 |
Universität
des Saarlandes Mathematik und Informatik Prof. Dr. Frank-Olaf Schreyer |
Tel.: +49 (0)681/302-2785 schreyer@math.uni-sb.de Zi. 425, Geb. 27.1 D-66123 Saarbrücken |
Seminar on Computational and Algebraic Geometry
Kurt
Mehlhorn, Frank Olaf Schreyer
Winter Term
05/06
The aim of this seminar is to bring together knowledge from Computationaland Algebraic Geometry. Master students as well as PhD students are cordially invited to participate. We want to reach the frontier of current research in Exact Geometric Computing (EGC) and to develop some background knowledge in geometry of plane algebraic curves. During the last years Exact Geometric Computing has become an important topic in Computational Geometry. EGC studies the phenomenon of numerical non-robustness in geometric problems, especially when going from straight-line to curved objects, and provides robust and effective algorithmic solutions.
For preparation please have a look at the book by C.G. Gibson, Elementary Geometry of Algebraic Curves, Cambridge University Press, 2001.
| The Descartes method |
W. Krandick and K. Mehlhorn. New bounds for the Descartes method |
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| Bernstein polynomials | J. Hoschek, D. Lasser, Fundamentals of Computer Aided Geometric Design, Ak Peters, 1993, Chapter 4.1, additionally E-I. Prantsch, W. Boehm, M. Palusmy, Bezier and B-Spline Techniques, Springer Verlag, 2000; Chapters 2 and 3 |
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| The Descartes algorithm for polynomials with bitstream coefficients | A. Eigenwillig et al., A Descartes Algorithm for Polynomials with Bit-Stream Coefficients |
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Resultants and subresultants |
J. von zur Gathen, J. Gerhard, Modern Computer Algebra., Cambridge University Press, 1999, Chapter. 6 |
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Bezout's Theorem |
C.G. Gibson, Elementary Geometry of Algebraic Curves, Cambridge University Press, 2001, Chapter 14 |
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R. Seidel, N. Wolpert, On the Exact Computation of the Topology of Real Algebraic Curves |
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Puiseux Expansions |
R.J. Walker, Algebraic Curves, Springer-Verlag, 1978, Chapter 4.1 - 4.4, additionally E. Brieskorn, H. Knörrer, Ebene algebraische Kurven, Birkhäuser, 1981, Abschnitt III.8.3 |
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| Cremona Transformations | W. Decker, F.O. Schreyer, Varieties, Gröbner Bases, and Algebraic Curves, Manuscript, Sections 7.1, 7.2 |
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| Resolution of Singularities | W. Decker, F.O. Schreyer, Varieties, Gröbner Bases, and Algebraic
Curves, Manuscript, Sections 7.1, 7.2, additionally E. Brieskorn, H. Knörrer, Ebene algebraische Kurven, Birkhäuser, 1981, Abschnitt III.8.4 |
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If you are interested in participating, please contact schreyer@math.uni-sb.de and Christian Klein (MPI, Zi 321, cklein@mpi-sb.mpg.de).
The Seminar will take place Wedensday 16-18 in Geb. 46, Room 024, and starts on October 26, with an overview talk.
References
| Brieskorn, Knörrer | Ebene algebraische Kurven | Birkhäuser | 1981 |
| Decker, Schreyer | Varieties, Groebner Bases, and Algebraic Curves | This book manuscript in preparation might still contain many missprints. There will be updates frequently. |
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| Eigenwillig et al. | The Descartes algorithm for polynomials with bitstream coefficients |
|
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| Gibson | Elementary Geometry of Algebraic Curves | Cambridge University Press | 2001 |
| Hoschek, Lasser | Fundamentals of Computer Aided Geometric Design | Ak Peters | 1993 |
| Krandick and Mehlhorn |
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| Seidel, Wolpert |
On the Exact Computation of the Topology of Real Algebraic Curves |
|
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| von zur Gathen, Gerhard |
Modern Computer Algebra |
Cambridge University Press | 1999 |
| Walker | Algebraic Curves | Springer-Verlag | 1978 |
Hauptseite der Fachrichtung
Arbeitsgruppe Frank-Olaf Schreyer
