We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits. To this end, we present affine Lagrangian relations by a particular class of undirected coloured graphs. In order to reason about composite systems, we introduce a powerful scalable notation where the vertices of these graphs are themselves coloured by graphs. In the setting of stabiliser quantum mechanics, this scalable notation gives an extremely concise description of graph states, which can be composed via ``phased spider fusion.'' Likewise, in the classical mechanical setting of electrical circuits, we show that impedance matrices for reciprocal networks are presented in essentially the same way.

翻译：我们给出了任意域上仿射拉格朗日关系和余同位关系的dagger-compact props的完整表示。这为仿射约束经典力学系统以及奇素数维稳定子量子电路提供了一组统一的图形语言。为此，我们通过一类特定的无向彩色图来表示仿射拉格朗日关系。为了推理复合系统，我们引入了一种强大的可扩展记法，其中这些图的顶点本身由彩色图着色。在稳定子量子力学的情境中，这种可扩展记法提供了图态的极其简洁的描述，这些图态可以通过“相位蜘蛛融合”进行组合。同样，在电路的经典力学情境中，我们展示了互易网络的阻抗矩阵基本上以相同的方式呈现。