Speed up is_homogeneous (#4119)

Some measurements taking the example from the `is_homogeneous` docstring:

    R, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"], [1, 2, 3])
    f = x^2+y*z
    W = [1 2 1 0; 3 4 0 1]
    S, (w, x, y, z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"], W)
    F = w^3*y^3*z^3 + w^2*x*y^2*z^2 + w*x^2*y*z + x^3

Before:

    julia> @Btime is_homogeneous(f);
      1.533 μs (62 allocations: 2.28 KiB)

    julia> @Btime is_homogeneous(F);
      3.932 μs (152 allocations: 5.53 KiB)

After:

    julia> @Btime is_homogeneous(f);
      334.071 ns (10 allocations: 416 bytes)

    julia> @Btime is_homogeneous(F);
      556.150 ns (12 allocations: 656 bytes)

---------

Co-authored-by: Lars Göttgens <lars.goettgens@rwth-aachen.de>

Author: fingolfin

Project.toml

@@ -29,7 +29,7 @@ AbstractAlgebra = "0.43.1"
 AlgebraicSolving = "0.7.0"
 Distributed = "1.6"
 GAP = "0.11.3"
-Hecke = "0.34.1"
+Hecke = "0.34.3"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"

src/Rings/mpoly-graded.jl

@@ -970,14 +970,17 @@ true
 function is_homogeneous(F::MPolyDecRingElem)
   D = parent(F).D
   d = parent(F).d
-  S = Set{elem_type(D)}()
+  S = nothing
+  u = zero(D)
   for c = MPolyExponentVectors(forget_decoration(F))
-    u = parent(F).D[0]
+    u = zero!(u)
     for i=1:length(c)
-      u += c[i]*d[i]
+      u = addmul_delayed_reduction!(u, d[i], c[i])
     end
-    push!(S, u)
-    if length(S) > 1
+    u = reduce!(u)
+    if S === nothing
+      S = deepcopy(u)
+    elseif S != u
       return false
     end
   end