Remove many calls to *cat(::Vector{...}) (#1253)

* Remove many calls to `hcat(::Vector{...})`

* Remove many calls to `vcat(::Vector{...})`

examples/Klueners.jl

@@ -186,7 +186,7 @@ function s3_extensions(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
   wild = [1*zk]
   for (P, e) = l3
     b = floor(Int, 3//2*(1+e))
-    wild = vcat([[P^i * x for x = wild] for i=1:b]...)
+    wild = reduce(vcat, [[P^i * x for x = wild] for i=1:b])
   end
   sort!(wild, lt = (a,b) -> norm(a) <= norm(b))
 
@@ -282,12 +282,12 @@ function s3_extensions(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
       return
     end
 
-    m2, map2 = sub(R.M, vcat([lift(mat(x[2])) for x = i2]), !false)
+    m2, map2 = sub(R.M, reduce(vcat, [lift(mat(x[2])) for x = i2]), !false)
     sub_m2 = Hecke.stable_subgroups(m2, [GrpAbFinGenMap(map2*x*pseudo_inv(map2)) for x = R.ac], quotype = [3, 3], op = (R, x) -> sub(R, x, !false))
     m1 = []
     target_ind = 0
     for (k,v) = ii
-      m, mp = sub(R.M, vcat([lift(mat(i1[x][2])) for x = v]))
+      m, mp = sub(R.M, reduce(vcat, [lift(mat(i1[x][2])) for x = v]))
       push!(m1, mp)
       if target == k
         target_ind = length(m1)
@@ -302,7 +302,7 @@ function s3_extensions(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
       if length(m1) == 1
         rest = sub(R.M, [R.M[0]])
       else
-        rest = sub(R.M, vcat([matrix(m1[j]) for j=1:length(m1) if i != j]), !false)
+        rest = sub(R.M, reduce(vcat, [matrix(m1[j]) for j=1:length(m1) if i != j]), !false)
       end
       for s = sub_m2
         rr = rest[1]+map2(s[2](s[1])[1])[1]
@@ -534,7 +534,7 @@ function s3_extensions2(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
   wild = [1*zk]
   for (P, e) = l3
     b = floor(Int, 3//2*(1+e))
-    wild = vcat([[P^i * x for x = wild] for i=1:b]...)
+    wild = reduce(vcat, [[P^i * x for x = wild] for i=1:b])
   end
   sort!(wild, lt = (a,b) -> norm(a) <= norm(b))
   _wild = sort(collect(Set(minimum(x) for x = wild)))
@@ -589,12 +589,12 @@ function s3_extensions2(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
       return
     end
 
-    m2, map2 = sub(R.M, vcat([lift(mat(x[2])) for x = i2]), !false)
+    m2, map2 = sub(R.M, reduce(vcat, [lift(mat(x[2])) for x = i2]), !false)
     sub_m2 = Hecke.stable_subgroups(m2, [GrpAbFinGenMap(map2*x*pseudo_inv(map2)) for x = R.ac], quotype = [3, 3], op = (R, x) -> sub(R, x, !false))
     m1 = []
     target_ind = 0
     for (k,v) = ii
-      m, mp = sub(R.M, vcat([lift(mat(i1[x][2])) for x = v]))
+      m, mp = sub(R.M, reduce(vcat, [lift(mat(i1[x][2])) for x = v]))
       push!(m1, mp)
       if target == k
         target_ind = length(m1)
@@ -609,7 +609,7 @@ function s3_extensions2(k::AnticNumberField, d::ZZRingElem, _T::Int = 0)
       if length(m1) == 1
         rest = sub(R.M, [R.M[0]])
       else
-        rest = sub(R.M, vcat([matrix(m1[j]) for j=1:length(m1) if i != j]), !false)
+        rest = sub(R.M, reduce(vcat, [matrix(m1[j]) for j=1:length(m1) if i != j]), !false)
       end
       for s = sub_m2
         rr = rest[1]+map2(s[2](s[1])[1])[1]

examples/MultiQuad.jl

@@ -58,7 +58,7 @@ function multi_quad_with_emb(d::Vector{ZZRingElem})
     for i=1:div(length(lp), 2)
       K, m1, m2 = compositum(lp[2*i-1], lp[2*i])
       push!(ld, K)
-      push!(lau, vcat([ m1(x) for x = aut[2*i-1]], [ m2(x) for x = aut[2*i]]))
+      push!(lau, vcat([m1(x) for x = aut[2*i-1]], [m2(x) for x = aut[2*i]]))
     end
     if isodd(length(lp))
       push!(ld, lp[end])

examples/Round2.jl

@@ -438,7 +438,7 @@ function ring_of_multipliers(O::Order, I::MatElem)
   II, d = pseudo_inv(I)
   @assert II*I == d
 #  return II, d, [representation_matrix(O(vec(collect(I[i, :])))) for i=1:nrows(I)]
-  m = hcat([divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)]...)
+  m = reduce(hcat, [divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)])
   m = m'
   n = degree(O)
   mm = hnf(m[1:n, 1:n])

examples/polymake.jl

@@ -141,10 +141,10 @@ function norm_equation2_fac_elem(R::NfAbsOrd, k::ZZRingElem; abs::Bool = false)
   @assert Hecke.is_maximal(R)
   lp = factor(k*R)
   s, ms = Hecke.sunit_mod_units_group_fac_elem(collect(keys(lp)))
-  C = vcat([matrix(FlintZZ, 1, ngens(s), [valuation(ms(s[i]), p) for i=1:ngens(s)]) for p = keys(lp)])
+  C = reduce(vcat, [matrix(FlintZZ, 1, ngens(s), [valuation(ms(s[i]), p) for i=1:ngens(s)]) for p = keys(lp)])
 
   lp = factor(k)
-  A = vcat([matrix(FlintZZ, 1, ngens(s), [valuation(Hecke.factored_norm(ms(s[i])), p) for i=1:ngens(s)]) for p = keys(lp.fac)])
+  A = reduce(vcat, [matrix(FlintZZ, 1, ngens(s), [valuation(Hecke.factored_norm(ms(s[i])), p) for i=1:ngens(s)]) for p = keys(lp.fac)])
   b = matrix(FlintZZ, length(lp.fac), 1, [valuation(k, p) for p = keys(lp.fac)])
 
   so = solve_mixed(A, b, C)
@@ -225,9 +225,9 @@ function norm_equation_fac_elem(R::Hecke.NfRelOrd{nf_elem,Hecke.NfOrdFracIdl}, a
   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 = reduce(vcat, [matrix(FlintZZ, 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)])
+  A = reduce(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)])
 
   so = solve_mixed(A, b, C)

src/AlgAssAbsOrd/LocallyFreeClassGroup.jl

@@ -540,7 +540,7 @@ function image(m::DiscLogLocallyFreeClassGroup, I::AlgAssAbsOrdIdl)
 
     # Put the components together and map it to C
     G = codomain(mR.into_product_of_groups)
-    r = mR.into_product_of_groups\(GrpAbFinGenElem(G, hcat([ e.coeff for e in elts_in_R ])))
+    r = mR.into_product_of_groups \ (GrpAbFinGenElem(G, reduce(hcat, [e.coeff for e in elts_in_R])))
     c += RtoC(r)
   end
   return c

src/GenOrd/GenOrd.jl

@@ -486,7 +486,7 @@ function ring_of_multipliers(O::GenOrd, I::MatElem{T}, p::T, is_prime::Bool = fa
   II, d = pseudo_inv(I)
   @assert II*I == d
 
-  m = hcat([divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)]...)
+  m = reduce(hcat, [divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)])
   m = transpose(m)
   if is_prime
     x = residue_field(parent(p), p)
@@ -534,7 +534,7 @@ function ring_of_multipliers(O::GenOrd, I::MatElem)
   II, d = pseudo_inv(I)
   @assert II*I == d
 
-  m = hcat([divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)]...)
+  m = reduce(hcat, [divexact(representation_matrix(O(vec(collect(I[i, :]))))*II, d) for i=1:nrows(I)])
   m = transpose(m)
   n = degree(O)
   mm = hnf(m[1:n, 1:n])

src/GenOrd/Ideal.jl

@@ -178,7 +178,7 @@ function assure_has_basis_matrix(A::GenOrdIdl)
 
   @hassert :NfOrd 1 has_2_elem(A)
 
-  V = hnf(vcat([representation_matrix(x) for x in [O(A.gen_one),A.gen_two]]),:lowerleft)
+  V = hnf(reduce(vcat, [representation_matrix(x) for x in [O(A.gen_one),A.gen_two]]),:lowerleft)
   d = ncols(V)
   A.basis_matrix = V[d+1:2*d,1:d]
   return nothing
@@ -272,7 +272,7 @@ function Base.:(*)(a::GenOrdIdl, b::GenOrdIdl)
   O = order(a)
   Ma = basis_matrix(a)
   Mb = basis_matrix(b)
-  V = hnf(vcat([Mb*representation_matrix(O([Ma[i,o] for o in 1:ncols(Ma)])) for i in 1:ncols(Ma)]),:lowerleft)
+  V = hnf(reduce(vcat, [Mb*representation_matrix(O([Ma[i,o] for o in 1:ncols(Ma)])) for i in 1:ncols(Ma)]),:lowerleft)
   d = ncols(V)
   return GenOrdIdl(O, V[d*(d-1)+1:d^2,1:d])
 end

src/GenOrd/Types.jl

@@ -138,7 +138,7 @@ end
   function GenOrdIdl(O::GenOrd, T::Vector{<:GenOrdElem})
     @assert all(x -> parent(x) === O, T)
     # One should do this block by block instead of the big matrix
-    V = hnf(vcat([representation_matrix(O) for x in T]), :lowerleft)
+    V = hnf(reduce(vcat, [representation_matrix(O) for x in T]), :lowerleft)
     d = ncols(V)
     n = length(T)
     return GenOrdIdl(O, V[((n - 1)*d + 1):(n*d), :])

src/GrpAb/GrpAbFinGen.jl

@@ -784,7 +784,7 @@ function matrix(M::Map{GrpAbFinGen, GrpAbFinGen})
     return M.map
   end
   G = domain(M)
-  return vcat([M(g).coeff for g = gens(G)])
+  return reduce(vcat, [M(g).coeff for g = gens(G)])
 end
 
 function matrix(M::Generic.IdentityMap{GrpAbFinGen})
@@ -814,7 +814,7 @@ function hom(G::GrpAbFinGen, H::GrpAbFinGen, A::Matrix{ <: Map{GrpAbFinGen, GrpA
     error("both groups need to be direct products")
   end
   @assert all(i -> domain(A[i[1], i[2]]) == dG[i[1]] && codomain(A[i[1], i[2]]) == dH[i[2]], Base.Iterators.ProductIterator((1:r, 1:c)))
-  h = hom(G, H, vcat([hcat([matrix(A[i,j]) for j=1:c]) for i=1:r]))
+  h = hom(G, H, reduce(vcat, [reduce(hcat, [matrix(A[i,j]) for j=1:c]) for i=1:r]))
   return h
 end
 
@@ -823,15 +823,15 @@ function _flat(G::GrpAbFinGen)
   if s === nothing
     return [G]
   end
-  return vcat([_flat(x) for x = s]...)
+  return reduce(vcat, [_flat(x) for x = s])
 end
 
 function _tensor_flat(G::GrpAbFinGen)
   s = get_attribute(G, :tensor_product)
   if s === nothing
     return [G]
   end
-  return vcat([_tensor_flat(x) for x = s]...)
+  return reduce(vcat, [_tensor_flat(x) for x = s])
 end
 
 

src/GrpAb/Map.jl

@@ -86,10 +86,10 @@ function haspreimage(M::GrpAbFinGenMap, a::Vector{GrpAbFinGenElem})
     isdefined(H, :exponent) && G.exponent == H.exponent
     e = G.exponent
     RR = Native.GF(Int(e))
-    fl, p = can_solve_with_solution(map_entries(RR, m), map_entries(RR, vcat([x.coeff for x = a])), side = :left)
+    fl, p = can_solve_with_solution(map_entries(RR, m), map_entries(RR, reduce(vcat, [x.coeff for x = a])), side = :left)
     p = map_entries(x -> lift(x), p)
   else
-    fl, p = can_solve_with_solution(m, vcat([x.coeff for x = a]), side = :left)
+    fl, p = can_solve_with_solution(m, reduce(vcat, [x.coeff for x = a]), side = :left)
   end
 
   if fl
@@ -159,7 +159,7 @@ function hom(A::Vector{GrpAbFinGenElem}, B::Vector{GrpAbFinGenElem}; check::Bool
     return hom(GA, GB, matrix(FlintZZ, ngens(GA), 0, ZZRingElem[]), check = check)
   end
 
-  M = vcat([hcat(A[i].coeff, B[i].coeff) for i = 1:length(A)])
+  M = reduce(vcat, [hcat(A[i].coeff, B[i].coeff) for i = 1:length(A)])
   RA = rels(GA)
   M = vcat(M, hcat(RA, zero_matrix(FlintZZ, nrows(RA), ncols(B[1].coeff))))
   if isdefined(GB, :exponent) && nrows(M) >= ncols(M)
@@ -180,7 +180,7 @@ Creates the homomorphism which maps $G[i]$ to $B[i]$.
 function hom(G::GrpAbFinGen, B::Vector{GrpAbFinGenElem}; check::Bool = true)
   GB = parent(B[1])
   @assert length(B) == ngens(G)
-  M = vcat([B[i].coeff for i = 1:length(B)])
+  M = reduce(vcat, [B[i].coeff for i = 1:length(B)])
   h = hom(G, GB, M, check = check)
   return h
 end
@@ -191,7 +191,7 @@ function hom(G::GrpAbFinGen, H::GrpAbFinGen, B::Vector{GrpAbFinGenElem}; check::
   if length(B) == 0
     M = zero_matrix(ZZ, ngens(G), ngens(H))
   else
-    M = vcat([x.coeff for x = B]...)
+    M = reduce(vcat, [x.coeff for x = B])
   end
   #=
   M = zero_matrix(FlintZZ, ngens(G), ngens(H))
@@ -620,7 +620,7 @@ function hom(G::GrpAbFinGen, H::GrpAbFinGen; task::Symbol = :map)
     if ngens(sG) == 0
       return R[0]
     end
-    local mm = transpose(vcat([preimage(mH, r(mG(sG[i]))).coeff for i = 1:ngens(sG)]))
+    local mm = transpose(reduce(vcat, [preimage(mH, r(mG(sG[i]))).coeff for i = 1:ngens(sG)]))
     return R([divexact(mm[j,i], c[(i-1)*m+j]) for i=1:n for j=1:m])
   end
   return R, MapFromFunc(R, MapParent(G, H, "homomorphisms"), phi, ihp)

src/GrpAb/stable_sub.jl

@@ -334,7 +334,7 @@ function maximal_submodules(M::ZpnGModule, ind::Int=-1)
     end
     mH = Hecke.GrpAbFinGenMap(S.V,K,A)
     sg, msg = kernel(mH)
-    push!(list, vcat([ (mS(msg(y))).coeff for y in gens(sg)]))
+    push!(list, reduce(vcat, [(mS(msg(y))).coeff for y in gens(sg)]))
   end
   return list
 
@@ -762,7 +762,7 @@ function submodules_order(M::ZpnGModule, ord::Int)
 
   MatSnf=map(mS.map, R)
   for j=1:length(list)
-    list[j]=list[j]*MatSnf #vcat([W(( mS( S.V([list[j][k,i].data for i=1:ngens(S.V)]))).coeff)  for k=1:nrows(list[j])])
+    list[j]=list[j]*MatSnf #reduce(vcat, [W(( mS( S.V([list[j][k,i].data for i=1:ngens(S.V)]))).coeff)  for k=1:nrows(list[j])])
   end
 
   #
@@ -771,7 +771,7 @@ function submodules_order(M::ZpnGModule, ord::Int)
 
   minlist=minimal_submodules(N,ord, lf)
   for x in minlist
-    push!(list, vcat([W((mS( S.V(ZZRingElem[FlintZZ(coeff(x[k,i],0))*((M.p)^(v[i]-1)) for i=1:ngens(S.V)]))).coeff) for k=1:nrows(x) ]))
+    push!(list, reduce(vcat, [W((mS( S.V(ZZRingElem[FlintZZ(coeff(x[k,i],0))*((M.p)^(v[i]-1)) for i=1:ngens(S.V)]))).coeff) for k=1:nrows(x) ]))
   end
   return (x for x in list)
 

src/LocalField/neq.jl

@@ -205,7 +205,7 @@ end
 function coordinates(a::Union{qadic, LocalFieldElem}, k)
   c = [coeff(a, i) for i=0:degree(parent(a))-1]
   while absolute_degree(parent(c[1])) > absolute_degree(k)
-    c = vcat([[coeff(x, i) for i=0:(degree(parent(c[1]))-1)] for x = c]...)
+    c = reduce(vcat, [[coeff(x, i) for i=0:(degree(parent(c[1]))-1)] for x = c])
   end
   if parent(c[1]) != k
     if isa(parent(c[1]), FlintQadicField) && degree(parent(c[1])) ==1
@@ -300,7 +300,7 @@ function solve_1_units(a::Vector{T}, b::T) where T
     end
 
     expo += s.coeff * expo_mult
-    expo_mult = vcat([_mk(x).coeff for x = gens(_k)]...)*expo_mult
+    expo_mult = reduce(vcat, [_mk(x).coeff for x = gens(_k)])*expo_mult
     cur_a = [prod(cur_a[i]^_mk(x)[i] for i=1:length(cur_a)) for x = gens(_k)]
 #    @show [e*valuation(x-1) for x = cur_a]
 
@@ -562,8 +562,8 @@ struct MapEvalCtx
     mat = matrix(prime_field(domain(M)),
                  absolute_degree(domain(M)),
                  absolute_degree(codomain(M)),
-                 vcat([absolute_coordinates(M(x))
-                      for x = absolute_basis(domain(M))]...))
+                 reduce(vcat, [absolute_coordinates(M(x))
+                      for x = absolute_basis(domain(M))]))
 
     return new(domain(M), codomain(M), mat)
   end

src/Map/GrpAb.jl

@@ -79,7 +79,7 @@ mutable struct GrpAbFinGenMap <: Map{GrpAbFinGen, GrpAbFinGen,
     if ngens(D) == 0
       r.map = matrix(FlintZZ, 0, ngens(codomain(M)), ZZRingElem[])
     else
-      r.map = vcat([M(D[i]).coeff for i=1:ngens(D)])
+      r.map = reduce(vcat, [M(D[i]).coeff for i=1:ngens(D)])
     end
     return r
   end

src/Misc/Poly.jl

@@ -723,7 +723,7 @@ end
 
 function roots(R::AcbField, f::Union{ZZPolyRingElem, QQPolyRingElem}, abs_tol::Int=R.prec, initial_prec::Int...)
   lf = factor(f)
-  return map(R, vcat([_roots(g, abs_tol, initial_prec...) for g = keys(lf.fac) if degree(g) > 0]...))
+  return map(R, reduce(vcat, [_roots(g, abs_tol, initial_prec...) for g = keys(lf.fac) if degree(g) > 0]))
 end
 
 function _roots(f::QQPolyRingElem, ::PosInf; prec::Int=64)

src/Misc/PseudoPolynomial.jl

@@ -82,7 +82,7 @@ function _contains(a::nf_elem, I)
   d = lcm(dena, lcm([denominator(id) for id in I]))
   v = matrix(FlintZZ, 1, degree(OK), coordinates(OK(d * a)))
   @assert all(isone(denominator(basis_matrix(d * id))) for id in I)
-  M = vcat([numerator(basis_matrix(d * id)) for id in I ])
+  M = reduce(vcat, [numerator(basis_matrix(d * id)) for id in I ])
   b, w = cansolve(M', v')
   @assert b
   res = nf_elem[]

src/NumField/NfAbs/MPolyAbsFact.jl

@@ -476,7 +476,7 @@ function symbolic_roots(f::ZZMPolyRingElem, r::ZZRingElem, pr::Int = 10; max_roo
   g = evaluate(f, [Hecke.Globals.Zx(r), gen(Hecke.Globals.Zx)])
   @assert is_squarefree(g)
   lg = factor(g)
-  rt = vcat([Hecke.roots(number_field(x)[1], x) for x = keys(lg.fac)]...)
+  rt = reduce(vcat, [Hecke.roots(number_field(x)[1], x) for x = keys(lg.fac)])
   rt = rt[1:min(length(rt), max_roots)]
   RT = []
   for i = 1:length(rt)

src/NumFieldOrd/NfOrd/LinearAlgebra.jl

@@ -1639,14 +1639,14 @@ function vcat(P::PMat, Q::PMat)
 end
 
 function vcat(A::Vector{ <: PMat })
-  m = vcat([ P.matrix for P in A ])
-  c = vcat([ P.coeffs for P in A ]...)
+  m = reduce(vcat, [P.matrix for P in A])
+  c = reduce(vcat, [P.coeffs for P in A])
   return pseudo_matrix(m, c)
 end
 
 function vcat(A::PMat...)
-  m = vcat([ P.matrix for P in A ])
-  c = vcat([ P.coeffs for P in A ]...)
+  m = reduce(vcat, [P.matrix for P in A])
+  c = reduce(vcat, [P.coeffs for P in A])
   return pseudo_matrix(m, c)
 end
 
@@ -1659,13 +1659,13 @@ end
 
 function hcat(A::Vector{ <: PMat })
   @assert all( P -> P.coeffs == A[1].coeffs, A)
-  m = hcat([ P.matrix for P in A ])
+  m = reduce(hcat, [P.matrix for P in A])
   return pseudo_matrix(m, A[1].coeffs)
 end
 
 function hcat(A::PMat...)
   @assert all( P -> P.coeffs == A[1].coeffs, A)
-  m = hcat([ P.matrix for P in A ])
+  m = reduce(hcat, [P.matrix for P in A])
   return pseudo_matrix(m, A[1].coeffs)
 end
 

src/NumFieldOrd/NfOrd/norm_eqn.jl

@@ -124,7 +124,7 @@ function is_norm(K::AnticNumberField, a::ZZRingElem; extra::Vector{ZZRingElem}=Z
     #@assert norm(evaluate(x)) == evaluate(image(mu, h[end]))
   end
   s, ms = sub(u, h)
-  mp = GrpAbFinGenMap(U, u, vcat([x.coeff for x=h]))
+  mp = GrpAbFinGenMap(U, u, reduce(vcat, [x.coeff for x=h]))
 
   fl, p = haspreimage(mp, preimage(mu, a))
   if fl