Parallel Square Modular Computer Algebra

摘要

The computer algebra of parallel modular operations with a square diapason for a variable is described. The base set of the algebra is a finite dimension metric space of modular integer vectors. Two metrics are introduced. An orthogonal normal basis is employed to reconstruct the value of the integer number corresponding to the vector. An analog of the inner product is used to advance beyond the additive range, and the vector product is defined in two ways. The algebra could serve as the basis for parallel computer arithmetic of unbounded digit integers, a theoretical foundation of parallel computing.