This gitter chat room is used to discuss about the GSoC'16 project "Implementation of Holonomic Function".
There doesn't seem to exist an algorithm converting Holonomic functions directly to G-functions.
Hi Kalevi! I couldn't write a blog post last week. Would it be Okay if I write about last week in this weeks blog post?
Also I am thinking about writing a code that itself finds the domain for the polynomial coefficients in the differential equation in a new PR. Is there anything else you have in mind we should do first?
Also I am thinking about writing a code that itself finds the domain for the polynomial coefficients in the differential equation in a new PR. Is there anything else you have in mind we should do first?
I think it is quite ok. I know what you have accomplished, and if the others will learn that a little later, it should not matter too much. Automatically finding the coefficient domain would surely be appreciated by the users. That would probably solve the issue sympy/sympy#11323 raised by Ondřej.
Good Evening Kalevi! I wanted to discuss a question regarding conditions at singular point in integration.
For instance we want to integrate with
For instance we want to integrate with
singular_ics = [(-1, [1, 0, -1])], i.e. the series is of the form or . If we integrate the initial terms of the series to compute singular_ics of the result, the term 1/x will become log(x). In cases where there is no term of x with power -1 we can compute the singular_ics directly by integration of initial terms of the series. What should be the singular_ics for this case?
General holonomic functions also have these logarithmic terms. They appear at regular singular points when some roots of the indicial equation differ by an integer (or there is a multiple root). Such expressions may become quite complicated in general if several roots are involved. In case of two roots the situation might be controllable. See e.g. the series expansions of the Bessel functions of the second kind. But it may be too ambitious to include them in this gsoc project. I am not sure of how the initial conditions should be defined. Probably something like this:
log(x) multiplied by an initial condition of the more general type (i.e. x**s multiplied by a constant and optionally some low order terms), in addition of the usual initial conditions at a regular singular point.
So we should probably stop with
NotImplementedError when something like this will appear.
Did I do something wrong when using symbolic variables as coefficients?
Does there exist a general algorithm to compute singular initial condition for functions? I actually was adding code to compute it one by one for specific families of functions like polynomials and algebraic functions.
It'd be possible to compute it easily for any function if the indicial equation have only one root r. We can then use g(x) = f(x)/x**r. So the singular initial condition should be {r:[g(x0), g'(x0), g''(x0)/2! ...]}.
The statement
a = int(a) is defined here before using range(a). So I guess a would be an integer while calling range().
According to issue the
str should be valid python.