In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical systems, especially coupled cell networks. We describe invariant polydiagonal subspaces in terms of coloring vectors. This approach gives an easy formulation of a constraint satisfaction problem for finding invariant polydiagonal subspaces. Solving the resulting problem with existing state-of-the-art constraint solvers greatly outperforms the currently known algorithms.

翻译：在欧几里得空间的多对角子空间中，向量的某些分量相等（同步）或相反（反同步）。在矩阵作用下不变的多对角子空间在图论和动力系统，尤其是耦合单元网络中具有诸多应用。我们利用着色向量来描述不变的多对角子空间。该方法为寻找不变多对角子空间提供了一个易于表述的约束满足问题。使用现有最先进的约束求解器来解决由此产生的问题，其性能远超当前已知的算法。