diff --git a/src/arithmetic.jl b/src/arithmetic.jl
index e613c3d..e806d82 100644
--- a/src/arithmetic.jl
+++ b/src/arithmetic.jl
@@ -75,3 +75,30 @@ for op in [:+, :-]
         end
     end
 end
+
+function MA.operate!(op::Union{typeof(+),typeof(-),typeof(*)}, p::_APL, q::_AE)
+    return MA.operate!(op, p, MP.polynomial(q))
+end
+
+# These are not implemented yet for arbitrary bases so we
+# fall back to polynomials
+
+function MP.substitute(
+    s::MP.AbstractSubstitutionType,
+    p::_AE,
+    args::MP.AbstractSubstitution...,
+)
+    return MP.substitute(s, MP.polynomial(p), args...)
+end
+
+function MP.subs(p::_AE, args::MP.AbstractSubstitution...)
+    return MP.substitute(MP.Subs(), p, args...)
+end
+
+function (p::_AE)(args::MP.AbstractSubstitution...)
+    return MP.substitute(MP.Eval(), p, args...)
+end
+
+function MP.differentiate(p::_AE, args...)
+    return MP.differentiate(MP.polynomial(p), args...)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 569f942..763c2c0 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -95,10 +95,15 @@ function api_test(B::Type{<:MB.AbstractMonomialIndexed}, degree)
         @test iszero(_test_op(-, other, const_alg_el))
         @test iszero(_test_op(-, const_alg_el, other))
     end
+    @test iszero(MA.operate!(-, polynomial(const_alg_el), const_alg_el))
+    @test iszero(MA.operate!(+, -polynomial(const_alg_el), const_alg_el))
     @test typeof(MB.sparse_coefficients(sum(x))) ==
           MA.promote_operation(MB.sparse_coefficients, typeof(sum(x)))
     @test typeof(MB.algebra_element(sum(x))) ==
           MA.promote_operation(MB.algebra_element, typeof(sum(x)))
+    @test const_alg_el(x => ones(length(x))) == const_mono
+    @test subs(const_alg_el, x => ones(length(x))) == const_mono
+    @test differentiate(const_alg_el, x) == differentiate(const_mono, x)
 end
 
 function univ_orthogonal_test(