[GiNaC-devel] GiNaC and polylogarithms

[Jens Vollinga]

Hi,

sorry for the late reply.

Emanuele Bagnaschi schrieb:
> First, G-functions currently evaluate numerically only for real
> arguments y >= 0. 

yes. But I have my doubts that "improving" this is really helpful for 
practice.

> Secondly, in the tutorial is written that there's no support 
> for compiling expressions containing polylogarithms to C function pointers.

True. This is badly missing. GiNaC should be able to generate a C 
function that numerically evaluates a specific polylog in double 
precision and whose name would be used in expression output. One reason 
for not having implemented this yet is a principle problem of the code, 
see below.

> Finally, I see that there are some "TODO" comments in inifcns_nsdsums.cpp which describe missing features. 

Yes, but a lot of them are not that urgent, I think.

> I'm also open to any other suggestions.
> All comments are welcome.

Two more issues (which are the most urgent in this):

- Multiple polylogs with roots of unity as arguments (x1,x2,...) produce 
for certain weights (m1,m2,...) wrong numeric results. There is still a 
bug in the transformations. I would have to look a while for the 
details. But while it is probably of no consequence for physics 
applications, it is still a bad bug and needs to be fixed.

- The code is badly written. It mixes purely algebraic operations 
(transformations) with numerics while using a (prematurely ...) 
optimized representation of the arguments. This had and has three 
consequences: bugs like above are very hard to catch, generating C 
functions for compiled expressions is very difficult because the formula 
  used in the end for the numerics is not available to the outside as a 
whole (i.e. other functions managing the expression compilation), and 
thirdly the functionality of just asking a polylog what its so and so 
transformation would yield is not available to the user (there are other 
nice math packages that offer this).

Regards,
Jens