On Tue, 22 May 2001, Christian Bauer wrote:
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
Yes, I think most of users who are familiar with Mathematica are willing to have this feature. Cheers, Son
- 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 \/ http://www.uni-mainz.de/~bauec002/