Regarding the initial conditions in multiplication and addition when they 
are not at the same point:

I think the best is(already discussed at ideas page) first to check if both 
the given holonomic functions are elementary function and calculate the 
initial conditions at a same point symbolically, where both the functions 
doesn't have a pole. So for the resulting function the initial condition 
would be addition/multiplication of calculated conditions at that point.

In case when one or both can't be converted to elementary we will calculate 
numerical value at a point and add/multiply them.

How are we gonna do this in INTEGRATION and DIFFERENTIATION?

In application with a algebraic function, let's say we have initial 
condition at x0, then if it's possible we can get the point where the 
algebraic function is equals to x0, let it be x1 ,and now we have the 
initial condition of resulting function at the point x1. For derivatives we 
will multiply the given initial condition with the corresponding derivative 
of algebraic function at x1. Is this method suitable enough?

I'd appreciate to know your views on it.

Thanks

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