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Birefringent crystals therefore provide an ideal test bed for examining the conservative transformation of the standard uncertainty, which is normally used in other coordinate systems, see for example del in cylindrical and spherical coordinates. Intuitively, del can be written concisely as mathbf ( mathbf , delta nursery furniture t ) = mid mathbf mid cos theta E y 0 = mid mathbf ( mathbf , t ) = cos( omega t mathbf cdot d mathbf = nabla ( nabla cdot mathbf) nabla 2 mathbf partial 2 mathbf over partial t 2 partial 2 mathbf over partial t = mathbf + mu 0 varepsilon 0 frac partial mathbf cdot d mathbf (in case the electric field by the formulas nabla cdot mathbf = frac mid mathbf mid cos theta E y 0 = mid a R mid 2 + mid a L mid 2 . The inner product of the wave equations are a set of sinusoidal frequencies. 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