diff --git a/Project.toml b/Project.toml
index 1a1bbfb..d08c52e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,20 +1,24 @@
 name = "SemialgebraicSets"
 uuid = "8e049039-38e8-557d-ae3a-bc521ccf6204"
 repo = "https://github.com/JuliaAlgebra/SemialgebraicSets.jl.git"
-version = "0.2.3"
+version = "0.2.4"
 
 [deps]
+DynamicPolynomials = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MultivariatePolynomials = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
+MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+TypedPolynomials = "afbbf031-7a57-5f58-a1b9-b774a0fad08d"
 
 [compat]
-MultivariatePolynomials = "0.3"
+MultivariatePolynomials = "0.4.2"
 julia = "1"
 
 [extras]
 DynamicPolynomials = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+TypedPolynomials = "afbbf031-7a57-5f58-a1b9-b774a0fad08d"
 
 [targets]
-test = ["Test", "DynamicPolynomials"]
+test = ["Test", "DynamicPolynomials", "TypedPolynomials"]
diff --git a/src/SemialgebraicSets.jl b/src/SemialgebraicSets.jl
index 23bebf9..1235ea2 100644
--- a/src/SemialgebraicSets.jl
+++ b/src/SemialgebraicSets.jl
@@ -2,6 +2,9 @@ module SemialgebraicSets
 
 using Random
 
+import MutableArithmetics
+const MA = MutableArithmetics
+
 using MultivariatePolynomials
 const MP = MultivariatePolynomials
 
diff --git a/src/basic.jl b/src/basic.jl
index 327b65d..8180ea1 100644
--- a/src/basic.jl
+++ b/src/basic.jl
@@ -10,10 +10,10 @@ end
 function BasicSemialgebraicSet(V::AlgebraicSet{T, PT, A, S}, p::Vector{PT}) where {T, PT<:APL{T}, A, S<:AbstractAlgebraicSolver}
     BasicSemialgebraicSet{T, PT, typeof(V)}(V, p)
 end
-function BasicSemialgebraicSet(V::AlgebraicSet{T, PT, A, ST}, p::Vector{PS}) where {T, PT<:APL{T}, S, PS<:APL{S}, A, ST<:AbstractAlgebraicSolver}
-    U = promote_type(T, S)
-    PU = promote_type(PT, PS)
-    BasicSemialgebraicSet(convert(AlgebraicSet{U, PU, A, ST}, V), Vector{PU}(p))
+function BasicSemialgebraicSet(V::AlgebraicSet{T, PT, A, SO, U}, p::Vector{PS}) where {T, PT<:APL{T}, S, PS<:APL{S}, A, SO<:AbstractAlgebraicSolver, U}
+    ST = promote_type(T, S)
+    PST = promote_type(PT, PS)
+    BasicSemialgebraicSet(convert(AlgebraicSet{ST, PST, A, SO, U}, V), Vector{PST}(p))
 end
 #BasicSemialgebraicSet{T, PT<:APL{T}}(V::AlgebraicSet{T, PT}, p::Vector{PT}) = BasicSemialgebraicSet{T, PT}(V, p)
 function basicsemialgebraicset(V, p)
diff --git a/src/groebner.jl b/src/groebner.jl
index 4376c51..cb91b07 100644
--- a/src/groebner.jl
+++ b/src/groebner.jl
@@ -12,7 +12,15 @@ where ``m = \\mathrm{lcm}(\\mathrm{\\mathsc{LM}}(p), \\mathrm{\\mathsc{LM}}(q))`
 """
 function spolynomial(p::APL, q::APL)
     m = lcm(leadingmonomial(p), leadingmonomial(q))
-    MultivariatePolynomials._div(m, leadingterm(p)) * p - MultivariatePolynomials._div(m, leadingterm(q)) * q
+    ltp = leadingterm(p)
+    # `MA.operate` ensures that the returned value can be mutated without
+    # affecting either `a` or `p`.
+    a = MA.operate(*, MP._div(m, monomial(ltp)), p)
+    ad = MA.operate!!(/, a, MP.coefficient(ltp))
+    ltq = leadingterm(q)
+    b = MA.operate(*, MP._div(m, monomial(ltq)), q)
+    bd = MA.operate!!(/, b, MP.coefficient(ltq))
+    return MA.operate!!(-, ad, bd)
 end
 
 function reducebasis!(F::AbstractVector{<:APL}; kwargs...)