Move even more stuff from NemoStuff.jl to the right places (#1441)

* Move `ngens(::MPolyRing)` from NemoStuff.jl to MPoly.jl

* move `preimage(::Generic.CompositeMap, ::Any)`

* Add test

* Fix import

src/Generic.jl

@@ -216,6 +216,7 @@ import ..AbstractAlgebra: order
 import ..AbstractAlgebra: parent_type
 import ..AbstractAlgebra: Perm
 import ..AbstractAlgebra: pol_length
+import ..AbstractAlgebra: preimage
 import ..AbstractAlgebra: pretty
 import ..AbstractAlgebra: primpart
 import ..AbstractAlgebra: promote_rule

src/MPoly.jl

@@ -83,6 +83,13 @@ function is_exact_type(a::Type{T}) where {S <: RingElement, T <: MPolyRingElem{S
    return is_exact_type(S)
 end
 
+@doc raw"""
+    ngens(R::MPolyRing)
+
+Return the number of variables in `R`.
+"""
+ngens(R::MPolyRing) = nvars(R)
+
 @doc raw"""
     vars(p::MPolyRingElem{T}) where {T <: RingElement}
 

src/NemoStuff.jl

@@ -561,10 +561,6 @@ end
 
 Base.:\(f::Map, x) = preimage(f, x)
 
-function preimage(f::Generic.CompositeMap, a)
-    return preimage(f.map1, preimage(f.map2, a))
-end
-
 export set_precision, set_precision!
 
 function set_precision(f::PolyRingElem{T}, n::Int) where {T<:SeriesElem}
@@ -598,8 +594,6 @@ function set_precision(a::SeriesElem, i::Int)
     return b
 end
 
-ngens(R::MPolyRing) = nvars(R)
-
 Random.gentype(::Type{T}) where {T<:FinField} = elem_type(T)
 
 import LinearAlgebra

src/generic/Map.jl

@@ -19,6 +19,10 @@ function (f::CompositeMap{D, C})(a) where {D, C}
    return f.map2(f.map1(a))::elem_type(C)
 end
 
+function preimage(f::Generic.CompositeMap{D, C}, a) where {D, C}
+   return preimage(f.map1, preimage(f.map2, a))
+end
+
 function show(io::IO, ::MIME"text/plain", M::CompositeMap)
    io = pretty(io)
    println(io, "Composite map")

test/generic/MPoly-test.jl

@@ -285,6 +285,7 @@ end
       @test ord == ordering(S)
 
       @test nvars(parent(f)) == num_vars
+      @test ngens(parent(f)) == num_vars
 
       @test isone(one(S))