diff --git a/src/MultivariateBases.jl b/src/MultivariateBases.jl
index e80ba8c..8e6f94b 100644
--- a/src/MultivariateBases.jl
+++ b/src/MultivariateBases.jl
@@ -32,5 +32,6 @@ include("hermite.jl")
 include("laguerre.jl")
 include("legendre.jl")
 include("chebyshev.jl")
+include("quotient.jl")
 
 end # module
diff --git a/src/monomial.jl b/src/monomial.jl
index 35078fa..6abc7bc 100644
--- a/src/monomial.jl
+++ b/src/monomial.jl
@@ -265,12 +265,15 @@ function MP.polynomial(Q::AbstractMatrix, mb::SubBasis{Monomial}, T::Type)
     return MP.polynomial(Q, mb.monomials, T)
 end
 
-function MP.coefficients(p, basis::SubBasis{Monomial})
+function MP.coefficients(
+    p::MP.AbstractPolynomialLike,
+    basis::SubBasis{Monomial},
+)
     return MP.coefficients(p, basis.monomials)
 end
 
-function MP.coefficients(p, ::FullBasis{Monomial})
-    return MP.coefficients(p)
+function MP.coefficients(p::MP.AbstractPolynomialLike, ::FullBasis{Monomial})
+    return p
 end
 
 # Overload some of the `MP` interface for convenience
diff --git a/src/quotient.jl b/src/quotient.jl
new file mode 100644
index 0000000..48c970b
--- /dev/null
+++ b/src/quotient.jl
@@ -0,0 +1,10 @@
+struct QuotientBasis{T,I,B<:SA.AbstractBasis{T,I},D} <: SA.ExplicitBasis{T,I}
+    basis::B
+    divisor::D
+end
+
+Base.length(basis::QuotientBasis) = length(basis.basis)
+
+function MP.coefficients(p, basis::QuotientBasis)
+    return MP.coefficients(rem(p, basis.divisor), basis.basis)
+end
diff --git a/test/quotient.jl b/test/quotient.jl
new file mode 100644
index 0000000..417edf3
--- /dev/null
+++ b/test/quotient.jl
@@ -0,0 +1,19 @@
+struct PlusMinusOne # Reduce modulo `x^2 = 1`
+end
+function Base.rem(m::AbstractMonomial, ::PlusMinusOne)
+    return prod(v^mod(e, 2) for (v, e) in powers(m))
+end
+function Base.rem(t::AbstractTerm, d::PlusMinusOne)
+    return coefficient(t) * rem(monomial(t), d)
+end
+function Base.rem(p::AbstractPolynomial, d::PlusMinusOne)
+    return sum(rem(t, d) for t in terms(p))
+end
+
+@testset "PlusMinusOne" begin
+    @polyvar x y
+    basis =
+        MB.QuotientBasis(MB.SubBasis{MB.Monomial}([1, y, x]), PlusMinusOne())
+    @test length(basis) == 3
+    @test coefficients(x^3 - 2x^2 * y + 3x^2, basis) == [3, -2, 1]
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 445e878..984dce0 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -147,3 +147,6 @@ end
 @testset "Chebyshev" begin
     include("chebyshev.jl")
 end
+@testset "Quotient" begin
+    include("quotient.jl")
+end