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 # Gauge-invariant discretization
 
 We do the discretization of the Usadel equation as follows. We first
-discretize the action $`S`$, and derive the discrete saddle-point
-equation from the discretized action. This simplifies things somewhat,
-because proper handling of the gauge fields is simpler to do
-in the action formulation.
+discretize the action $`S`$. The discrete saddle-point equation or expressions
+for currents are not derived analytically, but instead obtained from the computer
+implementation of the action via automatic differentiation (AD).
+This simplifies things somewhat, because proper handling of the gauge fields is
+simpler to do in the action formulation.
 
 The action is
 ```math