diff --git a/Project.toml b/Project.toml
index 714ae70..0331698 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "DynamicPolynomials"
 uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
 repo = "https://github.com/JuliaAlgebra/DynamicPolynomials.jl.git"
-version = "0.4.0"
+version = "0.4.1"
 
 [deps]
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
@@ -15,7 +15,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 DataStructures = "0.17, 0.18"
-MultivariatePolynomials = "0.4"
+MultivariatePolynomials = "0.4.1"
 MutableArithmetics = "0.3"
 Reexport = "0.2, 1.0"
 julia = "1"
diff --git a/src/mult.jl b/src/mult.jl
index 38a6c77..1321f53 100644
--- a/src/mult.jl
+++ b/src/mult.jl
@@ -49,22 +49,6 @@ function MP._multconstant(α::T, f, p::Polynomial{C,S} ) where {T, C, S}
     end
 end
 
-MP.mapcoefficientsnz(f::Function, p::Polynomial) = Polynomial(map(f, p.a), MA.mutable_copy(p.x))
-function MP.mapcoefficientsnz_to!(output::Polynomial, f::Function, t::MP.AbstractTermLike)
-    MP.mapcoefficientsnz_to!(output, f, polynomial(t))
-end
-function MP.mapcoefficientsnz_to!(output::Polynomial, f::Function, p::Polynomial)
-    resize!(output.a, length(p.a))
-    @. output.a = f(p.a)
-    Future.copy!(output.x.vars, p.x.vars)
-    # TODO reuse the part of `Z` that is already in `output`.
-    resize!(output.x.Z, length(p.x.Z))
-    for i in eachindex(p.x.Z)
-        output.x.Z[i] = copy(p.x.Z[i])
-    end
-    return output
-end
-
 # I do not want to cast x to TermContainer because that would force the promotion of eltype(q) with Int
 function Base.:(*)(x::DMonomialLike, p::Polynomial)
     Polynomial(MA.mutable_copy(p.a), x*p.x)
diff --git a/src/poly.jl b/src/poly.jl
index 87bb474..99e2725 100644
--- a/src/poly.jl
+++ b/src/poly.jl
@@ -271,3 +271,33 @@ function MA.operate!(::typeof(one), p::Polynomial{C, T}) where {C, T}
     end
     return p
 end
+
+function MP.mapcoefficients(f::Function, p::Polynomial; nonzero = false)
+    return Polynomial(map(f, p.a), MA.mutable_copy(p.x))
+end
+
+function MP.mapcoefficients!(f::Function, p::Polynomial; nonzero = false)
+    map!(f, p.a, p.a)
+    if !nonzero
+        _remove_zeros!(p)
+    end
+    return p
+end
+
+function MP.mapcoefficients_to!(output::Polynomial, f::Function, t::MP.AbstractTermLike; nonzero = false)
+    return MP.mapcoefficients_to!(output, f, polynomial(t); nonzero = nonzero)
+end
+function MP.mapcoefficients_to!(output::Polynomial, f::Function, p::Polynomial; nonzero = false)
+    resize!(output.a, length(p.a))
+    map!(f, output.a, p.a)
+    Future.copy!(output.x.vars, p.x.vars)
+    # TODO reuse the part of `Z` that is already in `output`.
+    resize!(output.x.Z, length(p.x.Z))
+    for i in eachindex(p.x.Z)
+        output.x.Z[i] = copy(p.x.Z[i])
+    end
+    if !nonzero
+        _remove_zeros!(output)
+    end
+    return output
+end