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迷向关系的dagger-紧致幺半范畴的完整表示。这为仿射约束经典力学系统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，我们通过一类特定的无向着色图来表示仿射拉格朗日关系。为了处理复合系统，我们引入了一种可扩展的强大符号表示，其中这些图的顶点本身由子图着色。在稳定子量子力学框架下，这种可扩展符号表示法能以极其简洁的方式描述图态，并且可通过“相蜘蛛融合”进行组合。同样，在电路的经典力学场景中，我们证明互易网络的阻抗矩阵本质上以相同方式表示。