Study of Algorithms and Applications of Approximate Algebra

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For computing Groebner bases with inaccurate input coefficients, we clarified origins of instability and proposed a stable method "high-precision method with effective floating-point numbers". As for series expansion of multivariate algebraic function at singular point, we devised a method which gives the series in a compact form, derived a simple expansion formula, and clarified many properties of convergence and many-valuedness. We devised a method which computes only eigenvalues located in a specified domain, and applied the method to large-scale chemical computations successfully. We made Japanese algebra system GAL run on C.