Add QuotientBasis

src/MultivariateBases.jl

@@ -32,5 +32,6 @@ include("hermite.jl")
 include("laguerre.jl")
 include("legendre.jl")
 include("chebyshev.jl")
+include("quotient.jl")
 
 end # module

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

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