Abstract
This paper shows the expressive power of the functional programming language Standard ML (SML) in the context of computer algebra. It is focused on a special application of the p-adic lifting technique, the Hensel algorithm, that is utilized in a symbolic but also numeric context. This experiment demonstrates that SML provides a suitable frame for the implementation of abstract algebraic notions together with the possibility to code related algorithms in a generic way on the corresponding level of abstraction.
This work has been partially supported by the Italian project MURST ex 40% “Rappresentazione della conoscenza e meccanismi di ragionamento”
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. Lauer. Computing by Homomorphic Images. In R. Loos, B. Buchberger, and Collins E.G., editors, Computer Algebra — Symbolic and Algebraic Computation. Springer-Verlag, 1983.
C. Limongelli. The Integration of Symbolic and Numeric Computation by padic Construction Methods. PhD thesis, Università degli Studi di Roma “La Sapienza”, 1993.
J.D. Lipson. Elements of Algebra and Algebraic Computing. Addison-Wesley Publishing Company, 1981.
R. Milner and M. Tofte. Commentary on Standard ML. MIT Press, 1991.
R. Milner, M. Tofte, and R. Harper. The Definition of Standard ML. MIT Press, 1990.
L.C. Paulson. ML for the Working Programmer. Cambridge University Press, 1991.
J.H. Reppy. CML: A Higher-Order Concurrent Language. In SIGPLAN'91 Conference on Programming Language Design and Implementation, pages 293–305, June 1991.
D. Sannella. Formal Program Development in Extended ML for the Working Programmer. Technical Report ECS-LFCS-89-102, LFCS, Department of Computer Science, University of Edinburgh, December 1989.
P.S. Santas. A Type System for Computer Algebra. Journal of Symbolic Computation, 19:79–109, 1995.
M. Tofte. Principal Signatures for Higher-Order Program Modules. Journal of Functional Programming, 4(3):285–335, July 1994.
J. Vuillemin. Exact Real Computer Arithmetic with Continued Fractions. Technical report, INRIA, Rocquencourt, France, 1987.
D.Y.Y. Yun. The Hensel Lemma in Algebraic Manipulation. PhD thesis, Massachusetts Institute of Technology, November 1974.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gehrke, W., Limongelli, C. (1996). Exploiting SML for experimenting with algebraic algorithms: The example of p-adic lifting. In: Calmet, J., Limongelli, C. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1996. Lecture Notes in Computer Science, vol 1128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61697-7_10
Download citation
DOI: https://doi.org/10.1007/3-540-61697-7_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61697-9
Online ISBN: 978-3-540-70635-9
eBook Packages: Springer Book Archive