Some Computations

· HilbertSeriesS1symplectic.nb (H.-C. Herbig and C. Seaton)
Implementation on Mathematica of an algorithm to compute the Hilbert series of the graded algebra of regular functions on the symplectic quotient associated to a unitary circle representation. The algorithm is described in Section 4 of https://doi.org/10.1080/10586458.2013.863745 .

· HilbertSeriesS1.nb (L. E. Cowie, D. Herden, H.-C. Herbig, and C. Seaton)
Implementation on Mathematica of an algorithm to compute the Hilbert series of the graded algebra of invariants of a generic circle representation (meaning that the negative weights are distinct). The algorithm is described in Section 4 of https://doi.org/10.1016/j.jpaa.2018.03.017 .

· HilbertSeriesSL2.nb (P. Cayres, D. Herden, H.-C. Herbig, and C. Seaton)
Implementation on Mathematica of an algorithm to compute the Hilbert series of the graded algebra of invariants of an arbitrary SL₂-representation. The algorithm is described in Section 6 of https://doi.org/10.1142/S0219199719500172 .

· HilbertSeriesSU2symplectic.nb (D. Herden, H.-C. Herbig, and C. Seaton)
Implementation on Mathematica of an algorithm to compute the Hilbert series of the graded algebra of regular functions on the symplectic quotient associated to an arbitrary unitary SU₂-representation. The algorithm is described in Section 3.2 of https://doi.org/10.1142/S0218196720500435 .

· Hilb_2torus.nb (D. Herden, H.-C. Herbig, and C. Seaton)
Implementation on Mathematica of an algorithm to compute the Hilbert series of the graded algebra of regular functions on the symplectic quotient associated to a representation of the 2-torus. The algorithm is described in Section 3.3 of https://arxiv.org/abs/2010.01708 .

gam0_2torus.nb (D. Herden, H.-C. Herbig, and C. Seaton)
Implementation on Mathematica of an algorithm to compute the first Laurent coefficient of the Hilbert series of the graded algebra of regular functions on the symplectic quotient associated to a representation of the 2-torus. The algorithm is described in Section 4.3 of https://arxiv.org/abs/2010.01708 .

· max_gradS1.nb (A. Barringer, H.-C. Herbig, D. Herden, S. Khalid, C. Seaton, and L. Walker)
Implementation on Mathematica of an algorithm to compute the maximally graded Hilbert series of covariants of a circle representation. The algorithm is described in a forthcoming paper.

HilbertSeriesO2Degenerate.nb Implementation on Mathematica of an algorithm to compute the Hilbert series of covariants of an O(2)-representation. The algorithm is described in a forthcoming paper.

· graph_spec.nb and graph_spec.pdf (C. Farsi, E. Proctor, and C. Seaton)
Implementation on Mathematica of the computation of the various graph spectra and graph moves contained in the paper https://arxiv.org/abs/2010.10769 , including the computation of each spectrum included in Section 5.