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Computer-Algebra für den Ingenieur

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Rechnerorientierte Verfahren

Part of the book series: Mathematische Methoden in der Technik ((MMT,volume 4))

Zusammenfassung

Numerische Mathematik befaßt sich mit algorithmischen (d.h. mit dem Computer realisierbaren) Verfahren für die Behandlung von Problemen, deren Angaben (Gleitkomma-) Zahlen sind und deren Lösungen wieder (Gleitkomma-) Zahlen sind.

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Zitierte Literatur

  • ARNON D.S., COLLINS G.E., MCCALLUM S., 1984: Cylindrical Algebraic Decomposition I: The Basic Algorithm. SIAM Journal of Computing, vol. 13, no. 4, S. 865–877.

    Article  MathSciNet  Google Scholar 

  • BUCHBERGER B., 1965: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Dissertation, Universität Innsbruck und Aequationes Mathematical vol. 4, fasc. 3, S. 374–383 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  • BUCHBERGER B., 1985: Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. In N.K. Bose (Hsg.): ‘Multidimensional Systems Theory’, S. 184–232, D.Reidel Publishing Company.

    Chapter  Google Scholar 

  • CAVINESS B.F., 1967: On Canonical Forms and Simplifikation. Ph.D. Diss., Pittsburgh, Carnegie-Mellon University, 1967 and Journal of the ACM, vol. 17, no. 2, S. 385–396 (1970).

    MathSciNet  MATH  Google Scholar 

  • CAVINESS B.F., 1985: Computer Algebra: Past and Future. Proc. EUROCAL 85, Linz, Austria, Lecture Notes in Computer Science, vol. 203, S. 1–18, Springer Verlag.

    MathSciNet  Google Scholar 

  • CHAR B.W., FEE G.J., GEDDES K.O., GONNET G.H., MONAGAN M.B., 1986: A Tutorial Introduction to Maple. Journal of Symbolic Computation, vol. 2, no. 2.

    Article  Google Scholar 

  • COLLINS G.E., 1985: The SAC-2 Computer Algebra System. Proc. EUROCAL 85, Linz, Austria, Lecture Notes in Computer Science, vol. 204, S. 34–35, Springer Verlag.

    Google Scholar 

  • DICKSON L.E., 1913: Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors. American Journal of Mathematics, vol. 35, S. 115–138.

    Article  MathSciNet  Google Scholar 

  • FATEMAN R.J., 1981: Symbolic and Algebraic Computer Programming Systems: SIGSAM Bulletin, vol. 15, no. 1, S. 21–32.

    MATH  Google Scholar 

  • GEBAUER R., KREDEL H., 1983: Buchberger Algorithm System. SIGSAM Bulletin, vol. 18, no. 1.

    Google Scholar 

  • HIRONAKA H., 1964: Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero: 1, 11. Annals of Math., vol. 79, S. 109–327.

    Article  MathSciNet  MATH  Google Scholar 

  • FITCH J., 1985: Solving Algebraic Problems with REDUCE. Journal of Symbolic Computation, vol. 1, no. 2, S. 211–227.

    Article  MathSciNet  MATH  Google Scholar 

  • JENKS R.D., 1984: A Primer — 11 Keys to New SCRATCHPAD. Proc. EUROSAM 84, Cambridge, England, Lecture Notes in Computer Science, vol. 174, S. 123–147, Springer Verlag.

    Google Scholar 

  • KALTOFEN E., 1982: Factorization of Polynomials. In B. Buchberger, G.E. Collins, R. Loos (Hsg.): ‘Computer Algebra — Symbolic and Algebraic Computation’, Springer Verlag, S. 95–113.

    Google Scholar 

  • KARATSUBA A., OFMAN Y., 1963: Multiplication of Multidigit Numbers on Automata, Soviet Phys. Dokl. 7, S. 595–596.

    Google Scholar 

  • KNUTH D.E., 1969: The Art of Computer Programming — Volume 2 / Seminumerical Algorithms. Addison-Wesley Publishing Company.

    Google Scholar 

  • KUTZLER B., STIFTER S., 1986: Automated Geometry Theorem Proving using Buchberger’s Algorithm. Proc. SYMSAC86, Waterloo, Kanada, erscheint demnächst.

    Google Scholar 

  • LICHTENBERGER F., 1981: REDUCE — Ein Beispiel eines Software-Systems für symbolisches und algebraisches Rechnen. Universität Linz, Institut für Mathematik, CAMP-Publ.81–11.0.

    Google Scholar 

  • LOOS R., 1982: Computing in Algebraic Extensions. In B. Buchberger, G.E. Collins, R. Loos (Hsg.): ‘Computer Algebra — Symbolic and Algebraic Computation’, Springer Verlag, S. 173–188.

    Google Scholar 

  • MAYR E.W., MEYER A.R., 1981: The Complexity of the Word Problems for Commutative Semigroups and Polynomial Ideals. Report LCS/TM-199, MIT Laboratory of Computer Science.

    Google Scholar 

  • PAVELLE R., 1985: Applications of Computer Algebra. Kluwer Academic Publishers.

    Book  MATH  Google Scholar 

  • PAVELLE R., WANG P.S., 1985: MACSYMA from F to G. Journal of Symbolic Computation, vol. 1, no. 1, S. 69–100.

    Article  MathSciNet  MATH  Google Scholar 

  • RAND R.H., 1984: Computer Algebra in Applied Mathematics: An Introduction to MACSYMA. Research Notes in Mathematics, vol. 94, Pitman Publishing Inc.

    MATH  Google Scholar 

  • RISCH R.H., 1970: The Solution of the Problem of Integration in Finite Terms. Bulletin AMS 76, S. 605–608.

    Article  MathSciNet  MATH  Google Scholar 

  • SCHWARTZ J.T., SHARIR M., 1983: On the ‘Piano Movers’ Problem — II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds. Advances in Applied Mathematics, vol. 4, S. 298–351.

    Article  MathSciNet  MATH  Google Scholar 

  • STOUTEMYER D.R., 1985: A Preview of the Next IBM-PC Version of muMATH. Proc. EUROCAL 85, Linz, Austria, Lecture Notes in Computer Science, vol. 203, S. 33–44.

    Google Scholar 

  • SUTOR R.S., 1985: The Scratchpad II Computer Algebra Language and System. Proc. EUROCAL 85, Linz, Austria, Lecture Notes in Computer Science, vol. 204, S. 32–33.

    Google Scholar 

  • TARSKI A., 1948: A Decision Method for Elementary Algebra and Geometry. Univ. of Calif. Press.

    MATH  Google Scholar 

  • TRINKS W., 1978: On B. Buchberger’s Method for Solving Systems of Algebraic Equations. J. Number Theory, vol. 10, no. 4, S. 475–488.

    Article  MathSciNet  MATH  Google Scholar 

  • Van HULZEN J.A., CALMET J., 1982: Computer Algebra Systems. In B. Buchberger, G.E. Collins, R. Loos (Hsg.): ‘Computer Algebra — Symbolic and Algebraic Computation’, Springer Verlag, S. 221–243.

    Google Scholar 

  • ZASSENHAUS H., 1969: On Hensel Factorization. International Journal of Number Theory, vol. 1, S. 291–311.

    Article  MathSciNet  MATH  Google Scholar 

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© 1986 B. G. Teubner Stuttgart

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Buchberger, B., Kutzler, B. (1986). Computer-Algebra für den Ingenieur. In: Rechnerorientierte Verfahren. Mathematische Methoden in der Technik, vol 4. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96690-2_1

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  • DOI: https://doi.org/10.1007/978-3-322-96690-2_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-519-02617-4

  • Online ISBN: 978-3-322-96690-2

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