NDLI: Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve

Content Provider	IEEE Xplore Digital Library
Author	Huang, M.-D. Ierardi, D.
Copyright Year	1991
Description	Author affiliation: Dept. of Comput. Sci., Univ. of Southern California, Los Angeles, CA, USA (Huang, M.-D.; Ierardi, D.)
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.<>
Starting Page	678
Ending Page	687
File Size	789105
Page Count	10
File Format	PDF
ISBN	0818624450
DOI	10.1109/SFCS.1991.185435
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1991-10-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Jacobian matrices Polynomials Poles and zeros Computer science Elliptic curves Mathematics Terminology
Content Type	Text
Resource Type	Article

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