Given an integral domain D and an indeterminate X over D, there exist many functionals mapping D[X]×D[X] into D that are similar to the resultant. If D is a Unique Factorization Domain, a specific functional, called the “minimal resultant”, could be useful in many places where a resultant would be required, and also for solving certain Diophantine Equations.
Key wordsresultants Sylvester Matrix commutative algebra Unique Factorization Domains P-adic Methods
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- [BCL 82]Buchberger, B., Collins, G. E. and Loos, R. editors, Computer Algebra, Symbolic and Algebraic Computation Springer-Verlag, Vienna, 1982, pages 173–188.Google Scholar
- [Col 67]Collins, G. E. “Subresultants and Reduced Polynomial Remainder Sequences” ACM Journal, January 1967, Vol 14 Nr. 1Google Scholar
- [Col 71]— “The Calculation of Multivariate Polynomial Resultants” ACM Journal, October 1971, Vol 18 Nr. 4Google Scholar
- [Gri 78]Griss, Martin L. “Using an Efficient Sparse Minor Expansion Algorithm to Compute Polynomial Subresultants and GCD” IEEE Transactions on Computing, C-27 (1978), 945–950.Google Scholar
- [Her 64]Herstein, I. N. Topics in Algebra Blaisdell Publishing Co. Waltham, Mass, 1964Google Scholar
- [Knu 69]Knuth, Donald E. The Art of Computer Programming Volume 2/Seminumerical Algorithms, Addison-Wesley Publishing Co., Reading, Mass., 1969.Google Scholar
- [KuA 69]Ku, S. Y. and Adler, R. J. “Computing Polynomial Resultants: Bezout's Determinant vs Collins' Reduced PRS Algorithm” CACM Vol 23 Nr 12 (Dec 1969)Google Scholar
- [LAU 83]Lauer, Markus “generalized p-Adic Constructions” SIAM J. Computing Vol 12 Nr 2, (May 1983), 395–410.Google Scholar
- [LoC 73]Loos P and Collins, G. E. “Resultant Algorithms for Exact Arithmetic on Algebraic Numbers” Paper presented at SIAM 1973 Natl Mtg, Hampton, Va.Google Scholar
- [Mio 82]Miola, Alfonso M. “The Conversion of Hensel Codes to their Rational Equivalents (or how to solve the Gregory's open problem)” SIGSAM Bulletin Number 64 (Vol 16 Number 4, November 1982)Google Scholar
- [Rot 76]Rothstein, M Aspects of Symbolic Integration and Simplification of Exponential and Primitive Functions Ph D Thesis, University of Wisconsin, Madison, 1976, (114 pages) Available from University Microfilms.Google Scholar
- [VdW 71]van der Waerden B L, Algebra I, Heidelberger Taschenbucher Nr 12, Springer-Verlag, Berlin, 1971 (German)Google Scholar