Move stuff, part 1

src/AbstractAlgebra.jl

@@ -1282,6 +1282,14 @@ include("Groups.jl")
 
 include("Deprecations.jl")
 
+################################################################################
+#
+#   Stuff moved from Nemo
+#
+################################################################################
+
+include("NemoStuff.jl")
+
 ###############################################################################
 #
 #   Array creation functions

src/NemoStuff.jl

@@ -0,0 +1,163 @@
+export neg!
+
+sub!(z::Rational{Int}, x::Rational{Int}, y::Int) = x - y
+
+neg!(z::Rational{Int}, x::Rational{Int}) = -x
+
+add!(z::Rational{Int}, x::Rational{Int}, y::Int) = x + y
+
+mul!(z::Rational{Int}, x::Rational{Int}, y::Int) = x * y
+
+################################################################################
+#
+#  Diagonal (block) matrix creation
+#
+################################################################################
+
+@doc raw"""
+    diagonal_matrix(x::T...) where T <: RingElem -> MatElem{T}
+    diagonal_matrix(x::Vector{T}) where T <: RingElem -> MatElem{T}
+    diagonal_matrix(Q, x::Vector{T}) where T <: RingElem -> MatElem{T}
+
+Returns a diagonal matrix whose diagonal entries are the elements of $x$.
+
+# Examples
+
+```jldoctest
+julia> diagonal_matrix(QQ(1), QQ(2))
+[1   0]
+[0   2]
+
+julia> diagonal_matrix([QQ(3), QQ(4)])
+[3   0]
+[0   4]
+
+julia> diagonal_matrix(QQ, [5, 6])
+[5   0]
+[0   6]
+```
+"""
+function diagonal_matrix(R::Ring, x::Vector{<:RingElement})
+    x = R.(x)
+    M = zero_matrix(R, length(x), length(x))
+    for i = 1:length(x)
+        M[i, i] = x[i]
+    end
+    return M
+end
+
+function diagonal_matrix(x::T, xs::T...) where {T<:RingElem}
+    return diagonal_matrix(collect((x, xs...)))
+end
+
+diagonal_matrix(x::Vector{<:RingElement}) = diagonal_matrix(parent(x[1]), x)
+
+@doc raw"""
+    diagonal_matrix(x::Vector{T}) where T <: MatElem -> MatElem
+
+Returns a block diagonal matrix whose diagonal blocks are the matrices in $x$.
+"""
+function diagonal_matrix(x::Vector{T}) where {T<:MatElem}
+    return cat(x..., dims=(1, 2))::T
+end
+
+function diagonal_matrix(x::T, xs::T...) where {T<:MatElem}
+    return cat(x, xs..., dims=(1, 2))::T
+end
+
+function diagonal_matrix(R::Ring, x::Vector{<:MatElem})
+    if length(x) == 0
+        return zero_matrix(R, 0, 0)
+    end
+    x = [change_base_ring(R, i) for i in x]
+    return diagonal_matrix(x)
+end
+
+base_ring(::Vector{Int}) = Int
+
+function is_symmetric(M::MatElem)
+    for i in 1:nrows(M)
+        for j in i:ncols(M)
+            if M[i, j] != M[j, i]
+                return false
+            end
+        end
+    end
+    return true
+end
+
+zero_matrix(::Type{Int}, r, c) = zeros(Int, r, c)
+
+#TODO: should be done in Nemo/AbstractAlgebra s.w.
+#      needed by ^ (the generic power in Base using square and multiply)
+Base.copy(f::Generic.MPoly) = deepcopy(f)
+Base.copy(f::Generic.Poly) = deepcopy(f)
+
+################################################################################
+#
+#  Minpoly and Charpoly
+#
+################################################################################
+
+function minpoly(M::MatElem)
+    k = base_ring(M)
+    kx, x = polynomial_ring(k, cached=false)
+    return minpoly(kx, M)
+end
+
+function charpoly(M::MatElem)
+    k = base_ring(M)
+    kx, x = polynomial_ring(k, cached=false)
+    return charpoly(kx, M)
+end
+
+###############################################################################
+#
+#  Sub
+#
+###############################################################################
+
+function sub(M::MatElem, rows::Vector{Int}, cols::Vector{Int})
+    N = zero_matrix(base_ring(M), length(rows), length(cols))
+    for i = 1:length(rows)
+        for j = 1:length(cols)
+            N[i, j] = M[rows[i], cols[j]]
+        end
+    end
+    return N
+end
+
+function sub(M::MatElem{T}, r::AbstractUnitRange{<:Integer}, c::AbstractUnitRange{<:Integer}) where {T}
+    z = similar(M, length(r), length(c))
+    for i in 1:length(r)
+        for j in 1:length(c)
+            z[i, j] = M[r[i], c[j]]
+        end
+    end
+    return z
+end
+
+#trivia to make life easier
+
+gens(L::SimpleNumField{T}) where {T} = [gen(L)]
+
+function gen(L::SimpleNumField{T}, i::Int) where {T}
+    i == 1 || error("index must be 1")
+    return gen(L)
+end
+
+function Base.getindex(L::SimpleNumField{T}, i::Int) where {T}
+    if i == 0
+        return one(L)
+    elseif i == 1
+        return gen(L)
+    else
+        error("index has to be 0 or 1")
+    end
+end
+
+ngens(L::SimpleNumField{T}) where {T} = 1
+
+is_unit(a::NumFieldElem) = !iszero(a)
+
+canonical_unit(a::NumFieldElem) = a