diff --git a/docs/src/DeveloperDocumentation/caching.md b/docs/src/DeveloperDocumentation/caching.md
index 00db05dcb431..220c6344e3d8 100644
--- a/docs/src/DeveloperDocumentation/caching.md
+++ b/docs/src/DeveloperDocumentation/caching.md
@@ -96,9 +96,9 @@ like `cyclotomic_polynomial`
 ```
 module Globals
   using Hecke
-  const Qx, _ = polynomial_ring(FlintQQ, :x, cached = false)
-  const Zx, _ = polynomial_ring(FlintZZ, :x, cached = false)
-  const Zxy, _ = polynomial_ring(FlintZZ, [:x, :y], cached = false)
+  const Qx, _ = polynomial_ring(QQ, :x, cached = false)
+  const Zx, _ = polynomial_ring(ZZ, :x, cached = false)
+  const Zxy, _ = polynomial_ring(ZZ, [:x, :y], cached = false)
 end
 ```
 You can use these in your own code as well, or imitate this pattern if convenient.
diff --git a/experimental/QuadFormAndIsom/test/runtests.jl b/experimental/QuadFormAndIsom/test/runtests.jl
index 766594875221..26e1ba69a901 100644
--- a/experimental/QuadFormAndIsom/test/runtests.jl
+++ b/experimental/QuadFormAndIsom/test/runtests.jl
@@ -48,7 +48,7 @@ end
   @test evaluate(minimal_polynomial(Vf), -1) == 0
   @test evaluate(characteristic_polynomial(Vf), 0) == 1
 
-  G = matrix(FlintQQ, 6, 6 ,[3, 1, -1, 1, 0, 0, 1, 3, 1, 1, 1, 1, -1, 1, 3, 0, 0, 1, 1, 1, 0, 4, 2, 2, 0, 1, 0, 2, 4, 2, 0, 1, 1, 2, 2, 4])
+  G = matrix(QQ, 6, 6 ,[3, 1, -1, 1, 0, 0, 1, 3, 1, 1, 1, 1, -1, 1, 3, 0, 0, 1, 1, 1, 0, 4, 2, 2, 0, 1, 0, 2, 4, 2, 0, 1, 1, 2, 2, 4])
   V = quadratic_space(QQ, G)
   f = matrix(QQ, 6, 6, [1 0 0 0 0 0; 0 0 -1 0 0 0; -1 1 -1 0 0 0; 0 0 0 1 0 -1; 0 0 0 0 0 -1; 0 0 0 0 1 -1])
   Vf = @inferred quadratic_space_with_isometry(V, f)
@@ -386,8 +386,8 @@ end
   @test length(reps) == 1
 
   ## Odd case
-  B = matrix(FlintQQ, 5, 5 ,[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]);
-  G = matrix(FlintQQ, 5, 5 ,[3, 1, 0, 0, 0, 1, 3, 1, 1, -1, 0, 1, 3, 0, 0, 0, 1, 0, 3, 0, 0, -1, 0, 0, 3]);
+  B = matrix(QQ, 5, 5 ,[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]);
+  G = matrix(QQ, 5, 5 ,[3, 1, 0, 0, 0, 1, 3, 1, 1, -1, 0, 1, 3, 0, 0, 0, 1, 0, 3, 0, 0, -1, 0, 0, 3]);
   L = integer_lattice(B, gram = G);
   k = lattice_in_same_ambient_space(L, B[2:2, :])
   N = orthogonal_submodule(L, k)
diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl
index 8e3ef37c81ac..7b5246099f7e 100644
--- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl
+++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl
@@ -579,7 +579,7 @@ end
 
 function Nemo.roots_upper_bound(f::ZZMPolyRingElem, t::Int = 0)
   @assert nvars(parent(f)) == 2
-  Qs, s = rational_function_field(FlintQQ, "t", cached = false)
+  Qs, s = rational_function_field(QQ, "t", cached = false)
   Qsx, x = polynomial_ring(Qs, cached = false)
   F = evaluate(f, [x, Qsx(s)])
   dis = numerator(discriminant(F))
diff --git a/src/NumberTheory/GaloisGrp/Qt.jl b/src/NumberTheory/GaloisGrp/Qt.jl
index 2b69cc4c8ef9..ad9791b87fba 100644
--- a/src/NumberTheory/GaloisGrp/Qt.jl
+++ b/src/NumberTheory/GaloisGrp/Qt.jl
@@ -88,7 +88,7 @@ for analysis of the denominator and the infinite valuations
 function _galois_init(F::Generic.FunctionField{QQFieldElem}; tStart::Int = -1)
   f = defining_polynomial(F)
   @assert is_monic(f)
-  Zxy, (x, y) = polynomial_ring(FlintZZ, 2, cached = false)
+  Zxy, (x, y) = polynomial_ring(ZZ, 2, cached = false)
   ff = Zxy()
   d = lcm(map(denominator, coefficients(f)))
   df = f*d
@@ -101,7 +101,7 @@ function _galois_init(F::Generic.FunctionField{QQFieldElem}; tStart::Int = -1)
   for i=0:degree(f)
     c = coeff(df, i)
     if !iszero(c)
-      ff += map_coefficients(FlintZZ, numerator(c))(y)*x^i
+      ff += map_coefficients(ZZ, numerator(c))(y)*x^i
     end
   end
   _subfields(F, ff, tStart = tStart)
diff --git a/src/NumberTheory/NmbThy.jl b/src/NumberTheory/NmbThy.jl
index 7f8921b85823..2cffd1ff3d00 100644
--- a/src/NumberTheory/NmbThy.jl
+++ b/src/NumberTheory/NmbThy.jl
@@ -89,7 +89,7 @@ function norm_equation_fac_elem(R::AbsNumFieldOrder, k::ZZRingElem; abs::Bool =
   S = Tuple{Vector{Tuple{Hecke.ideal_type(R), Int}}, Vector{ZZMatrix}}[]
   for (p, k) = lp.fac
     P = prime_decomposition(R, p)
-    s = solve_non_negative(matrix(FlintZZ, 1, length(P), [degree(x[1]) for x = P]), matrix(FlintZZ, 1, 1, [k]))
+    s = solve_non_negative(matrix(ZZ, 1, length(P), [degree(x[1]) for x = P]), matrix(ZZ, 1, 1, [k]))
     push!(S, (P, ZZMatrix[view(s, i:i, 1:ncols(s)) for i=1:nrows(s)]))
   end
   sol = FacElem{AbsSimpleNumFieldElem, AbsSimpleNumField}[]
@@ -144,10 +144,10 @@ function norm_equation_fac_elem(R::Hecke.RelNumFieldOrder{AbsSimpleNumFieldElem,
   q, mms = snf(q)
   mq = mq*inv(mms)
 
-  C = vcat([matrix(FlintZZ, 1, ngens(q), [valuation(mS(preimage(mq, q[i])), p) for i=1:ngens(q)]) for p = keys(lp)])
+  C = vcat([matrix(ZZ, 1, ngens(q), [valuation(mS(preimage(mq, q[i])), p) for i=1:ngens(q)]) for p = keys(lp)])
   
-  A = vcat([matrix(FlintZZ, 1, ngens(q), [valuation(norm(mkK, mS(preimage(mq, g))), p) for g in gens(q)]) for p = keys(la)])
-  b = matrix(FlintZZ, length(la), 1, [valuation(a, p) for p = keys(la)])
+  A = vcat([matrix(ZZ, 1, ngens(q), [valuation(norm(mkK, mS(preimage(mq, g))), p) for g in gens(q)]) for p = keys(la)])
+  b = matrix(ZZ, length(la), 1, [valuation(a, p) for p = keys(la)])
 
   so = solve_mixed(A, b, C)
   u, mu = Hecke.unit_group_fac_elem(parent(a))
@@ -189,16 +189,16 @@ function is_irreducible(a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFi
   # if this is possible, then a is not irreducible as a
   # is then ms(Ax) * ms(Ay) and neither is trivial.
 
-  I = identity_matrix(FlintZZ, length(S))
+  I = identity_matrix(ZZ, length(S))
   A = hcat(I, I)
   #so A*(x|y) = x+y = sol is the  1. condition
   C = cat(V, V, dims=(1,2))
   # C(x|y) >=0 iff Cx >=0 and Cy >=0
   #Cx <> 0 iff (1,..1)*Cx >= 1
-  one = matrix(FlintZZ, 1, length(S), [1 for p = S])
-  zer = matrix(FlintZZ, 1, length(S), [0 for p = S])
+  one = matrix(ZZ, 1, length(S), [1 for p = S])
+  zer = matrix(ZZ, 1, length(S), [0 for p = S])
   C = vcat(C, hcat(one, zer), hcat(zer, one))
-  d = matrix(FlintZZ, 2*length(S)+2, 1, [0 for i = 1:2*length(S) + 2])
+  d = matrix(ZZ, 2*length(S)+2, 1, [0 for i = 1:2*length(S) + 2])
   d[end-1, 1] = 1
   d[end, 1] = 1
   pt = solve_mixed(A, sol, C, d)
diff --git a/src/PolyhedralGeometry/solving_integrally.jl b/src/PolyhedralGeometry/solving_integrally.jl
index 7818e280a53e..4659cf58a221 100644
--- a/src/PolyhedralGeometry/solving_integrally.jl
+++ b/src/PolyhedralGeometry/solving_integrally.jl
@@ -49,11 +49,11 @@ Note that the output can be permuted, hence we sort it.
 ```jldoctest
 julia> A = ZZMatrix([1 1]);
 
-julia> b = zero_matrix(FlintZZ, 1,1); b[1,1]=7;
+julia> b = zero_matrix(ZZ, 1,1); b[1,1]=7;
 
 julia> C = ZZMatrix([1 0; 0 1]);
 
-julia> d = zero_matrix(FlintZZ,2,1); d[1,1]=2; d[2,1]=3;
+julia> d = zero_matrix(ZZ,2,1); d[1,1]=2; d[2,1]=3;
 
 julia> sortslices(Matrix{BigInt}(solve_mixed(A, b, C, d)), dims=1)
 3×2 Matrix{BigInt}:
@@ -101,7 +101,7 @@ Note that the output can be permuted, hence we sort it.
 ```jldoctest
 julia> A = ZZMatrix([1 1]);
 
-julia> b = zero_matrix(FlintZZ, 1,1); b[1,1]=3;
+julia> b = zero_matrix(ZZ, 1,1); b[1,1]=3;
 
 julia> C = ZZMatrix([1 0; 0 1]);
 
@@ -131,9 +131,9 @@ julia> for x in it
 """
 solve_mixed(
   as::Type{T}, A::ZZMatrix, b::ZZMatrix, C::ZZMatrix; permit_unbounded=false
-) where {T} = solve_mixed(T, A, b, C, zero_matrix(FlintZZ, nrows(C), 1); permit_unbounded)
+) where {T} = solve_mixed(T, A, b, C, zero_matrix(ZZ, nrows(C), 1); permit_unbounded)
 solve_mixed(A::ZZMatrix, b::ZZMatrix, C::ZZMatrix; permit_unbounded=false) =
-  solve_mixed(ZZMatrix, A, b, C, zero_matrix(FlintZZ, nrows(C), 1); permit_unbounded)
+  solve_mixed(ZZMatrix, A, b, C, zero_matrix(ZZ, nrows(C), 1); permit_unbounded)
 
 @doc raw"""
     solve_ineq(as::Type{T}, A::ZZMatrix, b::ZZMatrix) where {T}
@@ -151,7 +151,7 @@ Note that the output can be permuted, hence we sort it.
 ```jldoctest
 julia> A = ZZMatrix([1 0; 0 1; -1 0; 0 -1]);
 
-julia> b = zero_matrix(FlintZZ, 4,1); b[1,1]=1; b[2,1]=1; b[3,1]=0; b[4,1]=0;
+julia> b = zero_matrix(ZZ, 4,1); b[1,1]=1; b[2,1]=1; b[3,1]=0; b[4,1]=0;
 
 julia> sortslices(Matrix{BigInt}(solve_ineq(A, b)), dims=1)
 4×2 Matrix{BigInt}:
@@ -173,8 +173,8 @@ SubObjectIterator{PointVector{ZZRingElem}}
 solve_ineq(as::Type{T}, A::ZZMatrix, b::ZZMatrix; permit_unbounded=false) where {T} =
   solve_mixed(
     T,
-    zero_matrix(FlintZZ, 0, ncols(A)),
-    zero_matrix(FlintZZ, 0, 1),
+    zero_matrix(ZZ, 0, ncols(A)),
+    zero_matrix(ZZ, 0, 1),
     -A,
     -b;
     permit_unbounded,
@@ -198,7 +198,7 @@ Note that the output can be permuted, hence we sort it.
 ```jldoctest
 julia> A = ZZMatrix([1 1]);
 
-julia> b = zero_matrix(FlintZZ, 1,1); b[1,1]=3;
+julia> b = zero_matrix(ZZ, 1,1); b[1,1]=3;
 
 julia> sortslices(Matrix{BigInt}(solve_non_negative(A, b)), dims=1)
 4×2 Matrix{BigInt}:
@@ -219,6 +219,6 @@ SubObjectIterator{PointVector{ZZRingElem}}
 """
 solve_non_negative(
   as::Type{T}, A::ZZMatrix, b::ZZMatrix; permit_unbounded=false
-) where {T} = solve_mixed(T, A, b, identity_matrix(FlintZZ, ncols(A)); permit_unbounded)
+) where {T} = solve_mixed(T, A, b, identity_matrix(ZZ, ncols(A)); permit_unbounded)
 solve_non_negative(A::ZZMatrix, b::ZZMatrix; permit_unbounded=false) =
   solve_non_negative(ZZMatrix, A, b; permit_unbounded)
diff --git a/src/Rings/NumberField.jl b/src/Rings/NumberField.jl
index 4f3e651d85ef..85a3e0c8549f 100644
--- a/src/Rings/NumberField.jl
+++ b/src/Rings/NumberField.jl
@@ -138,7 +138,7 @@ parent(a::NfNSGenElem) = a.parent
 
 Hecke.data(a::NfNSGenElem) = a.f
 
-base_field(K::NfNSGen{QQFieldElem, QQMPolyRingElem}) = FlintQQ
+base_field(K::NfNSGen{QQFieldElem, QQMPolyRingElem}) = QQ
 
 base_field(K::NfNSGen) = base_ring(polynomial_ring(K))
 
@@ -616,7 +616,7 @@ end
 function basis_matrix(v::Vector{NfNSGenElem{QQFieldElem, QQMPolyRingElem}},
                       ::Type{Hecke.FakeFmpqMat})
   d = degree(parent(v[1]))
-  z = zero_matrix(FlintQQ, length(v), d)
+  z = zero_matrix(QQ, length(v), d)
   for i in 1:length(v)
     elem_to_mat_row!(z, i, v[i])
   end
diff --git a/src/Rings/binomial_ideals.jl b/src/Rings/binomial_ideals.jl
index c9dd600ef8eb..1cfa6e0d0bfb 100644
--- a/src/Rings/binomial_ideals.jl
+++ b/src/Rings/binomial_ideals.jl
@@ -393,7 +393,7 @@ function (Chi::PartialCharacter)(b::ZZMatrix)
 end
 
 function (Chi::PartialCharacter)(b::Vector{ZZRingElem})
-  return Chi(matrix(FlintZZ, 1, length(b), b))
+  return Chi(matrix(ZZ, 1, length(b), b))
 end
 
 function have_same_domain(P::PartialCharacter, Q::PartialCharacter)
@@ -482,7 +482,7 @@ function ideal_from_character(P::PartialCharacter, R::MPolyRing)
 
   @assert ncols(P.A) == nvars(R)
   #test if the domain of the partial character is the zero lattice
-  if isone(nrows(P.A)) && have_same_span(P.A, zero_matrix(FlintZZ, 1, ncols(P.A)))
+  if isone(nrows(P.A)) && have_same_span(P.A, zero_matrix(ZZ, 1, ncols(P.A)))
     return ideal(R, zero(R))
   end
 
@@ -582,7 +582,7 @@ function partial_character_from_ideal(I::MPolyIdeal, R::MPolyRing)
 
   Delta = cell[2]   #cell variables
   if isempty(Delta)
-    return partial_character(zero_matrix(FlintZZ, 1, nvars(R)), [one(QQAb)], Set{Int64}())
+    return partial_character(zero_matrix(ZZ, 1, nvars(R)), [one(QQAb)], Set{Int64}())
   end
 
   #now consider the case where Delta is not empty
@@ -598,12 +598,12 @@ function partial_character_from_ideal(I::MPolyIdeal, R::MPolyRing)
   end
   QQAbcl, = abelian_closure(QQ)
   if iszero(J)
-    return partial_character(zero_matrix(FlintZZ, 1, nvars(R)), [one(QQAbcl)], Set{Int64}())
+    return partial_character(zero_matrix(ZZ, 1, nvars(R)), [one(QQAbcl)], Set{Int64}())
   end
   #now case if J \neq 0
   #let ts be a list of minimal binomial generators for J
   gb = groebner_basis(J, complete_reduction = true)
-  vs = zero_matrix(FlintZZ, 0, nvars(R))
+  vs = zero_matrix(ZZ, 0, nvars(R))
   images = QQAbFieldElem{AbsSimpleNumFieldElem}[]
   for t in gb
     #TODO: Once tail will be available, use it.
@@ -612,7 +612,7 @@ function partial_character_from_ideal(I::MPolyIdeal, R::MPolyRing)
     u = exponent_vector(lm, 1)
     v = exponent_vector(tl, 1)
     #now test if we need the vector uv
-    uv = matrix(FlintZZ, 1, nvars(R), Int[u[j]-v[j] for j  =1:length(u)]) #this is the vector of u-v
+    uv = matrix(ZZ, 1, nvars(R), Int[u[j]-v[j] for j  =1:length(u)]) #this is the vector of u-v
     #TODO: It can be done better by saving the hnf...
     if !can_solve(vs, uv, side = :left)[1]
       push!(images, -QQAbcl(AbstractAlgebra.leading_coefficient(tl)))
@@ -1162,7 +1162,7 @@ function birth_death_ideal(m::Int, n::Int)
   R = Matrix{QQMPolyRingElem}(undef, m, n+1)
   D = Matrix{QQMPolyRingElem}(undef, m+1, m)
   L = Matrix{QQMPolyRingElem}(undef, m+1, n+1)
-  Qxy, gQxy = polynomial_ring(FlintQQ, length(U)+length(R)+length(D)+length(L); cached = false)
+  Qxy, gQxy = polynomial_ring(QQ, length(U)+length(R)+length(D)+length(L); cached = false)
   pols = Vector{elem_type(Qxy)}(undef, 4*n*m)
   ind = 1
   for i = 1:m+1
diff --git a/src/Rings/hilbert.jl b/src/Rings/hilbert.jl
index 26acdd148b69..cce1b152d364 100644
--- a/src/Rings/hilbert.jl
+++ b/src/Rings/hilbert.jl
@@ -934,9 +934,9 @@ end
 #  # Transpose while converting:
 #  ncols = length(W);
 #  nrows = length(W[1]);
-#  A = zero_matrix(FlintZZ, nrows,ncols);
+#  A = zero_matrix(ZZ, nrows,ncols);
 #  for i in 1:nrows  for j in 1:ncols  A[i,j] = W[j][i];  end; end;
-#  b = zero_matrix(FlintZZ, nrows,1);
+#  b = zero_matrix(ZZ, nrows,1);
 #  try
 #    solve_non_negative(A, b); # any non-zero soln gives rise to infinitely many, which triggers an exception
 #  catch e
diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl
index a6a2ffcd5cad..c6ed7d739a1a 100644
--- a/src/Rings/mpoly-graded.jl
+++ b/src/Rings/mpoly-graded.jl
@@ -1239,7 +1239,7 @@ function monomial_basis(W::MPolyDecRing, d::FinGenAbGroupElem)
      k, im = kernel(h)
      #need the positive elements in there...
      #Ax = b, Cx >= 0
-     C = identity_matrix(FlintZZ, ngens(W))
+     C = identity_matrix(ZZ, ngens(W))
      A = reduce(vcat, [x.coeff for x = W.d])
      k = solve_mixed(transpose(A), transpose(d.coeff), C)
      for ee = 1:nrows(k)
diff --git a/test/AlgebraicGeometry/Surfaces/K3Auto.jl b/test/AlgebraicGeometry/Surfaces/K3Auto.jl
index 0e637c52ff02..035c3f2ecee2 100644
--- a/test/AlgebraicGeometry/Surfaces/K3Auto.jl
+++ b/test/AlgebraicGeometry/Surfaces/K3Auto.jl
@@ -1,6 +1,6 @@
 @testset "elliptic fibrations" begin
-  B = matrix(FlintQQ, 16, 16 ,[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3//2, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 3//2, 3//2, 1//2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1//2, 3//2, 0, 1//2, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1//2, 1//2, 1//2, 0, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 1, 1//2, 0, 1//2, 0, 0, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 0, 1//2, 0, 3//5, 1//10]);
-  G = matrix(FlintQQ, 16, 16 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -170]);
+  B = matrix(QQ, 16, 16 ,[2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3//2, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 3//2, 3//2, 1//2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1//2, 3//2, 0, 1//2, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1//2, 1//2, 1//2, 0, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 1, 1//2, 0, 1//2, 0, 0, 1//2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//2, 0, 1//2, 0, 3//5, 1//10]);
+  G = matrix(QQ, 16, 16 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -170]);
   NS = integer_lattice(B, gram = G);
   V = ambient_space(NS)
   f =  QQFieldElem[2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
@@ -23,12 +23,12 @@ end
 @testset "walls of chamber" begin
   S = integer_lattice(gram=QQ[-2 1 0 0; 1 -2 1 1; 0 1 -2 1; 0 1 1 -2])
   # fix an embedding
-  B = matrix(FlintQQ, 10, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//3, 2//3, 1//3, 2//3, 2//3, 2//3, 1//3, 1//3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]);
-  G = matrix(FlintQQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
+  B = matrix(QQ, 10, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1//3, 2//3, 1//3, 2//3, 2//3, 2//3, 1//3, 1//3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]);
+  G = matrix(QQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
   L = integer_lattice(B, gram = G);
 
-  B = matrix(FlintQQ, 4, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]);
-  G = matrix(FlintQQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
+  B = matrix(QQ, 4, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]);
+  G = matrix(QQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
   S = integer_lattice(B, gram = G);
 
   weyl = QQ[31   61   52   71   5   -6   5   -2   -7   8]
@@ -171,11 +171,11 @@ end
 end
 
 @testset "weyl_vector_non_degenerate" begin 
-  B = matrix(FlintQQ, 10, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1//3, 2//3, 1//3, 2//3, 2//3, 2//3, 1//3, 1//3]);
-  G = matrix(FlintQQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
+  B = matrix(QQ, 10, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1//3, 2//3, 1//3, 2//3, 2//3, 2//3, 1//3, 1//3]);
+  G = matrix(QQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
   L = integer_lattice(B, gram = G);
-  B = matrix(FlintQQ, 4, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]);
-  G = matrix(FlintQQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
+  B = matrix(QQ, 4, 10 ,[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]);
+  G = matrix(QQ, 10, 10 ,[-2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -1, -1, 0, 0, 0, 0, -1, -2, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -2, -1, 0, 0, 0, 0, -1, -1, 1, -1, -1, -2]);
   S = integer_lattice(B, gram = G);
   u = QQ[90 157 218//3 346//3 -7//3 13//3 16//3 -11//3 -1//3 32//3]
   weyl = QQ[90 157 218//3 346//3 -7//3 13//3 16//3 -11//3 -1//3 32//3]
diff --git a/test/Groups/matrixgroups.jl b/test/Groups/matrixgroups.jl
index 5cc046652da0..61ca115ce1c7 100644
--- a/test/Groups/matrixgroups.jl
+++ b/test/Groups/matrixgroups.jl
@@ -752,7 +752,7 @@ end
    # L = lattice(q, QQ[0 0; 0 0], isbasis=false)
    # @test order(isometry_group(L)) == 1
 
-   Qx, x = polynomial_ring(FlintQQ, :x, cached = false)
+   Qx, x = polynomial_ring(QQ, :x, cached = false)
    f = x^2-2;
    K, a = number_field(f)
    D = matrix(K, 3, 3, [2, 0, 0, 0, 1, 0, 0, 0, 7436]);
diff --git a/test/PolyhedralGeometry/solve_integrally.jl b/test/PolyhedralGeometry/solve_integrally.jl
index b4acc42344e2..a592f39ae6e4 100644
--- a/test/PolyhedralGeometry/solve_integrally.jl
+++ b/test/PolyhedralGeometry/solve_integrally.jl
@@ -1,10 +1,10 @@
 @testset "solve_integrally" begin
   @testset "solve_mixed" begin
     A = ZZMatrix([1 1])
-    b = zero_matrix(FlintZZ, 1, 1)
+    b = zero_matrix(ZZ, 1, 1)
     b[1, 1] = 7
     C = ZZMatrix([1 0; 0 1])
-    d = zero_matrix(FlintZZ, 2, 1)
+    d = zero_matrix(ZZ, 2, 1)
     d[1, 1] = 2
     d[2, 1] = 3
     S0 = solve_mixed(A, b, C, d)
@@ -30,7 +30,7 @@
 
   @testset "solve_ineq" begin
     A = ZZMatrix([1 0; 0 1; -1 0; 0 -1])
-    b = zero_matrix(FlintZZ, 4, 1)
+    b = zero_matrix(ZZ, 4, 1)
     b[1, 1] = 1
     b[2, 1] = 1
     b[3, 1] = 0
@@ -48,7 +48,7 @@
 
   @testset "solve_non_negative" begin
     A = ZZMatrix([1 1])
-    b = zero_matrix(FlintZZ, 1, 1)
+    b = zero_matrix(ZZ, 1, 1)
     b[1, 1] = 3
     S0 = solve_non_negative(A, b)
     S1 = solve_non_negative(ZZMatrix, A, b)
diff --git a/test/Rings/NumberField.jl b/test/Rings/NumberField.jl
index 6776c019aa79..9beb6682e3c2 100644
--- a/test/Rings/NumberField.jl
+++ b/test/Rings/NumberField.jl
@@ -1,14 +1,14 @@
 @testset "Number field" begin
 
-  Qx, x = FlintQQ[:x]
+  Qx, x = QQ[:x]
   k, _ = number_field(x^2 + 1)
   ku, u = k[:u1, :u2]
   Ik = ideal(ku, [u[1]^3 + u[2]^3 - 3, u[1]^5 + u[2]^5 - 5])
 
-  Qy, y = FlintQQ[:y1, :y2]
+  Qy, y = QQ[:y1, :y2]
   IQ = ideal(Qy, [y[1]^3 + y[2]^3 - 3, y[1]^5 + y[2]^5 - 5])
 
-  for (Bk, Pk, I) in [(k, ku, Ik), (FlintQQ, Qy, IQ)]
+  for (Bk, Pk, I) in [(k, ku, Ik), (QQ, Qy, IQ)]
     gg = gens(Pk)
     @test_throws ErrorException number_field(ideal([gg[1]]))
     K,  = @inferred number_field(I, [:a1, :a2])
@@ -180,7 +180,7 @@
     end
 
     # denominator
-    if Bk === FlintQQ
+    if Bk === QQ
       b = rand(K, -2:2)
       d = @inferred denominator(b)
       @test d isa ZZRingElem
@@ -203,7 +203,7 @@
     end
 
     # basis matrix
-    if Bk == FlintQQ
+    if Bk == QQ
       for i in 1:10
         BB = [rand(K, -2:2) for j in 1:rand(1:10)]
         M = @inferred basis_matrix(BB, Hecke.FakeFmpqMat)
@@ -226,7 +226,7 @@
         @test b * B[n] == sum(M[n, m] * B[m] for m in 1:length(B))
       end
 
-      if Bk == FlintQQ
+      if Bk == QQ
         M, d = @inferred representation_matrix_q(b)
         @test nrows(M) == degree(K)
         @test ncols(M) == degree(K)
@@ -243,7 +243,7 @@
           c = rand(-10:10)
         end
         b = b//c
-        MM = zero_matrix(FlintZZ, nrows(M), ncols(M))
+        MM = zero_matrix(ZZ, nrows(M), ncols(M))
         dd = ZZRingElem()
         j = rand(1:nrows(MM))
         Oscar.Hecke.elem_to_mat_row!(MM, j, dd, b)
@@ -318,7 +318,7 @@
     end
 
     # simple extension
-    if Bk == FlintQQ
+    if Bk == QQ
       Ks, KstoK = simple_extension(K, simplify = true)
     else
       Ks, KstoK = simple_extension(K)
@@ -332,7 +332,7 @@
       @test KstoK(b + c) == KstoK(b) + KstoK(c)
       @test KstoK(b * c) == KstoK(b) * KstoK(c)
 
-      if Bk == FlintQQ
+      if Bk == QQ
         @test KstoK\(KstoK(b)) == b
         b = rand(K, -10:10)
         c = rand(K, -10:10)
diff --git a/test/Rings/binomial-ideals.jl b/test/Rings/binomial-ideals.jl
index 12390df54231..15aeca65fc6f 100644
--- a/test/Rings/binomial-ideals.jl
+++ b/test/Rings/binomial-ideals.jl
@@ -6,7 +6,7 @@
     @test is_binomial(f)
     J = ideal(R, [x^2-y^3, z^2])
     @test is_binomial(J)
-    Qxy, (x, y, z, t) = polynomial_ring(FlintQQ, 4)
+    Qxy, (x, y, z, t) = polynomial_ring(QQ, 4)
     I = ideal(elem_type(Qxy)[x*y, z*t^2-t^3, z^2-y^2])
     @test Oscar.is_binomial(I)
     @test Oscar.is_unital(I)
@@ -24,7 +24,7 @@
     @test is_cellular(I)[1]
     I = ideal(R, [x[1]*x[4]^2-x[2]*x[5]^2, x[1]^3*x[3]^3-x[2]^4*x[4]^2, x[2]*x[4]^8-x[3]^3*x[5]^6])
     @test !is_cellular(I)[1]
-    Qxy, (x, y, z, t) = polynomial_ring(FlintQQ, 4)
+    Qxy, (x, y, z, t) = polynomial_ring(QQ, 4)
     I = ideal(elem_type(Qxy)[x*y, z*t^2-t^3, z^2-y^2])
     @test !Oscar.is_cellular(I)[1]
     lI = Oscar.cellular_decomposition(I)
@@ -44,7 +44,7 @@
   end
 
   @testset "Binomial primary decomposition" begin
-    Qxy, (x, y, z, t) = polynomial_ring(FlintQQ, 4)
+    Qxy, (x, y, z, t) = polynomial_ring(QQ, 4)
     I = ideal(elem_type(Qxy)[x*y, z*t^2-t^3, z^2-y^2])
     lP = Oscar.binomial_primary_decomposition(I)