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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+deltat, A) = N(t, A+sigmasqrt(deltat))(1-p(t, A))+N(t, A-sigmasqrt(deltat))*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 all thing is very straightforward, but I really can't find a way to do the same in Sage. Any help will be much appreciated.

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+deltat, N(t+delta*t, A) = N(t, A+sigmasqrt(deltat))A+sigma sqrt(delta t)) (1-p(t, A))+N(t, A-sigmasqrt(deltat))*p(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 all thing is very straightforward, but I really can't find a way to do the same in Sage. Any help will be much appreciated.

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),
A),

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