skip to main content
10.1145/1277548.1277560acmconferencesArticle/Chapter ViewAbstractPublication PagesissacConference Proceedingsconference-collections
Article

A canonical form for piecewise defined functions

Published: 29 July 2007 Publication History

Abstract

We define a canonical form for piecewise defined functions. We show that the domains and ranges for which these functions are defined is larger than in previous work. Also, our canonical form algorithm is linear in the number of breakpoints instead of exponential. These results rely on the linear structure of the underlying domain of definition.

References

[1]
H. H. Bauschke and M. v. Mohrenschildt. Symbolic computation of fenchel conjugates. ACM Commun. Comput. Algebra, 40(1):18--28, 2006.
[2]
J. M. Borwein and C. H. Hamilton. Symbolic computation of multidimensional fenchel conjugates. In ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation.
[3]
J. Carette. A canonical form for piecewise defined functions. SQRL Report 42, Software Quality Research Laboratory, McMaster University, 2007.
[4]
J. Carette. A canonical form for piecewise defined functions. SQRL Report 42, Software Quality Research Laboratory, McMaster University, 2007.
[5]
W. M. Farmer. A partial functions version of Church's simple theory of types. Journal of Symbolic Logic, 55:1269--91, 1990.
[6]
W. M. Farmer. A simple type theory with partial functions and subtypes. Annals of Pure and Applied Logic, 64:211--240, 1993.
[7]
H. T. Kung. The computational complexity of algebraic numbers. In ACM, editor, Conference record of Fifth Annual ACM Symposium on Theory of Computing: papers presented at the Symposium, Austin, Texas, April 30-May 2, 1973, pages 152--159, New York, NY, USA, 1973. ACM Press.
[8]
M. Lawford, P. Froebel, and G. Moum. Application of tabular methods to the specification and verification of a nuclear reactor shutdown system. Submitted to Formal Methods in System Design.
[9]
M. V. Mohrenschildt. A normal form for function rings of piecewise functions. J. Symb. Comput., 26(5):607--619, 1998.
[10]
J. Mulholland and M. Monagan. Algorithms for trigonometric polynomials. In Proceedings of the 2001 international symposium on Symbolic and algebraic computation, pages 245--252. ACM Press, 2001.
[11]
D. Richardson. Some unsolvable problems involving elementary functions of a real variable. Journal of Symbolic Logic, 33:511--520, 1968.
[12]
A. Wassyng and M. Lawford. Lessons learned from a successful implementation of formal methods in an industrial project. In K. Araki, S. Gnesi, and D. Mandriioli, editors, FME 2003: International Symposium of Formal Methods Europe Proceedings, volume 2805 of Lecture Notes in Computer Science, pages 133--153. Springer-Verlag, Aug. 2003.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
July 2007
406 pages
ISBN:9781595937438
DOI:10.1145/1277548
  • General Chair:
  • Dongming Wang
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 July 2007

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. canonical form
  2. normal form
  3. piecewise

Qualifiers

  • Article

Conference

ISSAC07
Sponsor:
ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada

Acceptance Rates

Overall Acceptance Rate 395 of 838 submissions, 47%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)2
  • Downloads (Last 6 weeks)0
Reflects downloads up to 14 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2016)Simplifying Probabilistic Programs Using Computer AlgebraPractical Aspects of Declarative Languages10.1007/978-3-319-28228-2_9(135-152)Online publication date: 9-Jan-2016
  • (2015)A canonical form for the continuous piecewise polynomial functionsJournal of Computational and Applied Mathematics10.1016/j.cam.2014.11.033283:C(17-27)Online publication date: 1-Aug-2015
  • (2013)Simplifying products of fractional powers of powersACM Communications in Computer Algebra10.1145/2503697.250370747:1/2(26-58)Online publication date: 15-Jul-2013
  • (2010)Symbolic domain decompositionProceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics10.5555/1894483.1894501(172-188)Online publication date: 5-Jul-2010
  • (2010)Symbolic Domain DecompositionIntelligent Computer Mathematics10.1007/978-3-642-14128-7_16(172-188)Online publication date: 2010
  • (2009)Reasoning with Generic Cases in the Arithmetic of Abstract MatricesProceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics10.1007/978-3-642-02614-0_15(138-153)Online publication date: 3-Jul-2009
  • (2008)High-Level TheoriesProceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics10.1007/978-3-540-85110-3_19(232-245)Online publication date: 28-Jul-2008

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media