Allow variables of same positive degree in monomials_of_degree (#4497)

src/InvariantTheory/iterators.jl

@@ -54,8 +54,16 @@ end
 
 function AllMonomials(R::MPolyDecRing, d::Int, vars::Vector{Int})
   @req is_z_graded(R) "Iterator only implemented when the grading group is Z"
-  @req all(isequal(ZZ(1)), map(i -> degree(R[i])[1], vars)) "Iterator only implemented for variables of degree 1"
-  return AllMonomials{typeof(R)}(R, d, vars)
+  isempty(vars) && d !== 0 && return AllMonomials{typeof(R)}(R, 1, Int[])
+  isempty(vars) && return AllMonomials{typeof(R)}(R, 0, Int[])
+  deg_ZZ = degree(R[vars[1]])[1]
+  @req all(isequal(deg_ZZ), map(i -> degree(R[i])[1], vars)) "Iterator only implemented when all the given variables have the same nonzero degree"
+  deg = Int(deg_ZZ)
+  d == 0 && return AllMonomials{typeof(R)}(R, 0, Int[])
+  does_divide, quot = divides(d, deg)
+  does_divide || return AllMonomials{typeof(R)}(R, 1, Int[])
+  quot > 0 || return AllMonomials{typeof(R)}(R, 1, Int[])
+  return AllMonomials{typeof(R)}(R, quot, vars)
 end
 
 Base.eltype(::Type{AllMonomials{PolyRingT}}) where {PolyRingT} = elem_type(PolyRingT)

test/InvariantTheory/iterators.jl

@@ -10,7 +10,10 @@
     @test isempty(monomials_of_degree(R, 2, Int[]))
   end
 
-  R = graded_polynomial_ring(QQ, [:x, :y, :z], [1, 1, 3])[1]
-  x, y, z = gens(R)
+  R, (x, y, z, t) = graded_polynomial_ring(QQ, [:x, :y, :z, :t], [1, 1, 3, 3])
   @test collect(monomials_of_degree(R, 3, [1, 2])) == [x^3, x^2 * y, x * y^2, y^3]
+  @test collect(monomials_of_degree(R, 6, [3, 4])) == [z^2, z * t, t^2]
+  @test collect(monomials_of_degree(R, -1, [3, 4])) == Vector{elem_type(R)}[]
+  @test collect(monomials_of_degree(R, 2, [3, 4])) == Vector{elem_type(R)}[]
+  @test collect(monomials_of_degree(R, 0, [3, 4])) == [R(1)]
 end