On Sunday, March 6, 2016 at 8:42:42 AM UTC+1, Subham Tibra wrote: > > 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 > In general, one needs to allow generalized (singular) initial conditions. You could allow specifying a solution by a truncated series expansion, allowing singular terms, e.g. 1 + O(x^2) and x + O(x^2) for cos and sin, and as something like log(x) + x^(-1/3) + 5*x + O(x^2) for some function with a singularity.
I'm not sure if SymPy's way to represent series expansions is perfect for this (see the class for generalized series expansions in ore_algebra). Of course, you could just do it with a symbolic expression without explicitly giving the O term if that is a problem. However, ordinary initial conditions should be implemented first, and generalized conditions could be done later, so you could start by simply taking a list of initial values as input. Fredrik -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/a1565254-73de-4a99-9294-5246b77920f3%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
