Computing the Abel map

Physica D: Nonlinear Phenomena

Volumn 237, Issue 24, 2008, Pages 3214-3232

  Deconinck, Bernard ^a   Patterson, Matthew S ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Abel map; Algebraic curve; Computation; Riemann surface

Indexed keywords

CALCULATIONS; DIFFERENTIAL EQUATIONS;

ABEL MAP; ALGEBRAIC CURVES; ARBITRARY DEGREE; INTEGRABLE EQUATIONS; NUMERICAL COMPUTATIONS; PLANE ALGEBRAIC CURVES; RESEARCH PROGRAMS; RIEMANN SURFACES;

ALGEBRA;

EID: 55149115379     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.08.007     Document Type: Article

References (26)

1. Ablowitz M.J., and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press, Cambridge
2. Ablowitz M.J., and Segur H. Solitons and the Inverse Scattering Transform (1981), Society for Industrial and Applied Mathematics, Philadelphia, PA
3. Belokolos E.D., Bobenko A.I., Enol'skii V.Z., Its A.R., and Matveev V.B. Algebro-Geometric Approach to Nonlinear Integrable Problems. Springer Series in Nonlinear Dynamics (1994), Springer-Verlag, Berlin
4. Bliss G.A. Algebraic Functions (1966), Dover Publications Inc, New York, NY
5. 3 in terms of theta-functions. Math. Ann. 290 (1991) 209-245
6. Bobenko A.I., and Bordag L.A. Periodic multiphase solutions of the Kadomtsev-Petviashvili equation. J. Phys. A 22 (1989) 1259-1274
7. Compoint E., and Singer M.F. Computing Galois groups of completely reducible differential equations. J. Symbolic Comput. 28 (1999) 473-494
8. Davenport J.H. On the Integration of Algebraic Functions. Lecture Notes in Computer Science vol. 102 (1981), Springer-Verlag, Berlin
9. Davenport J.H., and Trager B.M. On the parallel Risch algorithm. II. ACM Trans. Math. Software 11 4 (1985) 356-362
10. Deconinck B., Heil M., Bobenko A., van Hoeij M., and Schmies M. Computing Riemann theta functions. Math. Comput. 73 (2004) 1417-1442
11. B. Deconinck, M.S. Patterson, Computing the vector of Riemann constants, 2008 (in preparation)
12. Deconinck B., and Segur H. The KP equation with quasiperiodic initial conditions. Physica D 123 (1998) 123-152
13. Deconinck B., and van Hoeij M. Computing Riemann matrices of algebraic curves. Physica D 152/153 (2001) 28-46
14. Dubrovin B.A. Theta functions and nonlinear equations. Russian Math. Surveys 36 2 (1981) 11-80
15. N.D. Elkies, http://www.math.harvard.edu/~elkies/g2_tors.html
16. Farkas H.M., and Kra I. Riemann Surfaces. second edition (1992), Springer-Verlag, New York, NY
17. Flynn E.V. Large rational torsion on abelian varieties. J. Number Theory 36 3 (1990) 257-265
18. Soliton theory: A survey of results. In: Fordy A.P. (Ed). Nonlinear Science: Theory and Applications (1990), Manchester University Press, Manchester
19. Griffiths P. Introduction to Algebraic Curves (1989), American Mathematical Society, Providence, RI
20. Griffiths P., and Harris J. Principles of Algebraic Geometry (1994), John Wiley & Sons Inc, New York, NY
21. Lenstra A.K., Lenstra Jr. H.W., and Lovász L. Factoring polynomials with rational coefficients. Math. Ann. 261 (1982) 515-534
22. Mumford D. Tata lectures on theta. I. Progress in Mathematics (1983), Birkhäuser Boston Inc, Boston, MA
23. Risch R.H. The problem of integration in finite terms. Trans. Amer. Math. Soc. 139 (1969) 167-189
24. Risch R.H. The solution of the problem of integration in finite terms. Bull. Amer. Math. Soc. 76 (1970) 605-608
25. Springer G. Introduction to Riemann Surfaces (1957), Addison-Wesley Publishing Company, Inc, Reading, MA
26. van Hoeij M. An algorithm for computing an integral basis in an algebraic function field. J. Symbolic. Comput. 18 (1994) 353-363