On Fri, Aug 29, 2014 at 2:06 PM, Dima Pasechnik dimp...@gmail.com wrote:
On 2014-08-29, kcrisman kcris...@gmail.com wrote:
Some of you may want to know about this question:
http://stackoverflow.com/questions/25570037/best-language-to-do-some-annoying-generating-function-computations
excerpt:
The computation relies on a few ingredients.
1. The first is that I need to be able to compute characters of the
symmetric group in an efficient manner.
Symmetrica implements the character values using Murnaghan-Nakayama rule
recursively and is very fast.
I think the method is symmetrica.char_values(la, mu)...
do you mean that the following
http://www.sagemath.org/doc/reference/combinat/sage/combinat/sf/sf.html#sage.combinat.sf.sf.SymmetricFunctions
(scroll down to Representation theory of the symmetric group)
is slow?
2. The next thing is that I need to arrange these into a generating
function. This will end up being a generating function in many, many
variables, although it will be truncated to a finite degree.
3. Finally, I need to take the formal logarithm (which will be a
generating function in the same number of variables, of the same
degree) of
this and to extract a specific coefficient.
I have coded this before in Maple, but I don't have access to Maple any
more. I was thinking of doing so in Sage, but step 1 seems not to be well
implemented (although there is a workaround, but it doesn't seem to be
very
efficient). Furthermore, I'm pretty sure that while steps 2 and 3 are
fine
in principle, they are very, very slow in Sage.
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