Is there a database, a collection or library of parametric linear systems(equations) of the form $$Ax=b$$ where $A\in \mathbb{Z}[y_1,\cdots, y_m]^{n \times n}$ and $b \in \mathbb{Z}[y_1,\cdots, y_m]^{n}$ with $\det(A) \neq 0$ and $m,n \ge 1.$ Here $y_i$ are the parameters and $x_i$ are the variables.
In other words, I want the coefficient matrix and/or the right hand side vector to involve multivariate polynomial entries with integer or rational coefficients.
Any recommendation or suggestions where I can find them? I am particularly interested in real systems from applied science fields. I'd like to test the efficiency of my new solver on them.