Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gr\"obner bases. This algorithm avoids the use of elimination, homological algebra and processing the input equations one-by-one present in previous algorithms. We experimentally demonstrate the practical interest of our algorithm compared to the state of the art.

翻译：基于Vasconcelos定理，我们提出了一种利用Gröbner基进行syzygy计算以实现代数集等维分解的算法。该算法避免了以往算法中使用的消元法、同调代数以及逐条处理输入方程的方法。通过实验，我们证明了本算法相较于现有技术具有实际应用价值。