Clean up src/NemoStuff.jl (#1769)

* Clean up `src/NemoStuff.jl`

* Some tests

* Don't deprecate `zero_matrix(MatElem, ...)` and
`identity_matrix(MatElem, ...)`

src/AbsSeries.jl

@@ -81,6 +81,14 @@ function Base.hash(a::AbsPowerSeriesRingElem, h::UInt)
    return b
 end
 
+function lift(R::PolyRing{T}, s::AbsPowerSeriesRingElem{T}) where {T}
+   t = R()
+   for x = 0:pol_length(s)
+      setcoeff!(t, x, polcoeff(s, x))
+   end
+   return t
+end
+
 ###############################################################################
 #
 #   Similar and zero

src/AbstractAlgebra.jl

@@ -286,11 +286,11 @@ using .Solve
 
 ################################################################################
 #
-#   Stuff moved from Nemo (to be cleaned up eventually)
+#   Number fields (some stuff moved from Nemo)
 #
 ################################################################################
 
-include("NemoStuff.jl")
+include("NumFields.jl")
 
 ################################################################################
 #

src/Deprecations.jl

@@ -54,3 +54,6 @@ import .Generic: exponent; @deprecate exponent(a::Generic.MPoly{T}, i::Int, j::I
 import .Generic: set_exponent_vector!; @deprecate set_exponent_vector!(a::Generic.MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{ord}}) where {T <: RingElement, ord} set_exponent_vector!(a, i, exps, Val(ord))
 import .Generic: is_gen; @deprecate is_gen(x::Generic.MPoly{T}, ::Type{Val{ord}}) where {T <: RingElement, ord} is_gen(x, Val(ord))
 import .Generic: degree; @deprecate degree(f::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} degree(f, i, Val(ord))
+
+# deprecated during 0.42.*
+@deprecate change_base_ring(p::MPolyRingElem{T}, g, new_polynomial_ring) where {T<:RingElement} map_coefficients(g, p, parent = new_polynomial_ring)

src/MPoly.jl

@@ -1209,6 +1209,55 @@ function coefficients_of_univariate(p::MPolyRingElem,
    return coeffs
 end
 
+###############################################################################
+#
+#   As univariate polynomials
+#
+###############################################################################
+
+@doc raw"""
+    coefficients(f::MPolyRingElem, i::Int)
+
+Return the coefficients of `f` when viewed as a univariate polynomial in the `i`-th
+variable.
+"""
+function coefficients(f::MPolyRingElem, i::Int)
+   d = degree(f, i)
+   cf = [MPolyBuildCtx(parent(f)) for j = 0:d]
+   for (c, e) = zip(coefficients(f), exponent_vectors(f))
+      a = e[i]
+      e[i] = 0
+      push_term!(cf[a+1], c, e)
+   end
+   return map(finish, cf)
+end
+
+#check with Nemo/ Dan if there are better solutions
+#the block is also not used here I think
+#functionality to view mpoly as upoly in variable `i`, so the
+#coefficients are mpoly's without variable `i`.
+function leading_coefficient(f::MPolyRingElem, i::Int)
+   g = MPolyBuildCtx(parent(f))
+   d = degree(f, i)
+   for (c, e) = zip(coefficients(f), exponent_vectors(f))
+      if e[i] == d
+         e[i] = 0
+         push_term!(g, c, e)
+      end
+   end
+   return finish(g)
+end
+
+@doc raw"""
+    content(f::MPolyRingElem, i::Int)
+
+Return the content of `f` as a polynomial in the variable `i`, i.e. the gcd of
+all the coefficients when viewed as univariate polynomial in `i`.
+"""
+function content(f::MPolyRingElem, i::Int)
+   return reduce(gcd, coefficients(f, i))
+end
+
 ################################################################################
 #
 #  Change base ring

src/Map.jl

@@ -55,6 +55,8 @@ end
 
 Base.broadcastable(M::Map) = Ref(M)
 
+Base.:\(f::Map, x) = preimage(f, x)
+
 ###############################################################################
 #
 #   CompositeMap

src/Matrix.jl

@@ -426,6 +426,8 @@ function _to_indices(x, rows, cols)
    (rows, cols)
 end
 
+sub(M::MatElem, r::AbstractVector{<:Integer}, c::AbstractVector{<:Integer}) = M[r, c]
+
 function Base.view(M::MatElem,
          rows::Union{Int,Colon,AbstractVector{Int}},
          cols::Union{Int,Colon,AbstractVector{Int}})
@@ -790,6 +792,52 @@ function *(x::MatElem{T}, y::MatElem{T}) where {T <: NCRingElement}
    return A
 end
 
+function add!(c::MatrixElem{T}, a::MatrixElem{T}, b::MatrixElem{T}) where T <: NCRingElement
+   check_parent(a, b)
+   check_parent(a, c)
+   for i = 1:nrows(c)
+      for j = 1:ncols(c)
+         c[i, j] = add!(c[i, j], a[i, j], b[i, j])
+      end
+   end
+   return c
+end
+
+function mul!(c::MatElem{T}, a::MatElem{T}, b::MatElem{T}) where T <: NCRingElement
+   @assert base_ring(a) === base_ring(b) && base_ring(a) === base_ring(c)
+   ncols(a) != nrows(b) && error("Incompatible matrix dimensions")
+   nrows(c) != nrows(a) && error("Incompatible matrix dimensions")
+   ncols(c) != ncols(b) && error("Incompatible matrix dimensions")
+
+   if c === a || c === b
+      d = parent(a)()
+      return mul!(d, a, b)
+   end
+
+   t = base_ring(a)()
+   for i = 1:nrows(a)
+      for j = 1:ncols(b)
+         c[i, j] = zero!(c[i, j])
+         for k = 1:ncols(a)
+            c[i, j] = addmul_delayed_reduction!(c[i, j], a[i, k], b[k, j], t)
+         end
+         c[i, j] = reduce!(c[i, j])
+      end
+   end
+   return c
+end
+
+function sub!(c::MatrixElem{T}, a::MatrixElem{T}, b::MatrixElem{T}) where T <: NCRingElement
+   check_parent(a, b)
+   check_parent(a, c)
+   for i = 1:nrows(c)
+      for j = 1:ncols(c)
+         c[i, j] = sub!(c[i, j], a[i, j], b[i, j])
+      end
+   end
+   return c
+end
+
 ###############################################################################
 #
 #   Ad hoc binary operators
@@ -1013,6 +1061,25 @@ function *(x::Vector{T}, y::MatrixElem{T}) where T <: NCRingElement
    return mul!(T[base_ring(y)() for j in 1:ncols(y)], x, y)
 end
 
+function mul!(c::MatrixElem{T}, a::MatrixElem{T}, b::T) where T <: NCRingElement
+   @assert base_ring(a) === parent(b) && base_ring(a) === base_ring(c)
+   nrows(c) != nrows(a) && error("Incompatible matrix dimensions")
+   ncols(c) != ncols(a) && error("Incompatible matrix dimensions")
+
+   if c === a
+      d = parent(a)()
+      return mul!(d, a, b)
+   end
+
+   t = base_ring(a)()
+   for i = 1:nrows(a)
+      for j = 1:ncols(a)
+         c[i, j] = mul!(c[i, j], a[i, j], b)
+      end
+   end
+   return c
+end
+
 ################################################################################
 #
 #  Promotion
@@ -1373,6 +1440,7 @@ julia> B = transpose(A)
 """
 transpose(x::MatrixElem{T}) where T <: NCRingElement
 
+transpose!(A::MatrixElem) = transpose(A)
 
 ###############################################################################
 #
@@ -6506,6 +6574,8 @@ function zero_matrix(R::NCRing, r::Int, c::Int)
    return z
 end
 
+zero_matrix(::Type{MatElem}, R::Ring, n::Int, m::Int) = zero_matrix(R, n, m)
+
 ################################################################################
 #
 #   Ones matrix
@@ -6560,6 +6630,8 @@ function identity_matrix(M::MatElem{T}, n::Int) where T <: NCRingElement
    z
 end
 
+identity_matrix(::Type{MatElem}, R::Ring, n::Int) = identity_matrix(R, n)
+
 ################################################################################
 #
 #   Scalar matrix

src/NCRings.jl

@@ -152,6 +152,8 @@ function addmul!(z::T, x::T, y::T, c::T) where T <: NCRingElem
    return z
 end
 
+addmul!(z::T, x::T, y::T) where T <: NCRingElem = addmul!(z, x, y, parent(z)())
+
 ###############################################################################
 #
 #   Basic manipulation