Factor symbolic expression involving exp()

I have a symbolic function exp(a+b), and would like to factor out A=exp(a) to produce exp(a+b) = A*exp(b), but I cannot figure out how to do this in MATLAB. Below is my attempt:

syms a b A
X = exp(a+b)
Y = subs(X,exp(a),A) % = A*exp(b)

however, Y = exp(a+b). For some reason, MATLAB cannot determine exp(a+b) = exp(a)*exp(b) = A*exp(b).

Any help is greatly appreciated.

Answer 1

[Walter Roberson]

subs() replaces one sub-expression tree with a different sub-expression tree. exp(a) is not present as a sub-expression in exp(a+b) so you cannot use subs() to make that replacement in it.

What might work is

Y = subs(expand(X), exp(a), A);

[Philip]

Thank you. That works great. What if I had:

 X = exp(2*a+b)

and wanted to produce Y = A^2 * exp(b), where A=exp(a). How could I get this result (just using expand doesn't work).

[Walter Roberson]

Try

Y = expand(subs(X, a, ln(A)))

[Philip]

That's perfect! Thanks again.