Two Neighbours and Hermitian Neighbours in C++

TwoNeighbours is an ongoing project to bring the Two Neighbours of B. Hemkemeier (TN) and the Hermitian Neighbours of A. Schiemann (HN) back to life. Written in modern C++, using parallel algorithms whenever possible and with CUDA support, TwoNeighbours is an algebra system with a focus on algorithms for integral lattices.

Documentation

An automatically created Doxygen documentation can be found here.

Currently Working On

Algorithms for group operations, especially parallel partition backtracking.

Bibliography

Construction of Lattices

• [CH1] Cohen H. --- A Course in Computational Algebraic Number Theory
• [HB] Hemkemeier, B. --- Algorithmische Konstruktion von Gittern
• [HV1] Hemkemeier, B. and Vallentin F. --- On the Decomposition of Lattices
• [HV2] Hemkemeier, B. and Vallentin F. --- Incremental Algorithms for Lattice Problems
• [SE] Schnorr C. P. and Euchner M. --- Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems

Lattices over Imaginary Quadratic Number Fields

• [BG] Bellot, G. --- Algorithmen für Isometrie von Gittern
• [GL] Gerstein, L. J. --- Integral Decomposition of Hermitian Forms
• [JM] Jürgens, M. --- Nicht-Existenz und Konstruktion extremaler Gitter
• [JR] Jacobowitz, R. --- Hermitian Forms over Local Fields
• [SA] Schiemann, A. --- Classification of Hermitian Forms with the Neighbour Method

The Lattice Isometry Problem

• [BG] Bellot, G. --- Algorithmen für Isometrie von Gittern
• [LJ1] Leon, J. S. --- Permutation Group Algorithms Based on Partitions
• [LJ2] Leon, J. S. --- Partitions, Refinements, and Permutation Group Computation
• [PS] Plesken W. and Souvignier, B. --- Computing Isometries of Lattices
• [RH] Regev O. and Haviv I. --- On the Lattice Isomorphism Problem