L. Langemyr. An asymptotically fast probabilistic algorithm for computing polynomial GCD's over an algebraic number field. In S. Sakata, editor, Proc. AAECC-8, Springer-Verlag, Berlin-Heidelberg-New York, 1990. to appear.

Digital Library

Google Scholar

[6]

L. Langemyr. Computing the GCD of two Polynomials Over an Algebraic Number Field. PhD thesis, NADA, Royal Institute of Technology, Stockholm, 1988.

Google Scholar

[7]

R. G. K. Loos. Generalized polynomial remainder sequences. In B. Buchberger, G. E. Collins, and R. G. K. Loos, editors, Computer Algebra, Symbolic and Algebraic Computation, pages 115-137, Springer-Verlag, Wien-New York, 1982.

Google Scholar

[8]

C. M. Rubald. Algorithms for Polynomials Over a Real Algebraic Number Field. PhD thesis, University of Wisconsin, Madison, January 1974.

Digital Library

Google Scholar

Cited By

View all

Khungurn PSekigawa HShirayanagi KWang D(2007)Minimum converging precision of the QR-factorization algorithm for real polynomial GCDProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277580(227-234)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277580
Langemyr L(2005)An asymptotically fast probabilistic algorithm for computing polynomial GCD's over an algebraic number fieldApplied Algebra, Algebraic Algorithms and Error-Correcting Codes10.1007/3-540-54195-0_53(222-233)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-54195-0_53

Index Terms

An analysis of the subresultant algorithm over an algebraic number field
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials
      2. Number-theoretic computations

Recommendations

On the subresultant PRS algorithm
SYMSAC '76: Proceedings of the third ACM symposium on Symbolic and algebraic computation

This paper is a sequel to two earlier papers [1, 2] on the generalization of Euclid's algorithm to domains of polynomials.

In attempting such a generalization one easily arrives at the concept of a polynomial remainder sequence (PRS), and then quickly ...
Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields
ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation

We present algorithms that compute all irreducible factors of degree ≤ d of supersparse (lacunary) multivariate polynomials in n variables over an algebraic number field in deterministic polynomial-time in (l+d)ⁿ, where l is the size of the input ...
Ruppert matrix as subresultant mapping
CASC'07: Proceedings of the 10th international conference on Computer Algebra in Scientific Computing

Ruppert and Sylvester matrices are very common for computing irreducible factors of bivariate polynomials and computing polynomial greatest common divisors, respectively. Since Ruppert matrix comes from Ruppert criterion for bivariate polynomial ...

Comments

Information & Contributors

Information

Published In

ISSAC '91: Proceedings of the 1991 international symposium on Symbolic and algebraic computation

June 1991

468 pages

ISBN:0897914376

DOI:10.1145/120694

Editor:
Stephen M. Watt

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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1991

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

ISSAC 91

Sponsor:

German Comp Soc
GMD
SIGSAM

ISSAC 91: International Symposium on Symbolic Algebraic Computation

July 15 - 17, 1991

Bonn, West Germany

Acceptance Rates

Overall Acceptance Rate 395 of 838 submissions, 47%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
234
Total Downloads

Downloads (Last 12 months)27
Downloads (Last 6 weeks)7

Reflects downloads up to 10 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Khungurn PSekigawa HShirayanagi KWang D(2007)Minimum converging precision of the QR-factorization algorithm for real polynomial GCDProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277580(227-234)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277580
Langemyr L(2005)An asymptotically fast probabilistic algorithm for computing polynomial GCD's over an algebraic number fieldApplied Algebra, Algebraic Algorithms and Error-Correcting Codes10.1007/3-540-54195-0_53(222-233)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-54195-0_53

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

On the subresultant PRS algorithm

Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields

Ruppert matrix as subresultant mapping