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Band-aid for zero precisions
For now, set zero precisions to 1, in the future we'll understand the theory better as to why this happens. Also add a test.
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src/ZetaFunction.jl

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@@ -188,6 +188,7 @@ function precision_information(f,basis,verbose=0)
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#N_m = series_precision(r_m, p, n) # series precision
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#M = algorithm_precision(r_m, N_m, p)
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N_m = series_precision(p,n,d,r_m)
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N_m[N_m .== 0] .= 1 #TODO: understand the meaning of zero precision better
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M = algorithm_precision(p,n,d,r_m,N_m)
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(hodge_polygon,r_m,N_m,M)

test/varieties/othersurfaces.csv

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n;p;f;zeta_function
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4;13;x1^3 + x2^3 + x3^3 + x4^3;ZZRingElem[4826809, -2227758, 428415, -43940, 2535, -78, 1]
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4;11;x1^3 + x2^3 + x3^3 + x4^3;ZZRingElem[-1771561, 0, 43923, 0, -363, 0, 1]
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4;13;x1^5 + x2^5 + x3^5 + x4^5;ZZRingElem[-8415003868347247618489696679505181495471801448798649088081,0,0,0,3830224792147131369362629348887201408953937846517364173,0,0,0,-804640900279499604921948674532516664462855890168558,0,0,0,103299953352175993535957371005423284771674833886,0,0,0,-9042046265202198236752684692887441333608315,0,0,0,569856912480793978717651078295486656647,0,0,0,-26603032689368671905402522241074036,0,0,0,931446121962419799916057639476,0,0,0,-24459388378271588877736887,0,0,0,475772875565973586315,0,0,0,-6663252345029566,0,0,0,63626996238,0,0,0,-371293,0,0,0,1]

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