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共各向同性关系的dagger-紧凑道具的完整表示。这为仿射约束的经典力学系统以及奇素数维稳定子量子电路提供了统一的图形语言家族。为此，我们通过特定类别的无向着色图来呈现仿射拉格朗日关系。为了推理复合系统，我们引入了一种强大的可缩放符号表示，其中这些图的顶点本身由图形着色。在稳定子量子力学的框架中，这种可缩放符号提供了图态的极简描述，可通过“相蛛融合”进行组合。同样地，在经典力学的电路系统中，我们展示了互易网络的阻抗矩阵本质上以相同方式呈现。