摘要：AbstractIn this paper, we provide an algorithm for verifying the validity of identities of the form∑A⊆n¯cA‖xA‖2=0, wherexA=∑i∈Axiandn¯={1,⋯,n}in inner-product spaces. Such algorithm is used to verify the validity, in inner-product spaces, for a number of identities. These include a generalization of the parallelepiped law. We also show that such identities hold only in inner-product spaces. Thus, the algorithm can be used to deduce characterizations of inner-product spaces.
