    * The prog1 stuff doesn't clearly answer the scope-question.
    * How are lambda(x, x+1) and function_definition(x, x+1) related?
    * When you claim that  "fns1.lambda" is the way to define a 'OM- 
function'
      (which is implicitly(!) done in many places), the CAS-people  
don't know how
      to marshal their functions in OM, especially if they consist of  
a sequence
      of commands.

(4) There are tons of stuff missing
    * a unary ^-1 (arith2.inverse *may* be understood in that way)
    * rational functions
    * accessors to numerator, denominator
    * solve-commands
    * simplification-commands (which tend to have a rather unspecified  
semantic, sure)
    * normalization-commands
    * a reasonable factor-command (we started developing one)
    * evaluation-commands
    ...

(x) more to come if you like.

I know these are not higher-mathematics kind-of-stuff, but they are  
immediately needed when you start using OM in the context of computer- 
algebra. I also know that OM was not designed to be a "generic cas- 
language", but from our point of view it is quite reasonable to  
develop it as-much in that direction as possible.

I don't want to gripe -- these are just some points that came up  
lately and I'd love them to be considered when OM3 is developed.

Best regards, Peter
--
Peter   Horn,   University  of  Kassel          *
Computational    Mathematics     Group      *       *
Heinrich Plett Str. 40,  34132  Kassel    *  [S] [C] [I] [E] [n] [c] [e]
Phone: + 4 9 - 5 6 1 - 8 0 4 - 4 1 9 2   *   http://www.symcomp.org
Fax:   + 4 9 - 5 6 1 - 8 0 4 - 4 6 4 6    *
E-Mail: hornp at mathematik.uni-kassel.de      *       *
            http://kassel.symcomp.org/          *