Wildcards for subs()

[Christian Bauer]

Hi!

It has been suggested to me that it would be a desirable feature for subs()
to be able to specify wildcards for indices and function arguments so you
could, for example

 - in "sin(x-1)+sin(2*y)", substitute sin(?) by cos(?)/2 to get
   "cos(x-1)/2+cos(2*y)/2"
 - in "atan2(x+y,z^2)", substitute atan2(?1,?2) by ?2/?1 to get
   "z^2/(x+y)"
 - in "F.mu*g.nu.rho+F.nu*g.mu.rho", substitute F.? by a.?+b.? to get
   "(a.mu+b.mu)*g.nu.rho+(a.nu+b.nu)*g.mu.rho"

This should be relatively easy to implement by extending indexed::subs() and
function::subs() and adding a new "wildcard/wild" class that has an integer
member to distinguish multiple wildcards. Function substitution would then
go something like

  e.subs(atan2(wild(1), wild(2)) == wild(2)/wild(1));

and substitution of base expressions of indexed objects is similar:

  e.subs(indexed(wild(), mu) == indexed(wild(), mu)/2+indexed(A, mu));

Wildcards for indices are a little more involved because indices must be of
class idx, so one would have to write

  e.subs(indexed(F, varidx(wild(), 4)) ==
         indexed(a, varidx(wild(), 4)) + indexed(b, varidx(wild(), 4)));

which is a little clumsy but has the advantage of taking index dimensions
and variance into account (this can also be a disadvantage because it could
only substitute F~mu, not F.mu).

Any comments/suggestions?

Bye,
Christian

-- 
  / Coding on PowerPC and proud of it
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