[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 678-687

M.-D. Huang , Dept. of Comput. Sci., Univ. of Southern California, Los Angeles, CA, USA

D. Ierardi , Dept. of Comput. Sci., Univ. of Southern California, Los Angeles, CA, USA

ABSTRACT

Several computational problems concerning the construction of rational functions and intersecting curves over a given curve are studied. The first problem is to construct a rational function with prescribed zeros and poles over a given curve. More precisely, let C be a smooth projective curve and assume as given an affine plane model F(x,y)=0 for C, a finite set of points P/sub i/=(X/sub i/, Y/sub i/) with F (X/sub i/, Y/sub i/)=0 and natural numbers n/sub i/, and a finite set of points Q/sub i/=(X/sub j/, Y/sub j/) with F(X/sub j/, Y/sub j/)=0 and natural numbers m/sub j/. The problem is to decide whether there is a rational function which has zeros at each point P/sub i/ of order n/sub i/, poles at each Q/sub j/ of order m/sub j/, and no zeros or poles anywhere else on C. One would also like to construct such a rational function if one exists. An efficient algorithm for solving this problem when the given plane curve has only ordinary multiple points is given.

INDEX TERMS

ordinary multiple points, Riemann-Roch problem, Jacobian, rational functions, intersecting curves, zeros and poles, smooth projective curve, affine plane model, natural numbers, plane curve

CITATION

D. Ierardi and M. Huang, "Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve,"

*[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS)*, San Juan, Puerto Rico, 1991, pp. 678-687.

doi:10.1109/SFCS.1991.185435

CITATIONS