We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality degree (a way to quantify contextuality) for a variety of point-line geometries located in binary symplectic polar spaces of small rank. With this code we were not only able to recover, in a more efficient way, all the results of a recent paper by de Boutray et al [(2022). Journal of Physics A: Mathematical and Theoretical 55 475301], but also arrived at a bunch of new noteworthy results. The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from 2 to 7. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension 2 and higher, (ii) non-existence of negative subspaces of dimension 3 and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for rank 4, as well as for a particular subgeometry of the three-qubit space whose contexts are the lines of this space, (iv) proof for the non-contextuality of perpsets and, last but not least, (v) contextual nature of a distinguished subgeometry of a multi-qubit doily, called a two-spread, and computation of its contextuality degree. Finally, in the three-qubit polar space we correct and improve the contextuality degree of the full configuration and also describe finite geometric configurations formed by unsatisfiable/invalid constraints for both types of quadrics as well as for the geometry whose contexts are all 315 lines of the space.

翻译：我们提出了算法和C语言代码，用于揭示量子上下文性并评估位于低秩二元辛极空间中的各类点线几何结构的上下文性度（一种量化上下文性的方法）。利用该代码，我们不仅能够以更高效率复现de Boutray等人近期论文[(2022). Journal of Physics A: Mathematical and Theoretical 55 475301]的所有结果，还获得了一系列值得关注的新结论。本文首先描述算法与C代码实现，随后通过在秩为2至7的辛极空间子空间上的应用展示其效能。最重要的新发现包括：（i）维度为2及以上的子空间构成构型的非上下文性；（ii）维度为3及以上的负子空间不存在性；（iii）针对秩为4的椭圆与双曲二次曲面，以及以三量子比特空间所有直线为上下文的特定子几何结构，其上下文性度界的显著改进；（iv）垂直集非上下文性的证明；（v）多量子比特doily结构中被称为二展形的特殊子几何的上下文性本质及其上下文性度计算。最后，我们在三量子比特极空间中修正并改进了完整构型的上下文性度，同时描述了由不可满足/无效约束构成的有限几何构型，涵盖两类二次曲面以及以空间全部315条直线为上下文的几何结构。