Algorithm and Implementation for Computation of Jordan Form over A[x1,...,xm]
I outline a sequential algorithm for computation of the Jordan form for matrices in K = A[x1,... ,xm], with A an unique factorization domain with separability. The algorithm has average cost (for K integers) of O(n4L(d)2). I have implemented this algorithm in MACSYMA and it is currently distributed as part of the Climax system.
Unable to display preview. Download preview PDF.
- 1.Buchberger B., Collins G.E., and Loos R.,–Computer Algebra:Symbolic and Algebraic Manipulation”, Springer, Wien, 1982.Google Scholar
- 2.Kaltofen E., Krishnamoorthy M., and Saunders B.D., “Fast Parallel Algorithms for Similarity of Matrices”, SYMSAC 1986, Proc. of 1986 Symposium on Symbolic and Alg. Computation, July 21–23, Waterloo, Ontario, B. Char ed., 1986, ACM.Google Scholar
- 3.ibid.“Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices”, SIAM J.Alg.Disc.Math., vol. 8, no. 4, October 1987, pp. 683–690.Google Scholar
- 6.Najid-Zejli H.“Computations in Radical Extensions”, in Proc. Eurosam 84:Springer Lecture Notes in Computer Science 174, Springer-Verlag, Berlin, 1984, pp. 115–122.Google Scholar
- 7.Strauss N.“Jordan Form and Eigen Finite Field”, The Macsyma Newsletter, Symbolics Inc., Cambridge, Massachusetts, October, 1985.Google Scholar
- 8.ibid.“Jordan Form of a Binomial Coefficient Matrix over Zp”, Linear Algebra and Its Applications, 90:65–72, no. 7, Elsevier.Google Scholar