export - How can I transfer mathematical expressions between Mathematica and Maple?

Is there a simple way to copy mathematical expressions between Mathematica and Maple (or at least in one direction)? I mean only expressions built from numbers and predefined mathematical functions, whithout any patterns or programmatical constructs like Function, Map or Nest.

Ideally, I want functions with different definitions to be automatically adjusted, for example the Mathematica expression EllipticF[Pi/6, 1/4] should be converted to the Maple expression EllipticF(1/2, 1/2).

Answer

I assume you have Maple to use. If so, Simply open Maple and type the Mathematica command itself directly into Maple using the FromMma package built-into Maple, like this:

restart; 
with(MmaTranslator); #load the package
(*[FromMma, FromMmaNotebook, Mma, MmaToMaple]*)

and now can use it

FromMma(`Integrate[Cos[x],x]`);

One can also use Maple convert command with the FromMma option, like this:

convert(`Integrate[Cos[x],x]`, FromMma);

For your example:

FromMma(`EllipticF[Pi/6, 1/4]`);

You can also use a Mathematica computational expression, not just single commands, like this, and then use the resulting Maple command inside Maple:

r:=convert(`Table[i,{i,10}];`, FromMma);
(* r := [seq(i, i = 1 .. 10)] *)

Now run the result in Maple:

r;
(*[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]*)

see http://www.maplesoft.com/support/help/Maple/view.aspx?path=MmaTranslator for information on the MmaTranslator package.

For translating Maple back to Mathematica: The only program I know about that converts Maple to Mathematica is http://library.wolfram.com/infocenter/Conferences/5397

From Maple 9 Worksheets to Mathematica Notebooks

by Yves Papegay. However, I can't find the actual program or the software. You can try to contact the author on this. This was from The 2004 Wolfram Technology Conference.