This gitter chat room is used to discuss about the GSoC'16 project "Implementation of Holonomic Function".
shubhamtibra on fixing_bugs
added uses in integration and l… (compare)
shubhamtibra on fixing_bugs
added uses in integration and l… (compare)
shubhamtibra on fixing_bugs
trying to fix build errors (compare)
shubhamtibra on fixing_bugs
made changes as per the suggest… uncomment statements in examples (compare)
shubhamtibra on fixing_bugs
changed to documentation to sup… (compare)
shubhamtibra on fixing_bugs
added docs for integration and … add autofunction in docs (compare)
shubhamtibra on fixing_bugs
better explanation of holonomic… (compare)
shubhamtibra on fixing_bugs
better explanation of holonomic… (compare)
shubhamtibra on fixing_bugs
better explanation of holonomic… (compare)
shubhamtibra on fixing_bugs
changed the structure of docume… (compare)
shubhamtibra on fixing_bugs
changed the structure of docume… (compare)
shubhamtibra on fixing_bugs
added a very basic sphinx docum… added things in documentation (compare)
shubhamtibra on test_doc
added a very basic sphinx docum… (compare)
shubhamtibra on fixing_bugs
Added tests for KanesMethod.rhs… Changed KanesMethod.rhs() such … Merge pull request #1 from krit… and 100 more (compare)
shubhamtibra on fixing_bugs
Fix #11490 and Fix #11491 (compare)
shubhamtibra on fixing_bugs
fixed a bug in computing initia… (compare)
shubhamtibra on fixing_bugs
change printing of holonomic fu… (compare)
shubhamtibra on singular_ics
change a to int(a) (compare)
shubhamtibra on singular_ics
fixed a bug and added tests computing singular initial cond… (compare)
shubhamtibra on singular_ics
fixed a bug in unify and added … (compare)
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! ...]}
.
a = int(a)
is defined here before using range(a)
. So I guess a
would be an integer while calling range()
.
str
should be valid python.
I think the better way to do this can be:
str
will use f = Function('f')
in printing so that one can use .subs()
. So it should return HolonomicFunction(f(x) + Derivative(f(x), x, x), x), f(0) = 0, f'(0) = 1
for our example.
And calling srepr
on the example should return HolonomicFunction(1 + Dx**2, x, 0, [0, 1])
which is valid python.
str
: This differs from __repr__()
in that it does not have to be a valid Python expression: a more convenient or concise representation may be used instead. On the other hand, srepr
in SymPy does represent e.g 1 + Dx**2
in the following form Add(Pow(Symbol('Dx'), Integer(2)), Integer(1))
, which is not very convenient here.
to_expr()
.p = q + 1
.
p
and q
in the above condition are the parameters of hyper which differ from those of G-functions where the condition would be p == q
. In that case there are Slater expansions at both zero and infinity. They are analytic continuations of each other. The equation has a third singular point at 1 (or -1 for the plus sign case). That singularity restricts the convergence of the power series of both x
and 1/x
.
p == q
. But even in this case, it should be possible to connect power series in x
with those in 1/x
by means of G-functions. They are all solutions of the same holonomic equation.
lenics
.
lenics
in the newer PR here.
I think it'd be fun to write an article for the module. However I think may be we should wait a little to get the module more mature and then we can have a better article. I mean after overcoming some limitations (in integration, converting to MeijerG and to expressions) we have now. After we successfully integrate large types of functions using Holonomic Functions
, we would be able to add it in the paper too. What are your thoughts about it?
I am also starting to work on Sphinx documentation.