17. Juli 2002. U. Schoenwaelder; http://www.math.rwth-aachen.de/∼Ulrich.Schoenwaelder HB = Hochschulbibl. RWTH, HBZ = http://www.hbz-nrw.de/ (HBZ-CD-ROM Online), MB = Mathematikbibl., DB = Didaktikbibl. (Winter), FH = Bibl. Fachhochschule Aachen, FL = Fernleihe, IB Nr. Institutsbibliothek Nr., LB = HB–Lehrbuchsammlung, LS = HB–Lesesaal

Lehrbücher zur Computeralgebra

[1] A. G. Akritas. Elements of Computer Algebra with Applications. J. Wiley & Sons, 1989. MB: 14888. S. 44-52: Euclid’s Algorithm and Continued Fractions.

[2] Dario Bini and Victor Pan. Polynomial and Matrix Computations. I. Fundamental Algorithms. Progress in Theoretical Computer Science 12. Boston: Birkhäuser, 1994. ISBN 3-7643-3786-9. HB: Bn1110-12+1.

[3] Wieb Bosma, editor. Computational Algebra and Number Theory, Mathematics and its applications 325. Dordrecht: Kluwer, 1995. ISBN 0-7923-3501-5. HBZ.

[4] Manuel Bronstein. Symbolic Integration I: Transcendental Functions. Algorithms and computation in mathematics 1. Berlin: Springer, 1997. ISBN 3-540-60521-5.

[5] James Harold Davenport, Y. Siret, and E. Tournier. Computer Algebra - Systems and Algorithms for Algebraic Computation. London: Academic Press, 1988, 1993. ISBN 0-12-204232-8. HB: Bb1924+2, MB: 15263.

[6] Keith O. Geddes, Stephen R. Czapor, and George Labahn. Algorithms for Computer Algebra. Kluwer Academic Publishers, 1992, 1993. ISBN 0-7923-9259-0. HB: Bb1905, MB: 16713.

[7] Donald E. Knuth. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Addison-Wesley Series in Computer Science and Information Processing. Addison-Wesley, 1969. Enthält Ch. 3–Random Numbers, Ch. 4–Arithmetic. Deutsche Übersetzung von Ch. 4 durch R. Loos in [8].

[8] Donald E. Knuth. Arithmetik. Berlin: Springer-Verlag, 2001. ISBN 3-540-66745-8. Deutsche Überseetzung durch R. Loos von [9], Ch. 4. Review: Computeralgebra-Rundbrief der GI, DMV und GAMM 30 (März 2002), 18–19.

[9] Donald E. Knuth. The Art of Computer Programming. Addison-Wesley, Ab 1968. 7 Volumes: Volume 1. Fundamental Algorithms: Ch. 1. Basic Concepts; Ch. 2. Information Structures. Volume 2. Seminumerical Algorithms: Ch. 3. Random Numbers; Ch. 4. Arithmetic (deutsch [8]). Volume 3. Sorting and Searching: Ch. 5. Sorting; Ch. 6. Searching. Volume 4. Combinatorial Algorithms: Ch. 7. Combinatorial Searching; Ch. 8. Recursion. Volume 5. Syntactical Algorithms: Ch. 9. Lexical Scanning; Ch. 10. Parsing Techniques. Volume 6. Theory of Languages: Ch. 11. Mathematical Linguistics. Volume 7. Compilers: Ch. 12. Programming Language Translation.

[10] M. Kreuzer and L. Robbiano. Computational Commutative Algebra 1. Berlin: Springer-Verlag, 2000. ISBN 3-387-67733-X. HBZ. Review in: Computeralgebra-Rundbrief 28 (März 2001), S. 23. Vgl. [16].

[11] K.-Y. Lam, I. Shparlinski, and H. Wang. Cryptography and Computational Number Theory. Birkhäuser, 2001. ISBN 3-7643-6510-2. DM 196,00.

[12] John D. Lipson. Elements of Algebra and Algebraic Computing. San Francisco: Benjamin/Cummings; Addison-Wesley, 1981. IB.

[13] M. Mignotte and D. Stefanescu. Polynomials: An Algorithmic Approach. Berlin: Springer-Verlag, 1999. ISBN 981-4021051-2. Hauptsächlich univariate Polynome; ggT, Pseudodivision, Resultanten, symmetrische Funktionen (Kap. 1); Faktorisierung ganzzahliger Polynome (Kap. 4): Berlekamp-Zassenhaus-Algorithmus mit Hensel-Lifting, LLL-Algorithlmus; keine Gröbnerbasen. Review: Computeralgebra-Rundbrief 25 (Oktober 1999), S. 27.

[14] Maurice Mignotte. Mathematics for Computer Algebra. Berlin: Springer-Verlag, 1992. ISBN 3-540-97675-2. HB: Bb1862.

[15] Bhubaneswar Mishra. Algorithmic Algebra. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1993. ISBN 3-540-94090-1. HB: Bb1923. Main four topics: Gröbner bases, characteristic sets, resultants, semialgebraic sets. S. 168: Pseudodivision. S. 213: EA und XEA für mehr als zwei Elemente. S. 225: Resultante und Susbresultanten.

[16] Lorenzo Robbiano, editor. Computational Aspects of Commutative Algebra: from a special issue of the Journal of Symbolic Computation. London: Acad. Press, 1989. ISBN 0-12-589590-9. MB: 15029.

[17] Igor E. Shparlinski. Finite Fields: Theory and Computation, the Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography. Mathematics and its Applications 477. Dordrecht: Kluwer, 1999. ISBN 0-7923-5662-4. MB: 19480.

[18] Joachim von zur Gathen and Jürgen Gerhard. Modern Computer Algebra. Cambridge, UK: Cambridge Univ. Press, 1999. ISBN 0-521-64176-4. HB: Bb5094, MB: 18970. Review in: Computeralgebra-Rundbrief 27 (Oktober 2000), S. 35–36.

[19] Chee Keng Yap. Fundamental Problems of Algorithmic Algebra. Oxford Univ. Press, 2000. ISBN 0-19-512516-9 (cloth). Ch. 14: Continued Fractions. MB: 19032.

[20] Richard Zippel. Effective Polynomial Computation. Boston: Kluwer Academic Publishers, 1993. HB: Dh9052-241+1.