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COMPGEOM
2005
ACM
15 years 6 months ago
On the exact computation of the topology of real algebraic curves
We consider the problem of computing a representation of the plane graph induced by one (or more) algebraic curves in the real plane. We make no assumptions about the curves, in p...
Raimund Seidel, Nicola Wolpert
ANTS
2008
Springer
106views Algorithms» more  ANTS 2008»
15 years 6 months ago
Computing in Component Groups of Elliptic Curves
Let K be a p-adic local field and E an elliptic curve defined over K. The component group of E is the group E(K)/E0(K), where E0(K) denotes the subgroup of points of good reduction...
J. E. Cremona
MICS
2010
102views more  MICS 2010»
15 years 2 months ago
Computing Zeta Functions of Superelliptic Curves in Larger Characteristic
Abstract. Following Gaudry and G¨urel who extended Kedlaya’s point-counting algorithm to superelliptic curves, we introduce Harvey’s running time improvements for large enough...
Moritz Minzlaff
DCC
2011
IEEE
14 years 11 months ago
Computing bilinear pairings on elliptic curves with automorphisms
In this paper, we present a novel method for constructing a super-optimal pairing with great efficiency, which we call the omega pairing. The computation of the omega pairing requi...
Changan Zhao, Dongqing Xie, Fangguo Zhang, Jingwei...
COMPGEOM
1989
ACM
15 years 8 months ago
Computing the Irreducible Real Factors and Components of an Algebraic Curve
We present algorithms that decompose an algebraic curve with rational coefficients in its defining bivariate equation into its irreducible real factors and its non-empty irreducib...
Erich Kaltofen