Can Maple or Lisp call the other?

[Jonathan King]

Perhaps someone with experience with a computer algebra system can
help me.  I am working on a combinatorial conjecture and am writing
Lisp code to compute it.  As a sub-step, the Lisp produces two lists
of values on which I would like to be able call a Maple routine to do:

  Interpret these lists as coefficient and exponents of two
  large polynomials, compute then simplify their ratio, and finally
  pass back to Lisp the resulting rational function as a list of
  coefficients/exponents.

  Is there a standard, easy way to do this?
  Can this be done by having Lisp write a file, invoking Maple, and
having Maple read the file?
  Or (less desirable) can I have Maple call Lisp?

Please followup either by email (squash at math.ufl.edu) or
to comp.unix.wizards

Thank you.
Jonathan

PS>  I prefer Maple since we have a site license for it.  If the task
is significantly easier for Macsyma or Mathematica, I can legally use
such -but on a remote machine.
PPS>  I am not knowledgeable about any of the computer algebra systems
and am learning a little Maple expressly for the purpose of the above
task.