Tenth Algorithmic Number Theory Symposium ANTSX

Solving quadratic equations in dimension 5 or more without factoring
Pierre Castel
Abstract: Let Q be a 5 x 5 symmetric matrix with integral entries and with det Q != 0, but neither positive nor negative definite. We describe a probabilistic algorithm which solves the equation x^t Q x = 0 over Z without factoring det Q. The method can easily be generalized to forms of higher dimensions by reduction to a suitable subspace.
Files available: paper (PDF), slides
© 201112 Kiran S. Kedlaya (with thanks to Pierrick Gaudry and Emmanuel ThomÃ©)
XHTML 1.1 valid, CSS valid
XHTML 1.1 valid, CSS valid