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American Mathematical Society analogous assumed coefficients components are functions contravariant tensor contravariant vectors coordinates xk covariant derivative covariant law covariant tensor covariant vectors denote differential form 1.1 Differential Parameters equation expression must satisfy expression of G ff^f formula functions f fundamental space Vn Geometry of Hyperspace hyperplane hypersurface independent variables independent vectors Ingold invariant normal invariant polynomial invariantive constituent Invariants of Quadratic linearly independent Maschke Maschke's fundamental theorem MASCHKE'S SYMBOLIC method necessary and sufficient non-scalar obtain orthogonal ennuple partial derivatives polynomial expression polynomial function positive square root Prom quadratic differential form Ricci's root of g rotation invariants scalar product scalar tensor set of functions set of independent set of quantities Sets of invariants sufficient condition symbolic function symbolic notation symbolic products Symbolic Treatment symmetric covariant tensor of order tensors whose components theorem four theorem three Theory of Invariants Transactions transform according University of Missouri variant Weitzenbock