kzoacn/sum4cubes

---
license: mit
---

# A Heuristic Algorithm for the Sum of Four Cubes Problem

This repository contains the implementation code and dataset for the paper **"A Heuristic Algorithm for the Sum of Four Cubes Problem"** by Kaiyi Zhang, Zhuo Huang, Anyu Wang, and Xiaoyun Wang.

The project provides an efficient heuristic algorithm that transforms the Diophantine equation into a series of generalized Pell's equations to find integer solutions.

## Code

**File:** `sum4cubes.sage`

This script contains the SageMath implementation of the algorithm described in the paper. It includes the `solve(n)` function which attempts to find integers for a given .

### Important Requirement

**Please use the latest version of SageMath (Version 10.4 or higher).**
The algorithm relies on the `BinaryQF` solver. Older versions of SageMath have a significantly slower implementation of the integer solver, which will drastically impact performance.

### Usage

```python
# Example usage within SageMath
load("sum4cubes.sage")

# Solve for a specific integer (e.g., n = 254)
print(solve(254))
# Output: (-12, 13, 1, -6)

```

## Data

**Files:** `cubes-00.txt` — `cubes-99.txt`

These text files contain the pre-computed solutions for the sum of four cubes problem.

* The dataset covers instances up to 10^9.

* The data is split into 100 parts (`00` to `99`) for easier handling.

## Reference

If you use this code or data, please cite the original paper:

> Kaiyi Zhang, Zhuo Huang, Anyu Wang, and Xiaoyun Wang. "A Heuristic Algorithm for the Sum of Four Cubes Problem."