  We provide evidence through two loops, that rational letters of
polylogarithmic Feynman integrals are captured by the Landau equations, when
the latter are recast as a polynomial of the kinematic variables of the
integral, known as the principal $A$-determinant. Focusing on one loop, we
further show that all square-root letters may also be obtained, by
re-factorizing the principal $A$-determinant with the help of Jacobi
identities. We verify our findings by explicitly constructing canonical
differential equations for the one-loop integrals in both odd and even
dimensions of loop momenta, also finding agreement with earlier results in the
literature for the latter case. We provide a computer implementation of our
results for the principal $A$-determinants, symbol alphabets and canonical
differential equations in an accompanying Mathematica file. Finally, we study
the question of when a one-loop integral satisfies the Cohen-Macaulay property
and show that for almost all choices of kinematics the Cohen-Macaulay property
holds. Throughout, in our approach to Feynman integrals, we make extensive use
of the Gel'fand, Graev, Kapranov and Zelevinski\u{\i} theory on what are now
commonly called GKZ-hypergeometric systems whose singularities are described by
the principal $A$-determinant.
