Asymptotically fast group operations on Jacobians of general curves

ABRAMOVICH D, 1996, INT MATH RES NOTICES, P1005; Aho A. V., 1975, DESIGN ANAL COMPUTER; Becker T., 1993, GRADUATE TEXTS MATH, V141; BRAWLEY J, 2004, DENSITY PRIMITIXE EL; BURGISSERR P, 1997, FUNDAMENTALS PRICNIP, V315; CANTOR DG, 1987, MATH COMPUT, V48, P95, DOI 10.2307-2007876; CHOW WL, 1954, AM J MATH, V76, P453, DOI 10.2307-2372585; COPPERSMITH D, 1990, J SYMB COMPUT, V9, P251, DOI 10.1016-S0747-7171(08)80013-2; DECKER WOLFRAM, 1999, ALGORITHMIC ALGEBRA, P187; Eberly W, 2000, J SYMB COMPUT, V29, P441, DOI 10.1006-jsco.1999.0308; GREG W, 2002, ADV MATH, V172, P169; Griffiths P., 1994, PRINCIPLES ALGEBRAIC; Hartshorne Robin, 1977, ALGEBRAIC GEOMETRY; HESS F, 1999, THESIS TECHNISCHE U; Hess F, 2002, J SYMB COMPUT, V33, P425, DOI 10.1006-jsco.2001.0513; HUANG MD, 1994, J SYMB COMPUT, V18, P519, DOI 10.1006-jsco.1994.1063; Kemper G, 2002, J SYMB COMPUT, V34, P229, DOI 10.1006-jsco.2002.0560; KEMPER G, 2004, MATH COMPUT, V73, P245; KHURIMAKDISI K, 2004, ASYMPTOTICALLY FAST; LAZARSFELD R, 1989, SAMPLING VECTOR BUND, P500; *PARI GROUP, BORD PARI GP; Stein W., MODULAR FORMS DATABA; Volcheck E., 1994, LECT NOTES COMPUTER, V877, P221

[1]  Gerhard Pfister,et al.  Primary Decomposition: Algorithms and Comparisons , 1997, Algorithmic Algebra and Number Theory.

[2]  D. Cantor.  Computing in the Jacobian of a hyperelliptic curve , 1987 .

[3]  B. Saint-Donat,et al.  On Petri's analysis of the linear system of quadrics through a canonical curve , 1973 .

[4]  Ming-Deh A. Huang,et al.  Efficient Algorithms for the Riemann-Roch Problem and for Addition in the Jacobian of a Curve , 1994, J. Symb. Comput..

[5]  Volker Strassen,et al.  Algebraic Complexity Theory , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[6]  Mark Giesbrecht,et al.  Efficient Decomposition of Associative Algebras over Finite Fields , 2000, J. Symb. Comput..

[7]  Kamal Khuri-Makdisi.  Linear algebra algorithms for divisors on an algebraic curve , 2004, Math. Comput..

[8]  Gregor Kemper.  The Calculation of Radical Ideals in Positive Characteristic , 2002, J. Symb. Comput..

[9]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[10]  ON DENSITY OF PRIMITIVE ELEMENTS FOR FIELD EXTENSIONS , 2004 .

[11]  Michael Clausen,et al.  Algebraic complexity theory , 1997, Grundlehren der mathematischen Wissenschaften.

[12]  Emil J. Volcheck.  Computing in the jacobian of a plane algebraic curve , 1994, ANTS.

[13]  Robert Lazarsfeld,et al.  A Sampling of Vector Bundle Techniques in the Study of Linear Series , 1989 .

[14]  Florian Hess,et al.  Computing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics , 2002, J. Symb. Comput..

[15]  Wei-Liang Chow,et al.  The Jacobian Variety of an Algebraic Curve , 1954 .

[16]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[17]  Joe W. Harris,et al.  Principles of Algebraic Geometry: Griffiths/Principles , 1994 .

[18]  임종인,et al.  Gröbner Bases와 응용 , 1995 .

[19]  A. Meyers.  Reading , 1999, Language Teaching.

[20]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[21]  T. Willmore.  Algebraic Geometry , 1973, Nature.

[22]  Marvin Tretkoff,et al.  Introduction to the Arithmetic Theory of Automorphic Functions , 1971 .

[23]  D. Abramovich.  A linear lower bound on the gonality of modular curves , 1996, alg-geom/9609012.