posible bug - clashing variable names in integrals

---------
>All?I?want?to?do?is?to?use?Maxima?to?do?proofs?where?factoring?expressions
>of?the?form
>
>integral(integral(f(x),x,a,b)*g(x),x,c,d)
>
>into
>
>integral(f(x),x,a,b)*(integral(g(x),x,a,b)

You can experiment with something like this:

(%i31) safe_op(e) := block([inflag :true], if not mapatom(e) then op(e)
else false)$

(%i32) myfreeof(x,e) := freeof(x,e) or (safe_op(e) = 'iint and freeof
(x,third(e)) and freeof(x,fourth(e)))$

(%i33) iint(e,x,a,b) := block([c : 1, f : 1],
  if safe_op(e) = "*" then (
    for ek in e do (
      if myfreeof(x,ek) then c : c * ek else f : f * ek),
    c * funmake('iint,[f,x,a,b]))
  else funmake('iint,[e,x,a,b]))$

(%i34) int_outative(e) := (
   e : subst('integral = 'iint, e),
   e : ev(e, nouns),
   subst('iint = 'integral,e))$

(%i35) int_outative(integral(integral(f(x),x,a,b)*g(x),x,c,d));

(%o35) integral(f(x),x,a,b)*integral(g(x),x,c,d)

I haven't tested this code, but it might be a start on something that is
useful to you. This code will fail on indefinite integrals.


Barton