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：我们提出了算法及C语言代码，用于判定量子上下文性并评估二元辛极空间中小秩点线几何的上下文程度（量化上下文性的一种方式）。利用该代码，我们不仅更高效地重现了de Boutray等人近期论文（J. Phys. A: Math. Theor. 55 475301, 2022）的全部结果，还获得了一系列值得关注的创新成果。本文首先阐述算法与C代码实现，随后在秩数从二到七的多个辛极子空间上展示其效能。最具吸引力的新结果包括：(i) 上下文为二维及以上子空间的构型具有非上下文性；(ii) 三维及以上负子空间不存在性；(iii) 四秩椭圆与双曲二次曲面上下文程度显著改进的界，以及三量子比特空间中特定子几何（其上下文为该空间中的直线）的对应结果；(iv) 垂线集的非上下文性证明，以及最后但同等重要的；(v) 多量子比特多利构型中特定子几何（称为双展形）的上下文性质及其上下文程度的计算。