julia> P, T = QQ[:T]
(Univariate polynomial ring in T over QQ, T)
julia> mipo_a = T^8 + 6*T^4 + 1
T^8 + 6*T^4 + 1
julia> K, a = number_field(mipo_a) # a stands for \alpha in the text
(Number field of degree 8 over QQ, _a)
julia> # Prepare for reduction modulo a prime ideal P of the ring of integers OK of K over 113
OK = maximal_order(K)
Maximal order
of number field with defining polynomial T^8 + 6*T^4 + 1
over rational field
with Z-basis [1, _a, _a^2, 1//2*_a^3 + 1//2*_a^2 + 1//2*_a + 1//2, 1//2*_a^4 + 1//2, 1//2*_a^5 + 1//2*_a, 1//4*_a^6 + 1//4*_a^4 + 3//4*_a^2 + 3//4, 1//4*_a^7 + 1//4*_a^5 + 1//4*_a^3 + 1//2*_a^2 + 1//4*_a + 1//2]
julia> P = ideal(OK, OK.([113,a+70]))
Ideal of maximal order of number field of degree 8 over QQ
with Z-basis [113, _a + 70, _a^2 + 72, 1//2*_a^3 + 1//2*_a^2 + 1//2*_a + 187//2, 1//2*_a^4 + 127//2, 1//2*_a^5 + 1//2*_a + 110, 1//4*_a^6 + 1//4*_a^4 + 3//4*_a^2 + 239//4, 1//4*_a^7 + 1//4*_a^5 + 1//4*_a^3 + 1//2*_a^2 + 1//4*_a + 59//2]
julia> @assert is_prime(P)
julia> valuation(a,P)
ERROR: UndefRefError: access to undefined reference
Stacktrace:
[1] getproperty
@ ./Base_compiler.jl:54 [inlined]
[2] val_func_no_index_small(p::AbsSimpleNumFieldOrderIdeal)
@ Hecke ~/.julia/dev/Hecke/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl:15
[3] assure_valuation_function(p::AbsSimpleNumFieldOrderIdeal)
@ Hecke ~/.julia/dev/Hecke/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl:280
[4] valuation(a::AbsSimpleNumFieldElem, p::AbsSimpleNumFieldOrderIdeal, no::QQFieldElem)
@ Hecke ~/.julia/dev/Hecke/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl:382
[5] valuation(a::AbsSimpleNumFieldElem, p::AbsSimpleNumFieldOrderIdeal)
@ Hecke ~/.julia/dev/Hecke/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl:372
[6] top-level scope
@ REPL[27]:1
