  We give a brief re-exposition of the theory due to Pauli and Sinclair of
ramification polygons of Eisenstein polynomials over p-adic fields, their
associated residual polynomials and an algorithm to produce all extensions for
a given ramification polygon. We supplement this with an algorithm to produce
all ramification polygons of a given degree, and hence we can produce all
totally ramified extensions of a given degree.
