Alfven dispersion: ω²=k²B²/(μ₀ρ); v_A = B/√(μ₀ρ); group vel = phase vel

Sympy-exact symbolic witness of the shear-Alfvén-wave dispersion relation and its group-velocity identity. Setup: k_∥, B₀, μ₀, ρ sp-symbols positive. Dispersion relation squared: ω² = k_∥²·B₀²/(μ₀·ρ) (sympy canonical…