Skip to main content

A Computer Algebra System: Risa/Asir

  • Conference paper

Abstract

Risa/Asir [20] is a computer algebra system developed for efficient algebraic computation. It is also designed to be a platform for parallel distributed computation under the OpenXM (Open Message eXchange for Mathematics) protocol [11]. OpenXM defines client-server communication between mathematical software systems and Risa/Asir is one of main components in the OpenXM package [21]. The source code of Risa/Asir is completely open and it is easy to modify the source code or to add new functions. In the present paper, we explain an overview of Risa/Asir, its functions and implemented algorithms with their performances, the OpenXM API and the way to add built-in functions.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anai, H., Noro., M., Yokoyama, K. (1996): Computation of the splitting fields and the Galois group of polynomials, Progress in Mathematics 143, Birkhäuser Verlag, 1–15.

    Google Scholar 

  2. Boehm, H.,Weiser, M. (1988): Garbage Collection in an Uncooperative Environment, Software Practice & Experience, 807-820. http://www.hpl.hp.com/personal/Hans\_Boehm/gc/.

  3. Faugère, J.-C., Gianni, P., Lazard, D., Mora, T. (1993): Efficient computation of zero-dimensional Gröbner bases by change of ordering, J. Symb. Comp. 16, 329–344.

    Article  MATH  Google Scholar 

  4. Faugère, J.C. (1999): A new efficient algorithm for computing Gröbner bases (F4), Journal of Pure and Applied Algebra 139 1-3, 61–88.

    Article  Google Scholar 

  5. Gebauer, R., Möller, H.M. (1989): On an installation of Buchberger’s algorithm, J. Symb. Comp. 6/2/3, 275–286.

    Google Scholar 

  6. Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C. (1991): “One sugar cube, please” OR Selection strategies in the Buchberger algorithm, Proc. ISSAC’91, ACM Press, 49–54.

    Google Scholar 

  7. van Hoeij, M. (2000): Factoring polynomials and the knapsack problem, to appear in Journal of Number Theory.

    Google Scholar 

  8. Izu, T., Kogure, J., Noro, M., Yokoyama, K. (1998): Efficient implementation of Schoof’s algorithm, ASIACRYPT’98, LNCS 1514, Springer-Verlag, 66–79.

    Google Scholar 

  9. Noro, M., Takeshima, T. (1992): Risa/Asir — a computer algebra system, Proc. ISSAC’92, ACM Press, 387–396.

    Google Scholar 

  10. Noro, M., McKay, J. (1997): Computation of replicable functions on Risa/Asir, Proc. PASCO’97, ACM Press, 130–138.

    Google Scholar 

  11. Maekawa, M., Noro, M., Ohara, K., Takayama, N., Tamura, Y. (2001): The Design and Implementation of OpenXM-RFC 100 and 101, Computer Mathematics, Proc. the Fifth Asian Symposium (ASCM 2001), World Scientific, 102–111.

    Google Scholar 

  12. Noro, M., Yokoyama, K. (1999): A Modular Method to Compute the Rational Univariate Representation of Zero-Dimensional Ideals, J. Symb. Comp. 28/1, 243–263.

    Article  MathSciNet  MATH  Google Scholar 

  13. Noro, M., Yokoyama, K. (2002): Yet Another Practical Implementation of Polynomial Factorization over Finite Fields, ISSAC 2002, ACM Press, 200–206.

    Google Scholar 

  14. Noro, M. (2002): An Efficient Modular Algorithm for Computing the Global b-function, Mathematical Software, Proc. International Congress of Mathematical Software (ICMS 2002), World Scientific, 147–157.

    Google Scholar 

  15. Shimoyama, T., Yokoyama, K. (1996): Localization and Primary Decomposition of Polynomial Ideals, J. Symb. Comp. 22, 247-277.

    Google Scholar 

  16. Trager, B.M. (1976): Algebraic Factoring and Rational Function Integration, Proc. SYMSAC 76, 219-226.

    Google Scholar 

  17. Traverso, C. (1988): Gröbner trace algorithms. Proc. ISSAC’88, LNCS 358, Springer-Verlag, 125–138.

    Google Scholar 

  18. Wang, P.S. (1978): An Improved Multivariate Polynomial Factoring Algorithm. Math. Comp. 32, 1215-1231.

    Google Scholar 

  19. http://www.math.uic.edu/~jan/demo.html.

  20. A computer algebra system Risa/Asir, http://www.math.kobe-u.ac.jp/Asir/asir.html. 162 Masayuki Noro

  21. OpenXM package, http://www.openxm.org/.

  22. The GNU MP Library, http://swox.com/gmp//gmp.

  23. Message Passing Interface, http://cs.utk.edu/netsolve/netsolve.

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Noro, M. (2003). A Computer Algebra System: Risa/Asir. In: Joswig, M., Takayama, N. (eds) Algebra, Geometry and Software Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05148-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-05148-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05539-3

  • Online ISBN: 978-3-662-05148-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics