If S is the Weierstrass semigroup S of a point p on a Riemann surface C, then the vanishing sequence (v_0,\dots, v_(g-1)) of the canonical series at p is the list of orders of vanishing of differential forms at p, and the ramification sequence at p is (v_0 - 0, v_1 - 1, .. ,v_(g-1) - (g-1)). The weight of the Weierstrass point p is the sum of the ramification sequence at p.
The vanishing sequence can be computed from the set G of gaps in S as v_i = G_i - 1, so the weight is sum(G_i - 1 - i) or as the number of pairs (a,b) such that a is in S, b is a gap, and a < b.
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The effective weight ewt is the number of such pairs where a is a minimal generator of S; this may be a better measure.
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The object weight is a method function.