Exterior powers of finitely presented modules

experimental/Schemes/Auxiliary.jl

@@ -383,3 +383,93 @@ end
 ### Generic pullback and pushforward for composite maps
 pushforward(f::Generic.CompositeMap, a::Any) = pushforward(map2(f), pushforward(map1(f), a))
 pullback(f::Generic.CompositeMap, a::Any) = pullback(map1(f), pullback(map2(f), a))
+
+### Iteration over monomials in modules of a certain degree
+struct AllModuleMonomials{ModuleType<:FreeMod}
+  F::ModuleType
+  d::Int
+
+  function AllModuleMonomials(F::FreeMod{T}, d::Int) where {T <: MPolyDecRingElem}
+    is_graded(F) || error("module must be graded")
+    S = base_ring(F)
+    is_standard_graded(S) || error("iterator implemented only for the standard graded case")
+    return new{typeof(F)}(F, d)
+  end
+end
+
+underlying_module(amm::AllModuleMonomials) = amm.F
+degree(amm::AllModuleMonomials) = amm.d
+
+function all_monomials(F::FreeMod{T}, d::Int) where {T<:MPolyDecRingElem}
+  return AllModuleMonomials(F, d)
+end
+
+Base.eltype(amm::AllModuleMonomials{T}) where {T} = elem_type(T)
+
+function Base.length(amm::AllModuleMonomials)
+  F = underlying_module(amm)
+  r = rank(F)
+  R = base_ring(F)
+  d = degree(amm)
+  result = 0
+  for i in 1:r
+    d_loc = d - Int(degree(F[i])[1])
+    d_loc < 0 && continue
+    result = result + length(all_monomials(R, d_loc))
+  end
+  return result
+end
+
+function Base.iterate(amm::AllModuleMonomials, state::Nothing = nothing)
+  i = 1
+  F = underlying_module(amm)
+  d = degree(amm)
+  R = base_ring(F)
+
+  d_loc = d - Int(degree(F[i])[1])
+  while i < ngens(F) && d_loc < 0
+    i = i+1
+    d_loc = d - Int(degree(F[i])[1])
+  end
+
+  i == ngens(F) && d_loc < 0 && return nothing
+
+  mon_it = all_monomials(R, d_loc)
+  res = iterate(mon_it, nothing)
+  res === nothing && i == ngens(F) && return nothing
+
+  x, s = res
+  return x*F[1], (i, mon_it, s)
+end
+
+function Base.iterate(amm::AllModuleMonomials, state::Tuple{Int, AllMonomials, Vector{Int}})
+  F = underlying_module(amm)
+  d = degree(amm)
+  R = base_ring(F)
+
+  i, mon_it, s = state
+  res = iterate(mon_it, s)
+  if res === nothing
+    i == ngens(F) && return nothing
+    i = i+1
+    d_loc = d - Int(degree(F[i])[1])
+
+    while i < ngens(F) && d_loc < 0
+      i = i+1
+      d_loc = d - Int(degree(F[i])[1])
+    end
+
+    i == ngens(F) && d_loc < 0 && return nothing
+
+    mon_it = all_monomials(R, d_loc)
+    res_loc = iterate(mon_it, nothing)
+    res_loc === nothing && i == ngens(F) && return nothing
+
+    x, s = res_loc
+    return x*F[i], (i, mon_it, s)
+  end
+
+  x, s = res
+  return x*F[i], (i, mon_it, s)
+end
+

test/Modules/GradedModules.jl

@@ -68,3 +68,16 @@ end
   K = kernel(phi)[1]
   @test (iszero(quo(M2,K)) && iszero(quo(K,M2))) # mathematical equality
 end
+
+@testset "all_monomials for graded free modules" begin
+  R, (x, y, u, v, w) = QQ[:x, :y, :u, :v, :w]
+  S, (x, y, u, v, w) = grade(R)
+
+  F = graded_free_module(S, [-1, 2])
+
+  for d in -4:4
+    amm = Oscar.all_monomials(F, d)
+    @test d < -1 || !isempty(amm)
+    @test all(x->degree(x) == grading_group(F)([d]), amm)
+  end
+end