diff --git a/experimental/FTheoryTools/src/LiteratureModels/constructors.jl b/experimental/FTheoryTools/src/LiteratureModels/constructors.jl
index 64d3789cacb3..b8f29935c632 100644
--- a/experimental/FTheoryTools/src/LiteratureModels/constructors.jl
+++ b/experimental/FTheoryTools/src/LiteratureModels/constructors.jl
@@ -259,7 +259,7 @@ function _construct_literature_model_over_concrete_base(model_dict::Dict{String,
 
   # Find divisor classes of the internal model sections
   auxiliary_base_grading = matrix(ZZ, transpose(hcat([[eval_poly(weight, ZZ) for weight in vec] for vec in model_dict["model_data"]["auxiliary_base_grading"]]...)))
-  auxiliary_base_grading = vcat([[Int(k) for k in auxiliary_base_grading[i,:]] for i in 1:nrows(auxiliary_base_grading)]...)
+  auxiliary_base_grading = vcat([[Int(k) for k in auxiliary_base_grading[i:i,:]] for i in 1:nrows(auxiliary_base_grading)]...)
   internal_model_sections = Dict{String, ToricDivisor}()
   for k in 2+length(model_sections):ngens(auxiliary_base_ring)
     divisor = sum([auxiliary_base_grading[l,k] * model_sections_divisor_list[l] for l in 1:nrows(auxiliary_base_grading)])
@@ -399,7 +399,7 @@ function _construct_literature_model_over_arbitrary_base(model_dict::Dict{String
 
   @req haskey(model_dict["model_data"], "auxiliary_base_grading") "Database does not specify auxiliary_base_grading, but is vital for model constrution, so cannot proceed"
   auxiliary_base_grading = matrix(ZZ, transpose(hcat([[eval_poly(weight, ZZ) for weight in vec] for vec in model_dict["model_data"]["auxiliary_base_grading"]]...)))
-  auxiliary_base_grading = vcat([[Int(k) for k in auxiliary_base_grading[i,:]] for i in 1:nrows(auxiliary_base_grading)]...)
+  auxiliary_base_grading = vcat([[Int(k) for k in auxiliary_base_grading[i:i,:]] for i in 1:nrows(auxiliary_base_grading)]...)
   
   base_dim = get(model_dict["model_data"], "base_dim", 3)
 
diff --git a/experimental/FTheoryTools/src/auxiliary.jl b/experimental/FTheoryTools/src/auxiliary.jl
index 221421060185..1df22edcefbb 100644
--- a/experimental/FTheoryTools/src/auxiliary.jl
+++ b/experimental/FTheoryTools/src/auxiliary.jl
@@ -29,7 +29,7 @@ function _ambient_space(base::NormalToricVariety, fiber_amb_space::NormalToricVa
   a_rays[1:nrows(b_rays), 1:ncols(b_rays)] = b_rays
   a_rays[1:nrows(b_rays), 1+ncols(b_rays):ncols(a_rays)] = transpose(u_matrix)
   a_rays[1+nrows(b_rays):nrows(a_rays), 1+ncols(b_rays):ncols(a_rays)] = f_rays
-  a_cones = [hcat([b for b in b_cones[i,:]], [c for c in f_cones[j,:]]) for i in 1:nrows(b_cones), j in 1:nrows(f_cones)]
+  a_cones = [hcat([b for b in b_cones[i:i,:]], [c for c in f_cones[j:j,:]]) for i in 1:nrows(b_cones), j in 1:nrows(f_cones)]
   a_space = normal_toric_variety(IncidenceMatrix(vcat(a_cones...)), a_rays; non_redundant = true)
   set_coordinate_names(a_space, vcat(b_var_names, f_var_names))
   
diff --git a/experimental/GITFans/src/GITFans.jl b/experimental/GITFans/src/GITFans.jl
index 2f49c61fdeff..2b6fd7e07a5e 100644
--- a/experimental/GITFans/src/GITFans.jl
+++ b/experimental/GITFans/src/GITFans.jl
@@ -465,7 +465,7 @@ function fan_traversal(orbit_list::Vector{Vector{Cone{T}}}, q_cone::Cone{T}, per
         neighbor_hashes = []
         for i in 1:length(facet_points)
           !any(f->facet_points[i] in f, facets(Cone, q_cone)) || continue
-          push!(neighbor_hashes, get_neighbor_hash(orbit_list, facet_points[i], Vector{T}([ic_facets[i, :]...])))
+          push!(neighbor_hashes, get_neighbor_hash(orbit_list, facet_points[i], Vector{T}([ic_facets[i:i, :]...])))
         end
 
         neighbor_hashes = [find_smallest_orbit_element(i, generators_new_perm, bitlist_oper_tuple, ==, less_or_equal_array_bitlist) for i in neighbor_hashes]
diff --git a/experimental/GaloisGrp/src/Solve.jl b/experimental/GaloisGrp/src/Solve.jl
index 20a78b042be5..748f53d9231c 100644
--- a/experimental/GaloisGrp/src/Solve.jl
+++ b/experimental/GaloisGrp/src/Solve.jl
@@ -687,7 +687,7 @@ function conj_from_basis(C::GaloisCtx, S::SubField, a, pr)
   for i=0:degree(S.fld)-1
     d = conjugates(C, S.coeff_field, coeff(a, i), pr)
     for j=1:length(d)
-      tmp[1, (j-1)*degree(S.fld)+1:j*degree(S.fld)] = d[j]*nb[i+1, (j-1)*degree(S.fld)+1:j*degree(S.fld)]
+      tmp[1, (j-1)*degree(S.fld)+1:j*degree(S.fld)] = d[j]*nb[i+1:i+1, (j-1)*degree(S.fld)+1:j*degree(S.fld)]
     end
     res += tmp
   end
diff --git a/experimental/LieAlgebras/src/CartanMatrix.jl b/experimental/LieAlgebras/src/CartanMatrix.jl
index e887ff3c6beb..0858454b9611 100644
--- a/experimental/LieAlgebras/src/CartanMatrix.jl
+++ b/experimental/LieAlgebras/src/CartanMatrix.jl
@@ -244,7 +244,7 @@ function cartan_bilinear_form(gcm::ZZMatrix; check::Bool=true)
   sym = cartan_symmetrizer(gcm; check)
   bil = deepcopy(gcm)
   for i in 1:length(sym)
-    mul!(view(bil, i, :), sym[i])
+    mul!(view(bil, i:i, :), sym[i])
   end
   return bil
 end
diff --git a/experimental/LieAlgebras/src/RootSystem.jl b/experimental/LieAlgebras/src/RootSystem.jl
index ab7256a7d321..21277ffde10b 100644
--- a/experimental/LieAlgebras/src/RootSystem.jl
+++ b/experimental/LieAlgebras/src/RootSystem.jl
@@ -812,7 +812,7 @@ end
 Reflects the `w` at the `s`-th simple root in place and returns `w`.
 """
 function reflect!(w::WeightLatticeElem, s::Int)
-  addmul!(w.vec, view(cartan_matrix(root_system(w)), :, s), -w.vec[s])
+  addmul!(w.vec, view(cartan_matrix(root_system(w)), :, s:s), -w.vec[s])
   return w
 end
 
diff --git a/experimental/QuadFormAndIsom/test/runtests.jl b/experimental/QuadFormAndIsom/test/runtests.jl
index c95172e9d597..940b57243b1c 100644
--- a/experimental/QuadFormAndIsom/test/runtests.jl
+++ b/experimental/QuadFormAndIsom/test/runtests.jl
@@ -364,7 +364,7 @@ end
   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]);
   L = integer_lattice(B, gram = G);
-  k = lattice_in_same_ambient_space(L, B[2, :])
+  k = lattice_in_same_ambient_space(L, B[2:2, :])
   N = orthogonal_submodule(L, k)
   ok, reps = primitive_extensions(k, N; glue_order=3)
   @test ok
diff --git a/experimental/Schemes/ToricIdealSheaves/constructors.jl b/experimental/Schemes/ToricIdealSheaves/constructors.jl
index c7cb50194f28..799a63843f67 100644
--- a/experimental/Schemes/ToricIdealSheaves/constructors.jl
+++ b/experimental/Schemes/ToricIdealSheaves/constructors.jl
@@ -85,7 +85,7 @@ function IdealSheaf(X::NormalToricVariety, I::MPolyIdeal)
     for m in hilbert_basis(weight_cone(U))
       img = one(help_ring)
       for j in 1:length(indices)
-        u_rho = matrix(ZZ,rays(X))[indices[j],:]
+        u_rho = matrix(ZZ,rays(X))[indices[j]:(indices[j]),:]
         expo = (u_rho*m)[1]
         img = img * x_rho[j]^expo
       end
diff --git a/experimental/SymmetricIntersections/src/homogeneous_polynomial_actions.jl b/experimental/SymmetricIntersections/src/homogeneous_polynomial_actions.jl
index c8867abb1f12..6ec8e79f693c 100644
--- a/experimental/SymmetricIntersections/src/homogeneous_polynomial_actions.jl
+++ b/experimental/SymmetricIntersections/src/homogeneous_polynomial_actions.jl
@@ -20,7 +20,7 @@ function is_semi_invariant_polynomial(rep::LinRep, f::S) where S <: MPolyDecRing
   R1, R1toR = homogeneous_component(R, 1)
   repd = dual_representation(rep)
   for m in matrix_representation(repd)
-    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i,:]))) for i in 1:nrows(m)]
+    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i:i,:]))) for i in 1:nrows(m)]
     fd = evaluate(f, poly_m)
     ok, k = divides(fd, f)
     if !ok || !is_constant(k)
@@ -48,7 +48,7 @@ function linear_representation(rep::LinRep, f::S) where S <: MPolyDecRingElem
   repd = dual_representation(rep)
   coll = eltype(matrix_representation(rep))[]
   for m in matrix_representation(rep)
-    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i,:]))) for i in 1:nrows(m)]
+    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i:i,:]))) for i in 1:nrows(m)]
     fd = evaluate(f, poly_m)
     ok, k = divides(fd, f)
     @req ok && is_constant(k) "Polynomial is not semi-invariant"
@@ -74,7 +74,7 @@ function is_invariant_ideal(rep::LinRep, I::S) where S <: MPolyIdeal{<: MPolyDec
   R1, R1toR = homogeneous_component(R, 1)
   repd = dual_representation(rep)
   for f in gene for m in matrix_representation(repd)
-    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i,:]))) for i in 1:nrows(m)]
+    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i:i,:]))) for i in 1:nrows(m)]
     fd = evaluate(f, poly_m)
     fd in I || return false
   end
@@ -147,7 +147,7 @@ function parametrization_data(symci::SymInter)
   for (B, n) in pd
     B2 = Vector{MPolyDecRingElem}[]
     for b in B
-      vv = elem_type(S)[j(R(reverse_cols!(b[i,:]))) for i in 1:nrows(b)]
+      vv = elem_type(S)[j(R(reverse_cols!(b[i:i,:]))) for i in 1:nrows(b)]
       push!(B2, vv)
     end
     push!(pd2, (B2, n))
@@ -169,7 +169,7 @@ function standard_element(symci::SymInter)
   std_el2 = elem_type(S)[]
   for B in std_el
     for b in B
-      vv = elem_type(S)[j(R(reverse_cols!(b[i,:]))) for i in 1:nrows(b)]
+      vv = elem_type(S)[j(R(reverse_cols!(b[i:i,:]))) for i in 1:nrows(b)]
       append!(std_el2, vv)
     end
   end
diff --git a/experimental/SymmetricIntersections/src/representations.jl b/experimental/SymmetricIntersections/src/representations.jl
index dd278fac14f4..e5ca6e2bedba 100644
--- a/experimental/SymmetricIntersections/src/representations.jl
+++ b/experimental/SymmetricIntersections/src/representations.jl
@@ -894,7 +894,7 @@ function _action_symmetric_power(mr::Vector{AbstractAlgebra.Generic.MatSpaceElem
   bsp = reverse!(RdtoR.(gens(Rd)))
   coll = eltype(mr)[]
   for m in mr
-    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i,:]))) for i in 1:nrows(m)]
+    poly_m = elem_type(R)[R1toR(R1(reverse_cols!(m[i:i,:]))) for i in 1:nrows(m)]
     @assert length(poly_m) == n
     m2 = zero_matrix(F, length(bsp), length(bsp))
     for i = 1:length(bsp)
@@ -1278,8 +1278,8 @@ function complement_submodule(rep::LinRep{S, T, U}, M::W) where {S, T, U, W <: M
       _K = zero_matrix(F, d*length(B1), d*length(B2))
       for j in 1:length(B2)
         B2j = B2[j]
-        B2jM = (B2j*M)[1,:]
-        B1u = reduce(vcat, [BB[1,:] for BB in B1])
+        B2jM = (B2j*M)[1:1,:]
+        B1u = reduce(vcat, [BB[1:1,:] for BB in B1])
         _Kj = solve_left(B1u, B2jM)
         for i in 1:d, k in 1:length(B1)
           _K[(k-1)*d + i, i + (j-1)*d] = _Kj[1, k]
diff --git a/src/AlgebraicGeometry/Surfaces/K3Auto.jl b/src/AlgebraicGeometry/Surfaces/K3Auto.jl
index d642cd4fb374..12d50f3a7af1 100644
--- a/src/AlgebraicGeometry/Surfaces/K3Auto.jl
+++ b/src/AlgebraicGeometry/Surfaces/K3Auto.jl
@@ -123,7 +123,7 @@ function BorcherdsCtx(L::ZZLat, S::ZZLat, weyl::ZZMatrix; compute_OR::Bool=true)
   I = identity_matrix(QQ,degree(L))
   # prS: L --> S^\vee given with respect to the standard basis of L and the basis of S
   prS = ibSR*I[:,1:rank(S)]#*basis_matrix(S)
-  @assert prS[rank(S)+1,:]==0
+  @assert prS[[rank(S)+1],:]==0
 
 
   if compute_OR
@@ -486,7 +486,7 @@ function _possible(D::K3Chamber, per, I, J)
     end
 
     for i in 1:I
-      if (vectorsj*T[:,i])[1,1] != gramB[J,per[i]]
+      if (vectorsj*T[:,i:i])[1,1] != gramB[J,per[i]]
         good_scalar = false
         break
       end
@@ -617,7 +617,7 @@ function separating_hyperplanes(gram::QQMatrix, v::QQMatrix, h::QQMatrix, d)
   ch = QQ((h*gram*transpose(h))[1,1])
   cv = QQ((h*gram*transpose(v))[1,1])
   b = basis_matrix(L)
-  prW = reduce(vcat,[b[i,:] - (b[i,:]*gram*transpose(h))*ch^-1*h for i in 1:n])
+  prW = reduce(vcat,[b[i:i,:] - (b[i:i,:]*gram*transpose(h))*ch^-1*h for i in 1:n])
   W = lattice(ambient_space(L), prW, isbasis=false)
   bW = basis_matrix(W)
   # set up the quadratic triple for SW
@@ -747,7 +747,7 @@ function alg319(D::K3Chamber, E::K3Chamber)
       k = nrows(img)
       gi = gram*transpose(img)
       for r in raysE
-        if (r*gram*transpose(r))[1,1] != gram_basis[k+1,k+1] || (k>0 && r*gi != gram_basis[k+1,1:k])
+        if (r*gram*transpose(r))[1,1] != gram_basis[k+1,k+1] || (k>0 && r*gi != gram_basis[k+1:k+1,1:k])
           continue
         end
         # now r has the correct inner products with what we need
@@ -816,7 +816,7 @@ function alg319(gram::MatrixElem, basis::ZZMatrix, gram_basis::QQMatrix, raysD::
       k = nrows(img)
       gi = gram*transpose(img)
       for r in raysE
-        if (r*gram*transpose(r))[1,1] != gram_basis[k+1,k+1] || (k>0 && r*gi != gram_basis[k+1,1:k])
+        if (r*gram*transpose(r))[1,1] != gram_basis[k+1,k+1] || (k>0 && r*gi != gram_basis[k+1:k+1,1:k])
           continue
         end
         # now r has the correct inner products with what we need
@@ -1732,8 +1732,8 @@ function weyl_vector(L::ZZLat, U0::ZZLat)
       v = (v + 2*x)*basis_matrix(R)
       @hassert :K3Auto 1 mod(inner_product(V,v,v)[1,1], 8)==0
       u = basis_matrix(U)
-      f1 = u[1,:]
-      e1 = u[2,:] + u[1,:]
+      f1 = u[1:1,:]
+      e1 = u[2:2,:] + u[1:1,:]
       f2 = -inner_product(V, v, v)*1//4*f1 + 2*e1 + v
       @hassert :K3Auto 1 inner_product(V, f2, f2)==0
 
@@ -1759,8 +1759,8 @@ function weyl_vector(L::ZZLat, U0::ZZLat)
         @vprint :K3Auto 1 "found a lattice of minimum $(m) \n"
         if m==4
           # R is isomorphic to the Leech lattice
-          fu = basis_matrix(U)[1,:]
-          zu = basis_matrix(U)[2,:]
+          fu = basis_matrix(U)[1:1,:]
+          zu = basis_matrix(U)[2:2,:]
           u0 = 3*fu+zu
           return fu,u0
         end
@@ -1770,8 +1770,8 @@ function weyl_vector(L::ZZLat, U0::ZZLat)
         # with the attached hyperbolic planes this can be engineered to give an isometry
         @hassert :K3Auto 1 mod(inner_product(V,v,v)[1,1],2*h^2)==0
         u = basis_matrix(U)
-        f1 = u[1,:]
-        e1 = u[2,:] + u[1,:]
+        f1 = u[1:1,:]
+        e1 = u[2:2,:] + u[1:1,:]
         f2 = -inner_product(V, v, v)*1//(2*h)*f1 + h*e1 + v
         @hassert :K3Auto 1 inner_product(V, f2, f2)==0
 
@@ -1821,7 +1821,7 @@ function borcherds_method_preprocessing(S::ZZLat, n::Integer; ample=nothing)
     u = u2*u1
     @assert g2 == u*G*transpose(u)
     B = u*basis_matrix(L)
-    B = vcat(B[1,:],B[end,:]-B[1,:])
+    B = vcat(B[1:1,:],B[end:end,:]-B[1:1,:])
     if inner_product(V,B,B) != QQ[0 1; 1 -2]
       # find an isotropic vector
       if gram_matrix(S)[1,1]==0
@@ -1882,7 +1882,7 @@ function ample_class(S::ZZLat)
   u = basis_matrix(S)[1:2,:]
   if inner_product(V,u,u) == QQ[0 1; 1 -2]
     h = zero_matrix(QQ,1,rank(S))
-    v = 3*u[1,:] + u[2,:]
+    v = 3*u[1:1,:] + u[2:2,:]
     fudge = 1
     nt = 0
     while true
@@ -1913,7 +1913,7 @@ function ample_class(S::ZZLat)
   G = gram_matrix(S)
   D, B = Hecke._gram_schmidt(G,identity,true)
   i = findfirst(x->x, [d>0 for d in diagonal(D)])
-  v = B[i,:]
+  v = B[i:i,:]
   v = denominator(v)*v
   vsq = (v*gram_matrix(S)*transpose(v))[1,1]
   @assert vsq > 0
@@ -2020,7 +2020,7 @@ function find_section(L::ZZLat, f::QQMatrix)
   g = [abs(i) for i in vec(collect(inner_product(ambient_space(L),f,basis_matrix(L))))]
   if 1 in g
     i = findfirst(x->x==1,g)
-    s = basis_matrix(L)[i,:]
+    s = basis_matrix(L)[i:i,:]
     s = sign(inner_product(ambient_space(L),f,s)[1,1])*s
   else
     # search a smallish section using a cvp
diff --git a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/standard_constructions.jl b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/standard_constructions.jl
index 2285fe161fde..79fdb9e837aa 100644
--- a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/standard_constructions.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/standard_constructions.jl
@@ -228,13 +228,13 @@ function normal_toric_variety_from_star_triangulation(P::Polyhedron)
   # Find position of origin in the lattices points of the polyhedron P
   pts = matrix(ZZ, lattice_points(P))
   zero = [0 for i in 1:ambient_dim(P)]
-  indices = findall(k -> pts[k,:] == matrix(ZZ, [zero]), 1:nrows(pts))
+  indices = findall(k -> pts[k:k,:] == matrix(ZZ, [zero]), 1:nrows(pts))
   @req length(indices) == 1 "Polyhedron must contain origin (exactly once)"
 
   # Change order of lattice points s.t. zero is the first point
-  tmp = pts[1,:]
-  pts[1,:] = pts[indices[1],:]
-  pts[indices[1],:] = tmp
+  tmp = pts[1:1,:]
+  pts[1:1,:] = pts[indices[1]:indices[1],:]
+  pts[indices[1]:indices[1],:] = tmp
 
   # Find one triangulation and turn it into the maximal cones of the toric variety in question. Note that:
   # (a) needs to be converted to incidence matrix
@@ -242,7 +242,7 @@ function normal_toric_variety_from_star_triangulation(P::Polyhedron)
   max_cones = IncidenceMatrix([[c[i]-1 for i in 2:length(c)] for c in _find_full_star_triangulation(pts)])
 
   # Rays are all but the zero vector at the first position of pts
-  integral_rays = reduce(vcat, [pts[k,:] for k in 2:nrows(pts)])
+  integral_rays = reduce(vcat, [pts[k:k,:] for k in 2:nrows(pts)])
 
   # construct the variety
   return normal_toric_variety(max_cones, integral_rays; non_redundant = true)
@@ -280,7 +280,7 @@ function normal_toric_varieties_from_star_triangulations(P::Polyhedron)
   # find position of origin in the lattices points of the polyhedron P
   pts = matrix(ZZ, lattice_points(P))
   zero = [0 for i in 1:ambient_dim(P)]
-  indices = findall(k -> pts[k,:] == matrix(ZZ, [zero]), 1:nrows(pts))
+  indices = findall(k -> pts[k:k,:] == matrix(ZZ, [zero]), 1:nrows(pts))
   @req length(indices) == 1 "Polyhedron must contain origin (exactly once)"
   
   # change order of lattice points s.t. zero is the first point
@@ -408,7 +408,7 @@ function normal_toric_varieties_from_glsm(charges::ZZMatrix)
   pts = vcat(matrix(QQ, transpose(zero)), matrix(QQ, pts))
   
   # construct varieties
-  integral_rays = reduce(vcat, [pts[k,:] for k in 2:nrows(pts)])
+  integral_rays = reduce(vcat, [pts[k:k,:] for k in 2:nrows(pts)])
   max_cones = [IncidenceMatrix([[c[i]-1 for i in 2:length(c)] for c in t]) for t in star_triangulations(pts; full = true)]
   varieties = [normal_toric_variety(cones, integral_rays; non_redundant = true) for cones in max_cones]
   
diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
index 91dde0fb7b3a..b478a69c21d5 100644
--- a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
@@ -77,8 +77,8 @@ Map
     for i in 1:nrows(images)
       v = [images[i,k] for k in 1:ncols(images)]
       j = findfirst(x -> x == true, [(v in maximal_cones(cod)[j]) for j in 1:nmaxcones(cod)])
-      m = reduce(vcat, [Int(ray_indices(maximal_cones(cod))[j, k]) * cod_rays[k, :] for k in 1:nrays(cod)])
-      mapping_matrix = hcat(mapping_matrix, solve(transpose(m), transpose(images[i, :])))
+      m = reduce(vcat, [Int(ray_indices(maximal_cones(cod))[j, k]) * cod_rays[k:k, :] for k in 1:nrays(cod)])
+      mapping_matrix = hcat(mapping_matrix, solve(transpose(m), transpose(images[i:i, :])))
     end
     return hom(torusinvariant_weil_divisor_group(d), torusinvariant_weil_divisor_group(cod), transpose(mapping_matrix))
 end
diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricSchemes/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/ToricSchemes/attributes.jl
index c80073bd1772..b61ed5347ec9 100644
--- a/src/AlgebraicGeometry/ToricVarieties/ToricSchemes/attributes.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/ToricSchemes/attributes.jl
@@ -183,12 +183,12 @@ end
 
 # Write the elements in `degs2` as linear combinations of `degs1`, allowing only non-negative 
 # coefficients for the vectors vᵢ of `degs1` with index i ∈ `non_local_indices`.
-function _convert_degree_system(degs1::ZZMatrix, degs2::ZZMatrix, non_local_indices_1::Vector{Int64})
+function _convert_degree_system(degs1::ZZMatrix, degs2::ZZMatrix, non_local_indices_1::Vector{Int})
   result = Vector{ZZMatrix}()
   for i in 1:nrows(degs2)
     C = identity_matrix(ZZ, nrows(degs1))[non_local_indices_1,:]
-    S = solve_mixed(transpose(degs1), transpose(degs2[i,:]), C; permit_unbounded=true)  
-    push!(result, S[1, :])
+    S = solve_mixed(transpose(degs1), transpose(degs2[i:i,:]), C; permit_unbounded=true)
+    push!(result, S[1:1, :])
   end
   return result
 end
diff --git a/src/Groups/matrices/FiniteFormOrthogonalGroup.jl b/src/Groups/matrices/FiniteFormOrthogonalGroup.jl
index ee413587e5b1..6af104943d62 100644
--- a/src/Groups/matrices/FiniteFormOrthogonalGroup.jl
+++ b/src/Groups/matrices/FiniteFormOrthogonalGroup.jl
@@ -368,14 +368,14 @@ function _lift(q::T, f::T, a) where T <: Union{ZZModMatrix, zzModMatrix}
   if mod(lift(q[end-1,end-1] + q[end,end]), 4) == 2
     g[end, end-1] = a
     g[1:end-2,end-1] = diagonal(divexact(G - f*G*transpose(f),2))
-    g[end,1:end-2] = transpose(fGinv * g[1:end-2,end-1])
+    g[end:end,1:end-2] = transpose(fGinv * g[1:end-2,end-1:end-1])
   else
     if a == 0
       a = zeros(R, ncols(q)-2)
     end
     g[1:end-2,end-1] = a
-    g[end,1:end-2] = transpose(fGinv * g[1:end-2,end-1])
-    t = (g[end,1:end-2]*G*transpose(g[end,1:end-2]))[1,1]
+    g[[end],1:end-2] = transpose(fGinv * g[1:end-2,end-1:end-1])
+    t = (g[end:end,1:end-2]*G*transpose(g[end:end,1:end-2]))[1,1]
     g[end,end-1] = divexact(t-mod(lift(t), 2), 2)
   end
   err = g*qb*transpose(g)-qb
@@ -642,9 +642,9 @@ function _ker_gens(G::Union{ZZModMatrix, zzModMatrix}, i1, i2, parity)
       end
       if parity[1]==1 && parity[3]==1
         # compensate
-        g[e+1, i1] = divexact((g[e+1,i1+1:i2]*G[i1+1:i2,i1+1:i2]*transpose(g[e+1,i1+1:i2]))[1,1],4)
+        g[e+1, i1] = divexact((g[e+1:e+1,i1+1:i2]*G[i1+1:i2,i1+1:i2]*transpose(g[e+1:e+1,i1+1:i2]))[1,1],4)
         # the second row depends on the third
-        g[i1+1:i2,i1] = - divexact((G[i1+1:i2,i1+1:i2]* transpose(g[i2+1:end,i1+1:i2]) * inv(G[i2+1:end,i2+1:end]))[:,end], 2)
+        g[i1+1:i2,i1:i1] = - divexact((G[i1+1:i2,i1+1:i2]* transpose(g[i2+1:end,i1+1:i2]) * inv(G[i2+1:end,i2+1:end]))[:,end:end], 2)
       end
       if g[i,j] == 1   # no need to append the identity
         push!(gens, g)
diff --git a/src/Groups/matrices/iso_nf_fq.jl b/src/Groups/matrices/iso_nf_fq.jl
index f83028f34a88..71b0020b0cbc 100644
--- a/src/Groups/matrices/iso_nf_fq.jl
+++ b/src/Groups/matrices/iso_nf_fq.jl
@@ -178,7 +178,7 @@ function test_modulus(matrices::Vector{T}, p::Int) where T <: MatrixElem{nf_elem
    # I don't want to invert everything in char 0, so I just check whether the
    # matrices are still invertible mod p.
    for i = 1:length(matrices)
-      matrices_Fq[i] = matrix(Fq, [ OtoFq(O(numerator(a)))//OtoFq(O(denominator(a))) for a in matrices[i] ])
+      matrices_Fq[i] = map_entries(a -> OtoFq(O(numerator(a)))//OtoFq(O(denominator(a))), matrices[i])
       if rank(matrices_Fq[i]) != nrows(matrices_Fq[i])
          return false, Fq, matrices_Fq, Hecke.NfOrdToFqMor()
       end
diff --git a/src/Groups/spinor_norms.jl b/src/Groups/spinor_norms.jl
index 50b46ebe0223..687fe04feb47 100644
--- a/src/Groups/spinor_norms.jl
+++ b/src/Groups/spinor_norms.jl
@@ -124,7 +124,7 @@ function reflection(gram::MatElem, v::MatElem)
   c = base_ring(gram)(2) * ((v * gram * transpose(v)))[1,1]^(-1)
   ref = zero_matrix(base_ring(gram), n, n)
   for k in 1:n
-    ref[k,:] = E[k,:] - c*(E[k,:] * gram * transpose(v))*v
+    ref[k:k,:] = E[k:k,:] - c*(E[k:k,:] * gram * transpose(v))*v
   end
   return ref
 end
@@ -206,7 +206,7 @@ function det_spin(G::QQMatrix, T::QQMatrix, p, nu)
 
   k = 1
   while k <= l
-    g = T[k,:]
+    g = T[k:k,:]
     # error estimates
     lambd = valuation(g, p)
     rho = min(delta + nu + gamma, 2*nu + gamma)
@@ -216,20 +216,20 @@ function det_spin(G::QQMatrix, T::QQMatrix, p, nu)
       # precision too low
       return ZZ(0), QQ(0)
     end
-    bm = g - E[k,:]
+    bm = g - E[k:k,:]
     qm = bm * G * transpose(bm)
     if valuation(qm, p) <= gammaL[k] + 2*delta
       tau1 = reflection(G, bm)
       push!(reflection_vectors, bm)
       tau2 = E
     else
-      bp = g + E[k,:]
+      bp = g + E[k:k,:]
       qp = bp * G * transpose(bp)
       @assert valuation(qp, p) <= gammaL[k] + 2*delta
       tau1 = reflection(G, bp)
-      tau2 = reflection(G, E[k,:])
+      tau2 = reflection(G, E[k:k,:])
       push!(reflection_vectors,bp)
-      push!(reflection_vectors,E[k,:])
+      push!(reflection_vectors,E[k:k,:])
     end
     lambdaT = valuation(T, p)
     alpha = valuation(tau1, p)
diff --git a/src/Modules/ModuleTypes.jl b/src/Modules/ModuleTypes.jl
index 02decdce8796..43bcc30af1b6 100644
--- a/src/Modules/ModuleTypes.jl
+++ b/src/Modules/ModuleTypes.jl
@@ -610,7 +610,7 @@ function FreeModuleHom(
   ) where {T<:RingElem,S<:AbstractFreeMod}
   @assert nrows(mat) == ngens(F)
   @assert ncols(mat) == ngens(G)
-  hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i,:]), G) for i=1:ngens(F)])
+  hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)])
   hom.matrix = mat
   return hom
 end
@@ -620,7 +620,7 @@ function FreeModuleHom(
   ) where {T<:RingElem, S<:ModuleFP}
   @assert nrows(mat) == ngens(F)
   @assert ncols(mat) == ngens(G)
-  hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i,:]), G) for i=1:ngens(F)])
+  hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)])
   hom.matrix = mat
   return hom
 end
@@ -631,7 +631,7 @@ function FreeModuleHom(
   @assert nrows(mat) == ngens(F)
   @assert ncols(mat) == ngens(G)
   @assert base_ring(mat) === base_ring(G)
-  hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i,:]), G) for i=1:ngens(F)], h)
+  hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h)
   hom.matrix = mat
   return hom
 end
@@ -642,7 +642,7 @@ function FreeModuleHom(
   @assert nrows(mat) == ngens(F)
   @assert ncols(mat) == ngens(G)
   @assert base_ring(mat) === base_ring(G)
-  hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i,:]), G) for i=1:ngens(F)], h)
+  hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h)
   hom.matrix = mat
   return hom
 end
diff --git a/src/Modules/Posur.jl b/src/Modules/Posur.jl
index cc2e94a84d29..a8d1099b5762 100644
--- a/src/Modules/Posur.jl
+++ b/src/Modules/Posur.jl
@@ -212,7 +212,7 @@ function has_solution(
   (success, u, a) = has_nonempty_intersection(U, I, check=check)
   success || return (false, zero_matrix(R, 1, ngens(I)), zero(R))
   l = a*L 
-  return (success, l[1, 2:end], l[1,1])
+  return (success, l[1:1, 2:end], l[1,1])
 end
 
 ########################################################################
@@ -494,8 +494,8 @@ function coordinates(u::FreeModElem{T}, M::SubquoModule{T}) where {T<:AbsLocaliz
   # 
   # with x = [y z]. Now we would like to cache v' as a new generator for the 
   # `pre_saturated_module(M)` and w' as a new relation of it. 
-  y = x[1, 1:r]
-  z = x[1, r+1:r+s]
+  y = x[1:1, 1:r]
+  z = x[1:1, r+1:r+s]
   v = y*A
   w = z*B
   (v_clear, d_v) = clear_denominators(v)
@@ -524,7 +524,7 @@ function coordinates(u::FreeModElem{T}, M::SubquoModule{T}) where {T<:AbsLocaliz
                 )
   set_attribute!(M, :pre_saturated_module, Mbext)
   # finally, return the computed coordinates
-  result = x[1, 1:r]
+  result = x[1:1, 1:r]
   return sparse_row(result)
 end
 
@@ -582,8 +582,8 @@ function represents_element(u::FreeModElem{T}, M::SubquoModule{T}) where {T<:Abs
   # 
   # with x = [y z]. Now we would like to cache v' as a new generator for the 
   # `pre_saturated_module(M)` and w' as a new relation of it. 
-  y = x[1, 1:r]
-  z = x[1, r+1:r+s]
+  y = x[1:1, 1:r]
+  z = x[1:1, r+1:r+s]
   v = y*A
   w = z*B
   (v_clear, d_v) = clear_denominators(v)
diff --git a/src/Modules/UngradedModules/SubModuleOfFreeModule.jl b/src/Modules/UngradedModules/SubModuleOfFreeModule.jl
index f911245db512..8a4e603433cb 100644
--- a/src/Modules/UngradedModules/SubModuleOfFreeModule.jl
+++ b/src/Modules/UngradedModules/SubModuleOfFreeModule.jl
@@ -47,7 +47,7 @@ module is `F`. In particular, `rank(F) == ncols(A)` must hold.
 """
 function SubModuleOfFreeModule(F::FreeMod{L}, A::MatElem{L}) where {L} 
   subModule = SubModuleOfFreeModule{L}(F)
-  O = [FreeModElem(sparse_row(A[i,:]), F) for i in 1:nrows(A)]
+  O = [FreeModElem(sparse_row(A[i:i,:]), F) for i in 1:nrows(A)]
   subModule.gens = ModuleGens(O, F)
   subModule.matrix = A
   return subModule
diff --git a/src/Modules/UngradedModules/SubQuoHom.jl b/src/Modules/UngradedModules/SubQuoHom.jl
index 0b2394f43eda..32c6cec52cc7 100644
--- a/src/Modules/UngradedModules/SubQuoHom.jl
+++ b/src/Modules/UngradedModules/SubQuoHom.jl
@@ -21,10 +21,10 @@ function SubQuoHom(D::SubquoModule, C::ModuleFP{T}, mat::MatElem{T}; check::Bool
   @assert nrows(mat) == ngens(D)
   @assert ncols(mat) == ngens(C)
   if C isa FreeMod
-    hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i,:]), C) for i=1:ngens(D)])
+    hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)])
     return hom
   else
-    hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i,:]), C) for i=1:ngens(D)])
+    hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)])
     return hom
   end
 end
@@ -1265,7 +1265,7 @@ function simplify(M::SubquoModule)
   for i=1:size(M_generators)[1]
     if i in to_delete
       index = findfirst(x -> x==i, to_delete)
-      assign_row!(projection_matrix, R(-1)*R(inv(coeff(K_gen[corresponding_row[index],i], 1)))*delete_columns(K_gen[corresponding_row[index],:], to_delete), i)
+      assign_row!(projection_matrix, R(-1)*R(inv(coeff(K_gen[corresponding_row[index],i], 1)))*delete_columns(K_gen[corresponding_row[index]:(corresponding_row[index]),:], to_delete), i)
     else
       standard_unit_vector_index = i-length(filter(x -> x < i, to_delete))
       standard_unit_vector = [j == standard_unit_vector_index ? R(1) : R(0) for j=1:size(projection_matrix)[2]]
diff --git a/src/Modules/missing_functionality.jl b/src/Modules/missing_functionality.jl
index 04087b22071b..9e96c88f4a18 100644
--- a/src/Modules/missing_functionality.jl
+++ b/src/Modules/missing_functionality.jl
@@ -42,7 +42,7 @@ function coordinates(f::MPolyQuoRingElem, I::MPolyQuoIdeal)
   J = modulus(Q)
   R = base_ring(Q)
   K = ideal(R, vcat(lift.(gens(I)), gens(J)))
-  return Q.(coordinates(lift(f), K)[1, 1:ngens(I)])
+  return Q.(coordinates(lift(f), K)[1:1, 1:ngens(I)])
 end
 
 function lift(f::MPolyRingElem, I::MPolyIdeal, o::MonomialOrdering)
diff --git a/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl b/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl
index 6105126bca72..f22a4eaa519a 100644
--- a/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl
+++ b/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl
@@ -106,7 +106,7 @@ function star_subdivision(Sigma::_FanLikeType, new_ray::AbstractVector{<:Integer
   
   old_rays = matrix(ZZ, rays(Sigma))
   # In case the new ray is an old ray.
-  new_ray_index = findfirst(i->vec(old_rays[i,:])==new_ray, 1:nrows(old_rays))
+  new_ray_index = findfirst(i->vec(old_rays[i:i,:])==new_ray, 1:nrows(old_rays))
   new_rays = old_rays
   if isnothing(new_ray_index)
     new_rays = vcat(old_rays, matrix(ZZ, [new_ray]))
diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index e6a9a6928be5..0b685a396177 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -1729,7 +1729,7 @@ function coordinates(a::RingElem, I::MPolyQuoLocalizedIdeal)
   parent(a) === L || return coordinates(L(a), I)
   a in I || error("the given element is not in the ideal")
   x = coordinates(lift(a), pre_image_ideal(I), check=false)
-  return map_entries(L, x[1, 1:ngens(I)])
+  return map_entries(L, x[1:1, 1:ngens(I)])
 end
 
 function saturated_ideal(I::MPolyQuoLocalizedIdeal)
diff --git a/src/Rings/orderings.jl b/src/Rings/orderings.jl
index 2a627f5e0208..c1cbbf169d9d 100644
--- a/src/Rings/orderings.jl
+++ b/src/Rings/orderings.jl
@@ -93,7 +93,7 @@ function _canonical_matrix(w)
     if is_zero_row(w, i)
       continue
     end
-    nw = w[i, :]
+    nw = w[i:i, :]
     c = content(nw)
     if !isone(c)
       nw = divexact(nw, c)
@@ -101,7 +101,7 @@ function _canonical_matrix(w)
     for j in 1:nrows(ww)
       h = findfirst(x->ww[j, x] != 0, 1:ncols(w))
       if !iszero(nw[1, h])
-        nw = abs(ww[j, h])*nw - sign(ww[j, h])*nw[1, h]*ww[j, :]
+        nw = abs(ww[j, h])*nw - sign(ww[j, h])*nw[1, h]*ww[j:j, :]
       end
     end
     if !iszero(nw)
@@ -1954,7 +1954,7 @@ end
 
 function _opposite_ordering(nvars::Int, o::MatrixOrdering)
   M = o.matrix
-  M = reduce(hcat, [M[:,i] for i in ncols(M):-1:1])
+  M = reduce(hcat, [M[:,i:i] for i in ncols(M):-1:1])
   return MatrixOrdering(reverse(nvars+1 .- o.vars), M, false)
 end
 
diff --git a/test/Rings/orderings.jl b/test/Rings/orderings.jl
index 10b25b0d7631..a0f7c397db45 100644
--- a/test/Rings/orderings.jl
+++ b/test/Rings/orderings.jl
@@ -212,7 +212,7 @@ function test_opposite_ordering(a)
   R = base_ring(a)
   b = opposite_ordering(R, a)
   M = matrix(a)
-  N = reduce(hcat, [M[:,i] for i in ncols(M):-1:1])
+  N = reduce(hcat, [M[:,i:i] for i in ncols(M):-1:1])
   @test b == matrix_ordering(gens(R), N)
   @test a == opposite_ordering(R, b)
 end