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MAGMA Computational Algebra System

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Algebraic Geometry

Computational Methods

14-04, 14Qxx

[1] Fatima K. Abu Salem and Kamal Khuri-Makdisi. Fast Jacobian group operations for C3, 4 curves over a large finite field. LMS J. Comput. Math., 10:307–328 (electronic), 2007.
[2] S. Arita, S. Miura, and T. Sekiguchi. An addition algorithm on the Jacobian varieties of curves. J. Ramanujan Math. Soc., 19(4):235–251, 2004.
[3] Tobias Beck and Josef Schicho. Adjoint computation for hypersurfaces using formal desingularizations. Journal of Algebra, 320(11):3984 – 3996, 2008.
[4] Tobias Beck and Josef Schicho. Curve parametrization over optimal field extensions exploiting the Newton polygon. In Geometric Modeling and Algebraic Geometry, pages 119–140. Springer, Berlin, 2008.
[5] Gavin Brown. A database of polarized K3 surfaces. Experiment. Math., 16(1):7–20, 2007.
[6] Gavin Brown and Daniel Ryder. Elliptic fibrations on cubic surfaces. Journal of Pure and Applied Algebra, In Press, 2009.
[7] Gavin Brown and Kaori Suzuki. Computing certain Fano 3-folds. Japan J. Indust. Appl. Math., 24(3):241–250, 2007.
[8] Laurent Busé and Marc Chardin. Implicitizing rational hypersurfaces using approximation complexes. J. Symbolic Comput., 40(4-5):1150–1168, 2005.
[9] Gweltaz Chatel and David Lubicz. A point counting algorithm using cohomology with compact support. arXiv:0805.4689v1 [math.AG], 32 pages, 2008.
[10] David A. Cox, John Little, and Donal O'Shea. Using Algebraic Geometry, volume 185 of Graduate Texts in Mathematics. Springer, New York, second edition, 2005.
[11] Willem A. de Graaf. Constructing algebraic groups from their Lie algebras. J. Symbolic Comput., 44(9):1223–1233, 2009.
[12] Wolfram Decker and Christoph Lossen. Computing in algebraic geometry, volume 16 of Algorithms and Computation in Mathematics. Springer-Verlag, Berlin, 2006.
[13] André Galligo and David Rupprecht. Irreducible decomposition of curves. J. Symbolic Comput., 33(5):661–677, 2002.
[14] Ralf Gerkmann, Mao Sheng, and Kang Zuo. Computational details on the disproof of modularity. arXiv:0709.1054v1, 16 pages, 2007.
[15] Martine Girard and Leopoldo Kulesz. Computation of sets of rational points of genus-3 curves via the Demjanenko-Manin method. LMS J. Comput. Math., 8:267–300 (electronic), 2005.
[16] Massimo Giulietti. Algebraic curves over finite fields and MAGMA. Ital. J. Pure Appl. Math., (8):19–32, 2000.
[17] Michael Harrison and Josef Schicho. Rational parametrisation for degree 6 Del Pezzo surfaces using Lie algebras. In ISSAC 2006, pages 132–137. ACM, New York, 2006.
[18] Hendrik Hubrechts. Memory efficient hyperelliptic curve point counting. arXiv:math.NT/0609032, 10 pages, 2006.
[19] Gabriela Jeronimo, Teresa Krick, Juan Sabia, and Martín Sombra. The computational complexity of the Chow form. Found. Comput. Math., 4(1):41–117, 2004.
[20] Tanja Lange. Formulae for arithmetic on genus 2 hyperelliptic curves. Appl. Algebra Engrg. Comm. Comput., 15(5):295–328, 2005.
[21] Alan G. B. Lauder. A recursive method for computing zeta functions of varieties. LMS J. Comput. Math., 9:222–269 (electronic), 2006.
[22] Walter D. Neumann and Penelope G. Wightwick. Algorithms for polynomials in two variables. In Combinatorial and Computational Algebra (Hong Kong, 1999), volume 264 of Contemp. Math., pages 219–235. Amer. Math. Soc., Providence, RI, 2000.
[23] Jana Pílniková. Parametrizing algebraic varieties using Lie algebras. arXiv:math.AG/0610727, 74 pages, 2006.
[24] Carlos Rito. On equations of double planes with pg = q = 1. arXiv:0804.2227v1 [math.AG], 18 pages, 2008.
[25] Mohab Safey El Din. Testing sign conditions on a multivariate polynomial and applications. Math. Comput. Sci., 1(1):177–207, 2007.
[26] Mohab Safey El Din and Éric Schost. Properness defects of projections and computation of at least one point in each connected component of a real algebraic set. Discrete Comput. Geom., 32(3):417–430, 2004.
[27] Tanush Shaska. Computational algebra and algebraic curves. Comm. Comp. Alg., 37(4):117–124, 2003.
[28] Dongming Wang. Decomposing algebraic varieties. In Automated Deduction in Geometry (Beijing, 1998), volume 1669 of Lecture Notes in Comput. Sci., pages 180–206. Springer, Berlin, 1999.

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