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Algebraic Algorithms (I.1.2...)
Complexity estimates for two uncoupling algorithms
Bostan A., Chyzak F., de Panafieu É. ISSAC 2013 (Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, Boston, ME, Jun 26-29, 2013) 85-92, 2013. Type: Proceedings
Uncoupling is the process of producing one (or several uncoupled) equivalent higher-order differential equation(s) from a matrix of first-order (coupled) differential equations
Feb 21 2014
Dijkstra, Floyd and Warshall meet Kleene
Höfner P., Möller B. Formal Aspects of Computing 24(4-6): 459-476, 2012. Type: Article
We have recently seen quite a resurgence of interest in semirings and related algebraic structures. While mathematicians have known about these structures for a long time, as with monoids, they have not received much attention. They do...
Nov 13 2013
Algebraic transformation of differential characteristic decompositions from one ranking to another
Golubitsky O., Kondratieva M., Ovchinnikov A. Journal of Symbolic Computation 44(4): 333-357, 2009. Type: Article
The problem of efficiently transforming differential sets from one ranking to another is studied in this paper. The major advantage of the authors’ approach over other approaches is the fact that the most time-consuming part ...
Nov 10 2009
State space analysis of Petri nets with relation-algebraic methods
Fronk A., Kehden B. Journal of Symbolic Computation 44(1): 15-47, 2009. Type: Article
This paper describes the applicability of relation-algebraic methods to state space analysis of Petri nets. It provides an in-depth summary of relation-algebraic methods--an area in which the authors, particularly Fronk, have ...
Mar 30 2009
Gröbner bases for public key cryptography
Caboara M., Caruso F., Traverso C. Symbolic and algebraic computation (Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation, Linz/Hagenberg, Austria, Jul 20-23, 2008) 315-324, 2008. Type: Proceedings, Reviews: (2 of 2)
The pseudonymous authors of an earlier paper  purport to show “why you cannot even hope to use Gröbner bases in cryptography,” although what they show, in fact, is that a particular scheme, often referre...
Nov 27 2008
Gröbner bases for public key cryptography
Caboara M., Caruso F., Traverso C. Symbolic and algebraic computation (Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation, Linz/Hagenberg, Austria, Jul 20-23, 2008) 315-324, 2008. Type: Proceedings, Reviews: (1 of 2)
The computation of Gröbner bases is a difficult task often encountered in cryptanalysis, the destructive aspect of cryptology. As a general rule, such difficult tasks can be reused constructively, as foundations for new crypto...
Sep 30 2008
Real root isolation for exp-log functions
Strzebonski A. Symbolic and algebraic computation (Proceedings of the Twenty-first International Symposium on Symbolic and Algebraic Computation, Linz/Hagenberg, Austria, Jul 20-23, 2008) 303-314, 2008. Type: Proceedings
are, roughly speaking, built up from polynomials by algebraic operations, exponentiation, and taking logarithms; therefore, they include reciprocals and radicals. This paper is concerned with root...
Sep 11 2008
Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities
Basu S. Computational Complexity 15(3): 236-251, 2006. Type: Article
In recent years, there has been a strong effort in computational real algebraic geometry to provide algorithms (and corresponding complexity estimates) for determining the geometric and topological properties of semialgebraic sets, nam...
Jul 31 2007
Modern computer algebra
von zur Gathen J., Gerhard J., Cambridge University Press, New York, NY, 2003. 800 pp. Type: Book (9780521826464)
This is the second edition of a comprehensive textbook on the mathematical and algorithmic foundations of computer algebra. This edition is similar to the first edition , with corrections and some changes to chapters 3, 15, and 22. ...
Dec 21 2004
Computer algebra systems
Grabmeier J., Kaltofen E., Weispfenning V. In
Computer algebra handbook
. New York, NY: Springer-Verlag New York, Inc., 2003. Type: Book Chapter
This chapter covers--in a very complete, exhaustive, clear, and comprehensive way--the state-of-the-art in computer algebra systems....
Jun 22 2004
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