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ΣIT — A strongly-typed embeddable computer algebra library

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Design and Implementation of Symbolic Computation Systems (DISCO 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1128))

Abstract

We describe the new computer algebra library ΣIT and its underlying design. The development of ΣIT is motivated by the need to provide highly efficient implementations of key algorithms for linear ordinary differential and (q)-difference equations to scientific programmers and to computer algebra system users, regardless of the programming language or interactive system they use. As such, ΣIT is not a computer algebra system per se, but a library (or substrate) which is designed to be “plugged” with minimal efforts into different types of client applications.

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References

  1. S. A. Abramov, M. Bronstein & M. Petkovšek (1995): On polynomial solutions of linear operator equations, Proceedings of ISSAC'95, ACM Press, 290–296.

    Google Scholar 

  2. S. A. Abramov & K. Yu. Kvashenko (1991): Fast Algorithms to Search for the Rational Solutions of Linear Differential Equations with Polynomial Coefficients, Proceedings of ISSAC'91, ACM Press, 267–270.

    Google Scholar 

  3. M. Bronstein (1992): On Solutions of Linear Ordinary Differential Equations in their Coefficient Field, Journal of Symbolic Computation 13, 413–439.

    Google Scholar 

  4. M. Bronstein & M. Petkovšek (1996): An introduction to pseudo-linear algebra, Theoretical Computer Science 157, 3–33.

    Google Scholar 

  5. R. D. Jenks & R. S. Sutor (1992): Axiom — The Scientific Computation System.

    Google Scholar 

  6. J. J. Kovacic (1986): An Algorithm for Solving Second Order Linear Homogeneous Differential Equations, Journal of Symbolic Computation 2 3–43.

    Google Scholar 

  7. N. Mannhart (1995): asdoc — Aldor documentation class for LATEX2e, ftp://ftp.inf.ethz.ch/org/cathode/asharp/asdoc/

    Google Scholar 

  8. F. Naegele (1995): Autour de quelques équations fonctionnelles analytiques, Thèse de Mathématiques Appliquées, INPG, Grenoble.

    Google Scholar 

  9. M. Singer & F. Ulmer (1993): Galois Groups of Second and Third Order Linear Differential Equations, Journal of Symbolic Computation 16, 9–36.

    Google Scholar 

  10. N. Takayama (1992): Kan, ftp://ftp.math.s.kobe-u.ac.jp/pub/kan/kan96.tgz

    Google Scholar 

  11. F. Ulmer & J. A. Weil (1994): Note on Kovacic's algorithm, Prépublication 94-13, IRMAR, Rennes.

    Google Scholar 

  12. S. M. Watt & al. (1994): A first report on the A# compiler, Proceedings of ISSAC'94, ACM Press, 25–31.

    Google Scholar 

  13. S. M. Watt & al. (1994): The A# user's guide, NAG Ltd.

    Google Scholar 

  14. R. Zippel (1990): The Weyl computer algebra substrate, Technical Report 90-1077, Dept. of Computer Science, Cornell University.

    Google Scholar 

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Jacques Calmet Carla Limongelli

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© 1996 Springer-Verlag Berlin Heidelberg

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Bronstein, M. (1996). ΣIT — A strongly-typed embeddable computer algebra library. 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_2

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  • DOI: https://doi.org/10.1007/3-540-61697-7_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61697-9

  • Online ISBN: 978-3-540-70635-9

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