diff --git a/src/chebyshev.jl b/src/chebyshev.jl
index 7a5dc77..a02f629 100644
--- a/src/chebyshev.jl
+++ b/src/chebyshev.jl
@@ -4,7 +4,7 @@ _promote_div(::Type{I}) where {I<:Integer} = Rational{I}
 _promote_div(::Type{T}) where {T<:Number} = MA.promote_operation(/, T, Int)
 # Could be for instance `MathOptInterface.ScalarAffineFunction{Float64}`
 # which does not support division with `Int`
-_promote_div(::Type{F}) where {F} = F
+_promote_div(::Type{F}) where {F} = _float(F)
 
 function _promote_coef(::Type{T}, ::Type{<:AbstractChebyshev}) where {T}
     return _promote_div(T)
diff --git a/src/monomial.jl b/src/monomial.jl
index 13ae659..0f1876b 100644
--- a/src/monomial.jl
+++ b/src/monomial.jl
@@ -155,6 +155,10 @@ end
 
 _explicit_basis(_, basis::SubBasis) = basis
 
+function explicit_basis(p::MP.AbstractPolynomialLike)
+    return SubBasis{Monomial}(MP.monomials(p))
+end
+
 function explicit_basis(a::SA.AlgebraElement)
     return _explicit_basis(SA.coeffs(a), SA.basis(a))
 end
diff --git a/src/scaled.jl b/src/scaled.jl
index b5d6c7a..fde028e 100644
--- a/src/scaled.jl
+++ b/src/scaled.jl
@@ -51,7 +51,7 @@ end
 _float(::Type{T}) where {T<:Number} = float(T)
 # Could be for instance `MathOptInterface.ScalarAffineFunction{Float64}`
 # which does not implement `float`
-_float(::Type{F}) where {F} = F
+_float(::Type{F}) where {F} = MA.promote_operation(*, Float64, F)
 
 _promote_coef(::Type{T}, ::Type{ScaledMonomial}) where {T} = _float(T)
 
diff --git a/test/monomial.jl b/test/monomial.jl
index 89bb4fb..2f55d4f 100644
--- a/test/monomial.jl
+++ b/test/monomial.jl
@@ -38,8 +38,10 @@ end
     # It will be sorted and 1 will be moved at the end
     basis = SubBasis{MB.Monomial}([1, x, y])
     @test polynomial_type(basis, Int) == polynomial_type(x, Int)
-    @test polynomial(i -> i^2, basis) == 9x + 4y + 1
+    poly = 9x + 4y + 1
+    @test polynomial(i -> i^2, basis) == poly
     @test coefficients(9 + x + 4y, basis) == [9, 4, 1]
+    @test MB.explicit_basis(poly) == basis
 end
 @testset "Quadratic" begin
     basis = SubBasis{MB.Monomial}([x^2, x * y, y^2])
diff --git a/test/runtests.jl b/test/runtests.jl
index 067c35f..52ccdb5 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -20,6 +20,11 @@ function _test_basis(basis)
           MB.constant_algebra_element_type(B, Int)
 end
 
+struct TypeA end
+struct TypeB end
+Base.zero(::Type{TypeA}) = TypeA()
+Base.:*(::Float64, ::TypeA) = TypeB()
+
 function api_test(B::Type{<:MB.AbstractMonomialIndexed}, degree)
     @polyvar x[1:2]
     M = typeof(prod(x))
@@ -65,7 +70,8 @@ function api_test(B::Type{<:MB.AbstractMonomialIndexed}, degree)
     p = MB.Polynomial{B}(mono)
     @test full_basis[p] == mono
     @test full_basis[mono] == p
-    @test polynomial_type(mono, String) == polynomial_type(typeof(p), String)
+    @test polynomial_type(mono, B == Monomial ? TypeA : TypeB) ==
+          polynomial_type(typeof(p), TypeA)
     a = MB.algebra_element(p)
     @test variables(a) == x
     @test typeof(polynomial(a)) == polynomial_type(typeof(a))