Algorithms for the Solution of Systems of Linear Equations in Commutative Rings
Solution methods for linear equation systems in a commutative ring are discussed. Four methods are compared, in the setting of several different rings: Dodgson’s method , Bareiss’s method  and two methods of the author — method by forward and back-up procedures  and a one-pass method .
We show that for the number of coefficient operations, or for the number of operations in the finite rings, or for modular computation in the polynomial rings the one-pass method  is the best. The method of forward and back-up procedures  is the best for the polynomial rings when we make use of classical algorithms for polynomial operations.
KeywordsCommutative Ring Polynomial Ring Linear Equation System Modular Method Forward Procedure
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- Malashonok G. I., A new solution method for linear equation systems over the commutative ring, in “Int. Algebraic Conf., Novosibirsk,” Aug. 21-26, 1989, Theses on the ring theory, algebras and modules, 1989, p. 82.Google Scholar