Manipulations with symbolic functions

edit

Hello! I'm trying to migrate to Sage from Maple and facing some difficulties with symbolic manipulations, which is the most important part of my work. For example, I want to define the following equality:

N(t + delta * t, A) = (   N(t, A + sigma * sqrt(delta * t)) * (1 - p(t, A))
                        + N(t, A - sigma * sqrt(delta * t)) * p(t, A)       )

where the function N(t,A) is yet unknown, and I can't find a way to to do correctly. After that I want to manipulate this equality, for example by substituting Taylor series of N instead of it. In Maple this whole thing is very straightforward, but I really can't find a way to do the same in Sage. Any help will be much appreciated.