Dispersify

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Dispersify, the singularity-subtracted quadrature for dispersion integrals, is now part of Nestor, the high-precision quadrature package, as the module nestor.dispersion. It computes $(1/\pi)\int\rho(w')\,K(w')\,\mathrm{d}w'$ to many digits when the spectral density $\rho$ switches on at known thresholds like a power times a logarithm and the kernel $K$ is smooth between them. Panel boundaries are placed at every threshold, the known singular form is subtracted on a short interval next to each one so that tanh-sinh quadrature converges exponentially, and the subtracted piece is added back in closed form. The main entry is disp_subtracted(rho, K, panels, dps=40), with the helpers moment_powerlog, kernel_taylor, addback_endpoint and tanhsinh_panel; the worked one-loop box kernel is tools/nestor/examples/box1_dilog.py, and the tests are tests/test_dispersion_moments.py and tests/test_dispersion_surrogate.py in the Nestor package. See the Nestor page for the description, routines and requirements.

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