Jürgen Gerhard

Welcome to my homepage!

MCA3 is out! (see below)

Research interests:

• Computational problems in symbolic summation and integration
• Polynomial factorization over finite fields and over Q
• Cryptography
• Computational aspects of finite fields
• Computing Laurent and asymptotic series expansions
• Computational algebraic geometry
• Symbolic methods in dynamical modeling, simulation, and control

Publications:

• J. von zur Gathen and J. Gerhard, Modern Computer Algebra, Cambridge University Press, 3rd edition, 2013, xiv+796 pages. (First edition 1999, 2nd edition 2003.)

• E. Shmoylova, J. Gerhard, E. Postma, and A. Roche, Simplification of Differential Algebraic Equations by the Projection Method, Proc. EOOLT 2013, Nottingham, UK, Linköping University Electronic Press, 2013, pp. 87-96.

• H. Ito, A. Ohata, K. Butts, J. Gerhard, M. Abbaszadeh, D. Linder, E. Postma, E. Shmoylova, Equation-Based Model Data Structure for High Level Physical Modelling, Model Simplification and Modelica-Export, Proc. EOOLT 2011, Zürich, Switzerland, Linköping University Electronic Press, 2011, pp. 27-34.

• S. Liang, J. Gerhard, D. J. Jeffrey, and G. Moroz, A Package for Solving Parametric Polynomial Systems, ACM Communications in Computer Algebra 43(3) (2009), pp. 61-72.

• J. Bakus, L. Bernardin, J. Gerhard, K, Kowalska, M. Léger, A. Wittkopf, High-Level Physical Modeling Description and Symbolic Computing, IFAC Proceedings of the 17th World Congress, Seoul, Korea, 2008, pp. 1054-1055.

• J. Gerhard, Modular algorithms in symbolic summation and symbolic integration (PhD thesis), LNCS 3218, Springer Verlag, 2004.

• M. P. Barnett, J. F. Capitani, J. von zur Gathen, and J. Gerhard, Symbolic calculation in chemistry: selected examples, International Journal of Quantum Chemistry 100(2) (2004), pp. 80-104.

• J. Gerhard, M. Giesbrecht, A. Storjohann, and E. Zima, Shiftless decomposition and polynomial time rational summation, Proc. ISSAC 2003, Philadelphia PA, ACM press, 2003, pp. 119-126.

• J. Gerhard and A. Sorgatz, MuPAD, Section 4.1.8 in Computer Algebra Handbook - Foundations, Applications, Systems, ed. J. Grabmeier, E. Kaltofen, and V. Weispfenning, Springer Verlag, 2003, pp. 321-332.

• J. von zur Gathen and J. Gerhard, Polynomial factorization over F₂, Mathematics of Computation 71(240) (2002), pp. 1677-1698.

• O. Bonorden, J. von zur Gathen, J. Gerhard, O. Müller, and M. Nöcker, Factoring a binary polynomial of degree over one million, ACM SIGSAM Bulletin 35(1) (2001), pp. 16-18.

• J. Gerhard, Fast Modular Algorithms for Squarefree Factorization and Hermite Integration, AAECC 11(3) (2001), pp. 203-226.
  Preliminary version: Technical Report tr-ri-99-206, University of Paderborn, Germany, 1999, 22 pages. Abstract Postscript

• J. Gerhard, W. Oevel, F. Postel, and S. Wehmeier, MuPAD Tutorial - English Edition, Springer Verlag, 2000.

• J. Gerhard, Modular algorithms for polynomial basis conversion and greatest factorial factorization. Proceedings of the Seventh Rhine Workshop on Computer Algebra (RWCA'00), Bregenz, 2000, pp. 125--141. Abstract Postscript

• J. Gerhard, High degree solutions of low degree equations, Proc. ISSAC 1998, Rostock, Germany, ACM press, 1998, pp. 284-289. Abstract Postscript

• J. von zur Gathen and J. Gerhard, Fast algorithms for Taylor shifts and certain difference equations, Proc. ISSAC 1997, Maui HI, ACM press, 1997, pp. 40-47. Postscript

• J. von zur Gathen and J. Gerhard, Arithmetic and Factorization of Polynomials over F₂, Proc. ISSAC 1996, Zürich, Switzerland, ACM press, 1996, pp. 1-9. Postscript

• J. von zur Gathen and J. Gerhard, Arithmetic and Factorization of Polynomials over F₂, Technical Report tr-rsfb-96-018, University of Paderborn, Germany, 1996, 43 pages. Postscript

Other available documents:

• J. Gerhard, Faktorisierung von Polynomen über GF(q), Diplomarbeit, University of Erlangen-Nürnberg, Germany, 1994, 87 pages (in German). Postscript

• J. Gerhard, Elliptische Kurven - Theorie und Anwendungen, Studienarbeit, University of Erlangen-Nürnberg, Germany, 1993, 101 pages (in German). Postscript (ZIP file) (only for printing, does not show well in ghostview)