Points on algebraic curves and the parametrization problem

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1360, Issue , 1997, Pages 189-207

  Hillgarter, Erik ^a   Winkler, Franz ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION; COMPUTER AIDED DESIGN; POLYNOMIAL APPROXIMATION; THEOREM PROVING;

ALGEBRAIC CURVES; BIVARIATE POLYNOMIALS; COMPUTER AIDED GEOMETRIC DESIGNS; GEOMETRIC OBJECTS; GEOMETRIC REASONING; IMPLICIT REPRESENTATION; RATIONAL NUMBERS; RATIONAL PARAMETRIZATIONS;

GEOMETRY;

EID: 84956996938     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0022726     Document Type: Conference Paper

References (14)

1. Hilbert, D., Hurwitz, A.: Über die Diophantischen Gleichungen vom Geschlecht Null. Acta math. 14 (1890) 217-224.
2. Hillgarter, E.: Rational Points Oll Conics. Diploma Thesis, RISC-Linz, J. Kepler Universität Linz, Austria (1996).
3. Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design, A.K. Peters, Wellesley MA (1993).
4. Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory, Springer Verlag, New York Heidelberg Berlin (1982).
5. Krätzel, E.: Zahlentheorie, VEB Dt. Verlag der Wissenschaften, Berlin (1981).
6. Mňuk, M.: Algebraic and Geometric Approach to Parametrization of Rational Curves, Ph.D. Dissertation, RISC-Linz, J. Kepler Universität Linz, Austria (1995).
7. Mňuk, M., Sendra, J.R., Winkler, F.: On the Complexity of Parametrizing Curves. Beiträge zur Algebra und Geometrie 37/2 (1996) 309-328.
8. Nielson, G.M.: Cagd's Top Ten: What to Watch. IEEE Computer Graphics & Applications (Jan. 1993).
9. Peternell, M., Pottmaml, H.: Computing Rational Parametrizations of Canal Surfaces. J. Symbolic Comp. 23/2&3 (1996) 255-266.
10. Rose, H.E.: A Course in Number Theory, Clarendon Press, Oxford (1988).
11. Sendra, J.R., Winlder, F.: Symbolic Parametrization of Curves. J. Symbolic Comp. 12 (1991) 607-631.
12. Sendra, J.R., Winkler, F.: Parametrization of Algebraic Curves over Optimal Field Extensions. J. Symbolic Comp. 23/2&3 (1996) 191-207.
13. van Hoeij, M.: Rational Parametrization of Algebraic Curves using a Canonical Divisor. J. Symbolic Comp. 23/2&3 (1996) 209-227.
14. Walker, R.J.: Algebraic Curves, Princeton University Press (1950).