Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the...
For the families ax4 = by4 +z4 +v4 +w4 , a, b = 1, . . . , 100, and ax3 = by3 + z3 + v3 + w3 , a, b = 1, . . . , 100, of projective algebraic threefolds, we test numerically the co...
We propose a practical sampling reduction algorithm for lattice bases based on work by Schnorr [1] as well as two even more effective generalizations. We report the empirical behav...
Abstract. We describe the invariants of plane quartic curves -- nonhyperelliptic genus 3 curves in their canonical model -- as determined by Dixmier and Ohno, with application to t...