values of variables from points in the polyhedron defined by a linear program

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SageMath provides a function for constructing the polyhedron defined by a linear program. Given a point in such a polyhedron, how can I tell which coordinate of the point corresponds to which variable of the linear program?

ADDED: The documentation suggests that "the polyhedron is built from the variables stored by the LP solver" and that "they usually match the ones created explicitly when defining the LP", except possibly for Gurobi solver. So, the question seems to reduce to finding the order number of each variable in LP (or an accurate bookkeeping of their creations). Things are even more fuzzy for Gurobi, which one of the best solvers out there.