Realization space

The realization space of $M$ parametrizes the matrices whose column matroid is $M$, up to the natural symmetries. As in OSCAR's MatroidRealizationSpace, a reference basis is fixed and its columns are normalized to the identity. What remains is a chart, given by:

• a polynomial ring over $\mathbb Z$ in variables $x_1,\dots,x_m$;
• a defining ideal $I$ (coming from the non-basis minors);
• inequations: polynomials (basis minors) that must be nonzero;
• a realization matrix with entries in the ring.

The space is $V(I)$ with the zero sets of the inequations removed. For rigid matroids there are no variables, and the ideal is an ideal of $\mathbb Z$, e.g. $(2)$ for the Fano matroid. The ideal $(0)$ means the space is free.

Full details: docs/my_realization_space.md, docs/concrete_realization.md.