Abstract: Symbolology is the language that organizes the analytic structure of Feynman integrals and is encoded in the canonical
differential equations (CDE). Using the d log-bases and simple formulas for the first- and second-order contributions
to the intersection numbers, we give a streamlined procedure to compute the entries in the coefficient matrix of CDE,
including the symbol letters and the rational coefficients. We also provide a selection rule to decide whether a given
matrix element of CDE must be zero. This procedure shows that the symbol letters are deeply related to the poles of the
integrands, and also have interesting connections to the geometry of Newton polytopes. Our results relate the reduction
structure and the analytic structure of Feynman integral together and its simplicity hints at the possible underlying
structure in perturbative quantum field theories.
