# Computation of Clebsch-Gordan cofficients for point groups

In my work I have to deal with space and point groups and their representation. A lot of computations need Clebsch-Gordan coefficients. I am aware of the fact that these coefficients may be found in textbooks, however due to some reasons (one must be really careful with the basis and it is rather tricky to follow the basis changes and putting these tables in the code is error-prone) I would prefer to compute them when needed.

I have found (quite) few reсipes in the literature, but they are formulated in the way which is rather tricky to implement using standard linear algebra packages. For example, in this paper equation for CG coefficients is formulated as a square root of some matrix (10) which "can be utilized to derive all or individual CG coefficients which are associated with ... irreducible representations". Actually, I have derived somewhat similar equations by myself and they are also not suitable 'as is' for standard linear algebra libraries.

The question is: is there some ready-to-use algorithm (not a development code in Maple) of this procedure which is modern libraries-friendly? Or maybe result can be obtained by few lines code in some specialized CAS? Probably, this should be relatively easy to do in GAP, I am reading UG now, but can't figure out yet how this can be done.

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Could you state which group you need CG for ? It is SO(3) ? If so, CG can be implemented using factorials and a hypergeometric polynomial. – Sasha Jul 30 '11 at 16:06
Point groups like $T_d$ or $O_h$, crystallographic space groups if possible. But at least $T_d$ and $O_h$. They are very simple groups with few elements so it should be trivial. Unfortunately, it is not that trivial to write it in a short time by myself. – Misha Jul 30 '11 at 16:31