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Some tweaks for p-adic regulators #1301

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Nov 29, 2023
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Some tweaks for p-adic regulators #1301

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25 changes: 20 additions & 5 deletions examples/NFDB.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1175,9 +1175,10 @@ function _p_adic_regulator(K, p)
end
C, mC = completion(K, P, prec)
Rmat = zero_matrix(C, r, r)
D = Dict{nf_elem, LocalFieldElem{qadic, EisensteinLocalField}}()
for i in 1:r
for j in 1:r
Rmat[i, j] = _evaluate_log_of_fac_elem(mC, P, mA(A[i])(mU(U[j + 1]))) # j + 1, because the fundamental units correspond to U[2],..,U[r + 1]
Rmat[i, j] = _evaluate_log_of_fac_elem(mC, P, mA(A[i])(mU(U[j + 1])), D) # j + 1, because the fundamental units correspond to U[2],..,U[r + 1]
end
end
z = _det(Rmat)
Expand All @@ -1189,14 +1190,28 @@ function _p_adic_regulator(K, p)
end
end

function _evaluate_log_of_fac_elem(mC, P, e)
function _evaluate_log_of_fac_elem(mC, P, e::FacElem{nf_elem, AnticNumberField}, D = Dict{nf_elem, LocalFieldElem{qadic, EisensteinLocalField}}())
C = codomain(mC)
K = base_ring(e)
pi = K(uniformizer(P))
# at the moment log() works only for valuation == 0,
# We want to compute
# sum(n * log(mC(pi^(-valuation(b, P)) * b)) for (b, n) in e; init = zero(C))
# but we cache the result of the individual log(), since the elements we look
# at have large intersection for their bases.
#
# At the moment log() works only for valuation == 0,
# but since we have a unit, we can just scale in every factor
l = sum(n * log(mC(pi^(-valuation(b, P)) * b)) for (b, n) in e; init = zero(C))
return l
res = zero(C)
for (b, n) in e
l = get!(D, b) do
bb = mC(pi^(-valuation(b, P)) * b)
push!(Main.elts, bb)

return log(bb)
end
res = res + n * l
end
return res
end

function _padic_regulator_non_normal(K, p)
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