  We reformulate the analysis of singularities of Feynman integrals in a way
that can be practically applied to perturbative computations in the Standard
Model in dimensional regularization. After highlighting issues in the textbook
treatment of Landau singularities, we develop an algorithm for classifying and
computing them using techniques from computational algebraic geometry. We
introduce an algebraic variety called the principal Landau determinant, which
captures the singularities even in the presence of massless particles or UV/IR
divergences. We illustrate this for 114 example diagrams, including a
cutting-edge 2-loop 5-point non-planar QCD process with multiple mass scales.
The algorithms introduced in this work are implemented in the open-source Julia
package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.
