We present algorithms and a C code to decide 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 (J. Phys. A: Math. Theor. 55 475301, 2022), 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 two to seven. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension two and higher, (ii) non-existence of negative subspaces of dimension three and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for ranks four, 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.

翻译：我们提出了算法和C代码，用于判定量子语境性并评估位于低秩二元辛极化空间中的多种点线几何结构的语境性程度（量化语境性的一种方式）。利用该代码，我们不仅更高效地复现了de Boutray等人近期论文（J. Phys. A: Math. Theor. 55 475301, 2022）的所有结果，还获得了一系列值得关注的新发现。本文首先描述算法及C代码，随后在秩从二到七的多个辛极化子空间上展示其效能。最具意义的新结果包括：（i）上下文为二维及以上子空间时构型的非语境性；（ii）三维及以上负子空间的不存在性；（iii）秩四椭圆与双曲二次曲面语境性度量的显著改进上界，以及三量子比特空间中某特定子几何（其上下文为该空间中的直线）的对应结果；（iv）垂线集的非语境性证明，以及（v）多量子比特"多利"构型中一类特殊子几何（称为双展形）的语境性本质及其语境性程度的计算。