70,524 research outputs found
Algorithms for Lattice QCD with Dynamical Fermions
We consider recent progress in algorithms for generating gauge field
configurations that include the dynamical effects of light fermions. We survey
what has been achieved in recent state-of-the-art computations, and examine the
trade-offs between performance and control of systematic errors. We briefly
review the use of polynomial and rational approximations in Hybrid Monte Carlo
algorithms, and some of the theory of on-shell chiral fermions on the lattice.
This provides a theoretical framework within which we compare algorithmic
alternatives for their implementation; and again we examine the trade-offs
between speed and error control.Comment: Review presented at Lattice2004(plenary), Fermilab, June 21-26, 2004.
14 pages, 8 figure
Computing in Jacobians of projective curves over finite fields
We give algorithms for computing with divisors on projective curves over
finite fields, and with their Jacobians, using the algorithmic representation
of projective curves developed by Khuri-Makdisi. We show that many desirable
operations can be done efficiently in this setting: decomposing divisors into
prime divisors; computing pull-backs and push-forwards of divisors under finite
morphisms, and hence Picard and Albanese maps on Jacobians; generating
uniformly random divisors and points on Jacobians; computing Frobenius maps and
Kummer maps; and finding a basis for the -torsion of the Picard group, where
is a prime number different from the characteristic of the base field.Comment: 42 page
Fast algorithms for computing isogenies between elliptic curves
We survey algorithms for computing isogenies between elliptic curves defined
over a field of characteristic either 0 or a large prime. We introduce a new
algorithm that computes an isogeny of degree ( different from the
characteristic) in time quasi-linear with respect to . This is based in
particular on fast algorithms for power series expansion of the Weierstrass
-function and related functions
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