Homomorphisms and Chinese Remainder Algorithms
In the previous three chapters we have introduced the general mathematical framework for computer algebra systems. In Chapter 2 we discussed the algebraic domains which we will be working with. In Chapter 3 we concerned ourselves with the representations of these algebraic domains in a computer environment. In Chapter 4 we discussed algorithms for performing the basic arithmetic operations in these algebraic domains.
KeywordsCommutative Ring Integral Domain Computer Algebra Homomorphic Image Quotient Ring
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- 1.W.S. Brown, “On Euclid’s Algorithm and the Computation of Polynomial Greatest Divisors,” J. ACM, 18 pp. 476–504 (1971).Google Scholar
- 2.H. Garner, “The Residue Number System,” IRE Transactions, EC-8, pp. 140–147 (1959).Google Scholar
- 3.D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (second edition), Addison-Wesley (1981).Google Scholar
- 4.M. Lauer, “Computing by Homomorphic Images,” pp. 139–168 in Computer Algebra — Symbolic and Algebraic Computation, ed. B. Buchberger, G.E. Collins and R. Loos, Springer-Verlag (1982).Google Scholar
- 5.J.D. Lipson, “Chinese Remainder and Interpolation Algorithms,” pp. 372–391 in Proc. SYMSAM’ 71, ed. S.R. Petrick, ACM Press (1971).Google Scholar
- 6.J.D. Lipson, Elements of Algebra and Algebraic Computing, Addision-Wesley (1981).Google Scholar
- 7.B.L. van der Waerden, Modern Algebra (Vols. I and II), Ungar (1970).Google Scholar