On the parallelization of characteristic-set-based algorithms
This paper presents a parallelized version of algorithms for computing characteristic sets, characteristic series and irreducible characteristic series of sets of multivariate polynomials, decomposing algebraic varieties into irreducible components and proving theorems mechanically in elementary geometries. These algorithms have been implemented with up to 12 processors in MAPLE system by utilizing distributed workstations connected by a local network. The timing statistics on a set of test problems with remarks is given. The encountered problems of using parallelism for these algorithms are discussed.
KeywordsAlgebraic Variety Garbage Collection Sequential Algorithm Decomposition Tree Parallel Processor
Unable to display preview. Download preview PDF.
- Chou, S. C. and Gao, X. S., Techniques for Ritt-Wu's Decomposition Algorithm, Technical Report TR-90-2, Department of Computer Sciences, University of Texas at Austin, 1990.Google Scholar
- Hodge W. V. D. and Pedoe, D., Methods of Algebraic Geometry, Vol. I, II, Cambridge University Press, Cambridge, 1947/1952.Google Scholar
- Ritt, J. F., Differential Equations from the Algebraic Standpoint, Amer. Math. Soc., New York, 1932.Google Scholar
- Ritt, J. F., Differential Algebra, Amer. Math. Soc., New York, 1950.Google Scholar
- Wang, D. M., Characteristic Sets and Zero Structure of Polynomial Sets, Lecture Notes, RISC-LINZ, Johannes Kepler University, Austria, 1989.Google Scholar
- Wang, D. M., Some Notes on Algebraic Methods for Geometry Theorem Proving, Preprint, RISC-LINZ, Johannes Kepler University, November 1990.Google Scholar
- Wang, D. M., An Implementation of Characteristic Sets Method in MAPLE, RISC-Linz Series no. 91-25.0, Johannes Kepler University, Austria, May 1991.Google Scholar
- Wu, W. T., Basic Principles of Mechanical Theorem Proving in Elementary Geometries, J. Sys. Sci. & Math. Scis., 4(1984), 207–235; J. Automated Reasoning, 2 (1986), 221–252.Google Scholar
- Wu, W. T., Basic Principles of Mechanical Theorem Proving in Geometries (Part on elementary geometries, in Chinese), Science Press, Beijing, 1984.Google Scholar
- Wu, W. T., Some Recent Advances in Mechanical Theorem-Proving of Geometries, Automated Theorem Proving: After 25 years, Contemp. Math., 29(1984), AMS, 235–242.Google Scholar