doctest failure in src/number_fields/elements.md:27-40 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field(x^2 - 2, "a"); julia> K([1, 2]) 2*a + 1 julia> L, b = radical_extension(3, a, "b") (Relative number field of degree 3 over number field, b) julia> L([a, 1, 1//2]) 1//2*b^2 + b + a ``` Subexpression: L, b = radical_extension(3, a, "b") Evaluated output: ERROR: MethodError: no method matching polynomial_ring(::AnticNumberField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] radical_extension(n::Int64, a::nf_elem, s::String; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/SimpleNumField/Field.jl:70 [2] radical_extension(n::Int64, a::nf_elem, s::String) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/SimpleNumField/Field.jl:67 [3] top-level scope @ none:1 Expected output: (Relative number field of degree 3 over number field, b) diff = Warning: Diff output requires color. (Relative number field of degree 3 over number field, b)ERROR: MethodError: no method matching polynomial_ring(::AnticNumberField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] radical_extension(n::Int64, a::nf_elem, s::String; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/SimpleNumField/Field.jl:70 [2] radical_extension(n::Int64, a::nf_elem, s::String) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/SimpleNumField/Field.jl:67 [3] top-level scope @ none:1

doctest failure in src/number_fields/elements.md:27-40 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field(x^2 - 2, "a"); julia> K([1, 2]) 2*a + 1 julia> L, b = radical_extension(3, a, "b") (Relative number field of degree 3 over number field, b) julia> L([a, 1, 1//2]) 1//2*b^2 + b + a ``` Subexpression: L([a, 1, 1//2]) Evaluated output: ERROR: UndefVarError: L not defined Stacktrace: [1] top-level scope @ none:1 Expected output: 1//2*b^2 + b + a diff = Warning: Diff output requires color. 1//2*b^2 + b + aERROR: UndefVarError: L not defined Stacktrace: [1] top-level scope @ none:1

doctest failure in src/number_fields/complex_embeddings.md:110-137 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field([x^2 + 1, x^3 + 2], "a"); julia> emb = complex_embeddings(K) 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field julia> k, b = quadratic_field(-1); julia> i = hom(k, K, a[1]); julia> restrict(emb[1], i) Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field julia> restrict(emb[3], i) Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field ``` Subexpression: K, a = number_field([x^2 + 1, x^3 + 2], "a"); Evaluated output: ERROR: MethodError: no method matching polynomial_ring(::QQField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] trace_assure @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1052 [inlined] [2] tr(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1073 [3] minpoly_via_trace(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1098 [4] minpoly @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:573 [inlined] [5] _check_consistency(K::NfAbsNS) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:121 [6] number_field(f::Vector{QQPolyRingElem}, S::Vector{Symbol}; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:942 [7] number_field(f::Vector{QQPolyRingElem}, s::String; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:925 [8] number_field(f::Vector{QQPolyRingElem}, s::String) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:918 [9] top-level scope @ none:1 Expected output: diff = Warning: Diff output requires color. ERROR: MethodError: no method matching polynomial_ring(::QQField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] trace_assure @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1052 [inlined] [2] tr(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1073 [3] minpoly_via_trace(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1098 [4] minpoly @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:573 [inlined] [5] _check_consistency(K::NfAbsNS) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:121 [6] number_field(f::Vector{QQPolyRingElem}, S::Vector{Symbol}; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField

doctest failure in src/number_fields/complex_embeddings.md:110-137 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field([x^2 + 1, x^3 + 2], "a"); julia> emb = complex_embeddings(K) 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field julia> k, b = quadratic_field(-1); julia> i = hom(k, K, a[1]); julia> restrict(emb[1], i) Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field julia> restrict(emb[3], i) Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field ``` Subexpression: emb = complex_embeddings(K) Evaluated output: ERROR: UndefVarError: K not defined Stacktrace: [1] top-level scope @ none:1 Expected output: 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field diff = Warning: Diff output requires color. 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number fieldERROR: UndefVarError: K not defined Stacktrace: [1] top-level scope @ none:1

doctest failure in src/number_fields/complex_embeddings.md:110-137 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field([x^2 + 1, x^3 + 2], "a"); julia> emb = complex_embeddings(K) 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field julia> k, b = quadratic_field(-1); julia> i = hom(k, K, a[1]); julia> restrict(emb[1], i) Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field julia> restrict(emb[3], i) Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field ``` Subexpression: i = hom(k, K, a[1]); Evaluated output: ERROR: UndefVarError: a not defined Stacktrace: [1] top-level scope @ none:1 Expected output: diff = Warning: Diff output requires color. ERROR: UndefVarError: a not defined Stacktrace: [1] top-level scope @ none:1

doctest failure in src/number_fields/complex_embeddings.md:110-137 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field([x^2 + 1, x^3 + 2], "a"); julia> emb = complex_embeddings(K) 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field julia> k, b = quadratic_field(-1); julia> i = hom(k, K, a[1]); julia> restrict(emb[1], i) Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field julia> restrict(emb[3], i) Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field ``` Subexpression: restrict(emb[1], i) Evaluated output: ERROR: UndefVarError: emb not defined Stacktrace: [1] top-level scope @ none:1 Expected output: Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field diff = Warning: Diff output requires color. Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational fieldERROR: UndefVarError: emb not defined Stacktrace: [1] top-level scope @ none:1

doctest failure in src/number_fields/complex_embeddings.md:110-137 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, a = number_field([x^2 + 1, x^3 + 2], "a"); julia> emb = complex_embeddings(K) 6-element Vector{Hecke.NumFieldEmbNfAbsNS}: Complex embedding corresponding to [1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 + 1.09 * i] of non-simple number field Complex embedding corresponding to [-1.00 * i, -1.26] of non-simple number field Complex embedding corresponding to [-1.00 * i, 0.63 - 1.09 * i] of non-simple number field Complex embedding corresponding to [1.00 * i, 0.63 - 1.09 * i] of non-simple number field julia> k, b = quadratic_field(-1); julia> i = hom(k, K, a[1]); julia> restrict(emb[1], i) Complex embedding corresponding to 1.00 * i of number field with defining polynomial x^2 + 1 over rational field julia> restrict(emb[3], i) Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field ``` Subexpression: restrict(emb[3], i) Evaluated output: ERROR: UndefVarError: emb not defined Stacktrace: [1] top-level scope @ none:1 Expected output: Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational field diff = Warning: Diff output requires color. Complex embedding corresponding to -1.00 * i of number field with defining polynomial x^2 + 1 over rational fieldERROR: UndefVarError: emb not defined Stacktrace: [1] top-level scope @ none:1

doctest failure in ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:53-64 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, (a1, a2) = number_field([x^2 - 2, x^2 - 3], "a"); julia> basis(K) 4-element Vector{NfAbsNSElem}: 1 a1 a2 a1*a2 ``` Subexpression: K, (a1, a2) = number_field([x^2 - 2, x^2 - 3], "a"); Evaluated output: ERROR: MethodError: no method matching polynomial_ring(::QQField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] trace_assure @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1052 [inlined] [2] tr(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1073 [3] minpoly_via_trace(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1098 [4] minpoly @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:573 [inlined] [5] _check_consistency(K::NfAbsNS) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:121 [6] number_field(f::Vector{QQPolyRingElem}, S::Vector{Symbol}; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:942 [7] number_field(f::Vector{QQPolyRingElem}, s::String; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:925 [8] number_field(f::Vector{QQPolyRingElem}, s::String) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:918 [9] top-level scope @ none:1 Expected output: diff = Warning: Diff output requires color. ERROR: MethodError: no method matching polynomial_ring(::QQField; cached=false) Closest candidates are: polynomial_ring(::Ring, !Matched::Tuple{}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1367 polynomial_ring(::Ring, !Matched::Tuple{Union{Char, AbstractString, Symbol}, Vararg{Union{Char, AbstractString, Symbol}}}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1364 polynomial_ring(::Ring, !Matched::Vector{Symbol}; kw...) at ~/.julia/packages/AbstractAlgebra/YkCOC/src/MPoly.jl:1370 ... Stacktrace: [1] trace_assure @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1052 [inlined] [2] tr(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1073 [3] minpoly_via_trace(a::NfAbsNSElem) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:1098 [4] minpoly @ ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:573 [inlined] [5] _check_consistency(K::NfAbsNS) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:121 [6] number_field(f::Vector{QQPolyRingElem}, S::Vector{Symbol}; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:942 [7] number_field(f::Vector{QQPolyRingElem}, s::String; cached::Bool, check::Bool) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:925 [8] number_field(f::Vector{QQPolyRingElem}, s::String) @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumField/NfAbs/NonSimple.jl:918 [9] top-level scope @ none:1

doctest failure in ~/work/Hecke.jl/Hecke.jl/src/NumField/NonSimpleNumField/Field.jl:53-64 ```jldoctest julia> Qx, x = QQ["x"]; julia> K, (a1, a2) = number_field([x^2 - 2, x^2 - 3], "a"); julia> basis(K) 4-element Vector{NfAbsNSElem}: 1 a1 a2 a1*a2 ``` Subexpression: basis(K) Evaluated output: ERROR: UndefVarError: K not defined Stacktrace: [1] top-level scope @ none:1 Expected output: 4-element Vector{NfAbsNSElem}: 1 a1 a2 a1*a2 diff = Warning: Diff output requires color. 4-element Vector{NfAbsNSElem}: 1 a1 a2 a1*a2ERROR: UndefVarError: K not defined Stacktrace: [1] top-level scope @ none:1