  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.
