Computational Algebra Seminar

We survey some recent additions and improvements to various functionality in MAGMA related to number theory. In particular, we will discuss: descent on elliptic curves, Heegner points on elliptic curves, a new method for computing the Weierstrass p-function, and the MAGMA implementation of LLL for indefinite Gram matrices (with particular consideration of nonzero isotropic vectors). Most of these functions require high-precision real-number calculations, and thus we will also give some comments regarding MAGMA's new real/complex numbers.