On Tue, 22 May 2001, Christian Bauer wrote:

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?

Well, it doesn't sound unreasonable to me. Apart from the question what sin(sin(x)).subs(sin(wild(1))==sqrt(1-pow(cos(wild1),2)) is supposed to produce. Is it sin(sqrt(1-pow(cos(x),2)))? Or rather sqrt(1-pow(cos(sqrt(1-pow(cos(x),2))),2))? subs(relational, int level=1)? All of these have their justification, I guess. Otherwise you could just stuff the subs into a while(foo.has(..)) { ... } loop, since that seems to be allowed now. Also, since until now nobody has complained about the tree traversal algorithm advertised in the Mini-FAQ at <http://www.ginac.de/FAQ.html#treetraverse> being incomplete in this respect one level is probably the most natural thing to do. But I may be wrong... Regards -richy. -- Richard Kreckel <Richard.Kreckel@Uni-Mainz.DE> <http://wwwthep.physik.uni-mainz.de/~kreckel/>