Abstract
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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Buchberger B., Collins G.E., and Loos R.,–Computer Algebra:Symbolic and Algebraic Manipulation”, Springer, Wien, 1982.
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.
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.
Kannan R., Bachem A.“Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix”, SIAM J. Computing, vol. 8, no. 4, November 1979, pp. 499–507.
Lang S.“Algebra”, Addison Wesley, Reading, Massachusetts, 1974.
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.
Strauss N.“Jordan Form and Eigen Finite Field”, The Macsyma Newsletter, Symbolics Inc., Cambridge, Massachusetts, October, 1985.
ibid.“Jordan Form of a Binomial Coefficient Matrix over Zp”, Linear Algebra and Its Applications, 90:65–72, no. 7, Elsevier.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag New York Inc.
About this paper
Cite this paper
Strauss, N. (1989). Algorithm and Implementation for Computation of Jordan Form over A[x 1,...,x m ]. In: Kaltofen, E., Watt, S.M. (eds) Computers and Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9647-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9647-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97019-6
Online ISBN: 978-1-4613-9647-5
eBook Packages: Springer Book Archive