Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Molien generating functions and integrity bases for the action of the
  SO(3) and O(3) groups on a set of vectors   The construction of integrity bases for invariant and covariant polynomials
built from aset of three dimensional vectors under the SO(3) and O(3)
symmetries is presented. Thispaper is a follow--up to our previous work that
dealt with a set of two dimensional vectorsunder the action of the SO(2) and
O(2) groups [G. Dhont and B. I. Zhilinski{\i}, J. Phys. A:Math. Theor., 46,
455202 (2013)]. The expressions of the Molien generating functions asone
rational function are a useful guide to build integrity bases for the rings of
invariantsand the free modules of covariants. The structure of the non--free
modules of covariants ismore complex. In this case, we write the Molien
generating function as a sum of rationalfunctions and show that its symbolic
interpretation leads to the concept of generalizedintegrity basis. The
integrity bases and generalized integrity bases for O(3) are deducedfrom the
SO(3) ones. The results are useful in quantum chemistry to describe the
potentialenergy or multipole moment hypersurfaces of molecules. In particular,
the generalizedintegrity bases that are required for the description of the
electric and magnetic quadrupolemoment hypersurfaces of tetratomic molecules
are given for the first time.

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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin