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\begin{thebibliography}{10}
\bibitem{burnikel:exact:thesis}
C.~Burnikel.
\newblock {\em Exact Computation of {Voronoi} Diagrams and Line Segment
Intersections}.
\newblock Ph.{D} thesis, Universit{\"a}t des Saarlandes, March 1996.
\bibitem{bfms:easy:99}
C.~Burnikel, R.~Fleischer, K.~Mehlhorn, and S.~Schirra.
\newblock Exact geometric computation made easy.
\newblock In {\em Proc. 15th ACM Symp. Comp. Geom.}, pages 341--450, 1999.
\bibitem{mehlhorn-etal:sep-bd:00}
C.~Burnikel, R.~Fleischer, K.~Mehlhorn, and S.~Schirra.
\newblock A strong and easily computable separation bound for arithmetic
expressi ons involving radicals.
\newblock {\em Algorithmica}, 27:87--99, 2000.
\bibitem{bfs:exact-cascaded:01}
C.~Burnikel, S.~Funke, and M.~Seel.
\newblock Exact geometric computation using cascading.
\newblock {\em International J. Comp. Geometry and Applications},
11(3):245--266, 2001.
\newblock Special Issue.
\bibitem{bkmnsu:exact:95}
C.~Burnikel, J.~K{\"o}nnemann, K.~Mehlhorn, S.~N{\"a}her, S.~Schirra, and
C.~Uhrig.
\newblock Exact geometric computation in {LEDA}.
\newblock In {\em Proc. 11th ACM Symp. Computational Geom.}, pages C18--C19,
1995.
\bibitem{fortune-vanwyk:exact}
S.~J. Fortune and C.~J. van Wyk.
\newblock Efficient exact arithmetic for computational geometry.
\newblock In {\em Proc. 9th ACM Symp. on Computational Geom.}, pages 163--172,
1993.
\bibitem{fortune-vanwyk:static:96}
S.~J. Fortune and C.~J. van Wyk.
\newblock Static analysis yields efficient exact integer arithmetic for
computational geometry.
\newblock {\em ACM Transactions on Graphics}, 15(3):223--248, 1996.
\bibitem{klpy:core:98}
V.~Karamcheti, C.~Li, I.~Pechtchanski, and C.~Yap.
\newblock A core library for robust numeric and geometric computation.
\newblock In {\em Proc.~15th ACM Symp.~on Computational Geometry}, pages
351--359, June 1999.
\newblock Miami Beach, Florida.
\bibitem{kln:delaunay:91}
M.~Karasick, D.~Lieber, and L.~R. Nackman.
\newblock Efficient {D}elaunay triangulation using rational arithmetic.
\newblock {\em ACM Trans. on Graphics}, 10:71--91, 1991.
\bibitem{li-pion-yap:progress:04}
C.~Li, S.~Pion, and C.~Yap.
\newblock Recent progress in exact geometric computation.
\newblock {\em Journal of Logic and Algebraic Programming}, 2004.
\newblock To appear. Special issue on ``Practical Development of Exact Real
Number Computation''.
\bibitem{li-yap:constructiveBound:00}
C.~Li and C.~Yap.
\newblock A new constructive root bound for algebraic expressions.
\newblock In {\em Proc.~12th ACM-SIAM Symposium on Discrete Algorithms (SODA)},
pages 496--505. ACM and SIAM, Jan. 2001.
\bibitem{orourke:bk}
J.~O'Rourke.
\newblock {\em Computational Geometry in {C}}.
\newblock Cambridge University Press, second edition edition, 1998.
\bibitem{ouchi:thesis}
K.~Ouchi.
\newblock {Real/Expr}: Implementation of an exact computation package.
\newblock Master's thesis, New York University, Department of Computer Science,
Courant Institute, January 1997.
\bibitem{pion-yap:kary:03}
S.~Pion and C.~Yap.
\newblock Constructive root bound method for $k$-ary rational input numbers.
\newblock In {\em 19th ACM Symp. on Comp.Geometry}, pages 256--263, San Diego,
California., 2003.
\bibitem{schirra:robustness-survey:98}
S.~Schirra.
\newblock Robustness and precision issues in geometric computation.
\newblock Report MPI-I-98-1-004, Max-Planck-Institut f{\"u}r Informatik,
Saarbr{\"u}cken, Germany, Jan 1998.
\newblock To appear in {\em Handbook on Computational Geometry}, edited by
J.R.~Sack and J.~Urrutia.
\bibitem{shewchuk:adaptive:96}
J.~R. Shewchuk.
\newblock Robust adaptive floating-point geometric predicates.
\newblock In {\em Proc.~12th ACM Symp.~on Computational Geom.}, pages 141--150.
Association for Computing Machinery, May 1996.
\bibitem{tyl:zero-test:00}
D.~Tulone, C.~Yap, and C.~Li.
\newblock Randomized zero testing of radical expressions and elementary
geometry theorem proving.
\newblock In {\em International Workshop on Automated Deduction in Geometry
(ADG'00), Zurich, Switzerland}, Sept. 2000.
\newblock Preprint: {\tt ftp://cs.nyu.edu/pub/local/yap/exact/}.
\bibitem{yap:brown-cgc:98}
C.~Yap.
\newblock A new number core for robust numerical and geometric libraries.
\newblock In {\em 3rd CGC Workshop on Geometric Computing}, 1998.
\newblock Invited Talk. Brown University, Oct 11--12, 1998. Abstracts, {\tt
http://www.cs.brown.edu/cgc/cgc98/home.html}.
\bibitem{yap:exact}
C.~K. Yap.
\newblock Towards exact geometric computation.
\newblock {\em Computational Geometry: Theory and Applications}, 7:3--23, 1997.
\bibitem{yap:algebra-bk}
C.~K. Yap.
\newblock {\em Fundamental Problems in Algorithmic Algebra}.
\newblock Oxford University Press, 2000.
\newblock A version is available at URL {\tt
ftp:/Preliminary/cs.nyu.edu/pub/local/yap/algebra-bk}.
\bibitem{yap:crc}
C.~K. Yap.
\newblock Robust geometric computation.
\newblock In J.~E. Goodman and J.~O'Rourke, editors, {\em Handbook of Discrete
and Computational Geometry}, chapter~41, pages 927--952. Chapmen \& Hall/CRC,
Boca Raton, FL, 2nd edition, 2004.
\newblock Expanded from 1997 version.
\bibitem{yap-dube:paradigm}
C.~K. Yap and T.~Dub\'e.
\newblock The exact computation paradigm.
\newblock In D.-Z. Du and F.~K. Hwang, editors, {\em Computing in Euclidean
Geometry}, volume~1 of {\em Lecture Notes Series on Computing}, pages
452--492. World Scientific, Singapore, 2nd edition, 1995.
\end{thebibliography}
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