Slate Slate Slate is a fine-grained, foliated, homogeneous metamorphic rock derived from an original shale-type sedimentary rock composed of clay or volcanic ash through low-grade regional metamorphism. It is the finest grained foliated metamorphic rock. Foliation may not correspond to the original sedimentary layering, but instead is in planes perpendicular to the direction of metamorphic compression. The foliation in slate is called "slaty cleavage". It is caused by strong compression causing fine grained clay flakes to regrow in planes perpendicular to the compression. When expertly "cut" by striking parallel to the foliation, with a specialized tool in the quarry, many slates
Polarization of an algebraic form "n" variables u = ("u", "u", ..., "u"). Suppose that "f" is homogeneous of degree "d", which means that Let u, u, ..., u be a collection of indeterminates with u = ("u", "u", ..., "u"), so that there are "dn" variables altogether. The polar form of "f" is a polynomial which is linear separately in each u (i.e., "F" is multilinear), symmetric in the u, and such that The polar form of "f" is given by the following construction In other words, "F" is a constant multiple of the coefficient of λ λ...λ in the expansion of "f"(λu +