Laguerre geometry provides a simple approach to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from...
We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-ra...
Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
Abstract. We generalize Ehrhart's idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n + 1...