Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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Difference equations or exact numerical integration scheme, which have general solutions, are treated algebraically. Eliminating the symmetry in mixed functions, we can construct numerical integration schemes correspond to some ordinary differential equations that have same mixed functions. When arbitrary functions are given, whether we can construct numerical integration schemes that have solution functions equal to given function or not are treated.