This project has been archived by its maintainers, and is no longer receiving any updates.
Enumerates lattice points $\{x\in\mathbb{Z}^{\text{dim}}: Hx\geq\text{rhs}\}$ for $H\in\mathbb{Z}^{N,\text{dim}}$ and $\text{rhs}\in\mathbb{Z}$.
The main use case is for finding lattice points in convex cones, for which $H$ are the inwards-facing hyperplanes. If $\text{rhs}=0$, this will find lattice points in the cone, including its boundary. If $\text{rhs}=1$, then this only finds lattice points in the strict interior of the cone.
Installation
pip install -e .
Requires a C compiler and Cython. NumPy must be installed first.
Algorithm Notes
This repo contains a Cython wrapper of a C implementation of Kannan's algorithm. See this webpage for some other relevant work. The core algorithm enumerates lattice points in square boxes $|x_i|\leq B$ for $B\geq 1$. I.e.,
$$ \{x\in\mathbb{Z}^{\text{dim}}: Hx\geq\text{rhs} \text{ and } |x|_\infty \leq B\}. $$
A helper method is provided in case the user wants $N$ points but doesn't care about box size. In this case, boxes of increasing sizes are studied until $\geq N$ lattice points are found.
Usage
The primary interface is enum_lattice_points, which handles box sizing automatically:
import numpy as np
from conevecs import enum_lattice_points
H = np.array([[1, 2], [3, -1]], dtype=np.int32)
rhs = 1
# Find at least 1000 lattice points in {H @ x >= rhs}
pts = enum_lattice_points(H=H, rhs=rhs, min_N_pts=1000)
# Optionally restrict to primitive vectors (GCD = 1)
pts = enum_lattice_points(H=H, rhs=rhs, min_N_pts=1000, primitive=True)
For direct control over the box size, box_enum enumerates all lattice points in $\{Hx \geq \text{rhs},\ |x|_\infty \leq B\}$:
from conevecs import box_enum
pts, status = box_enum(B=5, H=H, rhs=rhs, max_N_out=10_000)
# status: 0 = success, -1 = dim>256, -2 = hit max_N_out, -3 = hit max_N_iter
Organization
conevecs/
├── conevecs/
│ ├── box_enum.h # STB-style library for the Kannan enumeration
| ├── box_enum.pyx # Cython wrapper
| └── conevecs.py # a wrapper for box_enum, increasing box size until N points are found
├── tests/
│ ├── conftest.py # shared test helpers (pytest)
│ ├── test_box_enum.py # generic tests
│ ├── test_manwe.py # tests relating to 'Manwe' https://arxiv.org/abs/2406.13751
│ ├── test_enum_lattice_points.py # tests for enum_lattice_points
│ ├── benchmark_box_enum.py # B-dilation benchmark for 'Manwe'
│ ├── benchmark_enum_lattice_points.py # N-scaling benchmark for 'Manwe'
| └── c/ # simple C-kernel tests (no Python interface)
├── pyproject.toml
└── setup.py
Metadata
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