Fix variables with FullBasis (#32)

* Fix variables with FullBasis

* Fix

* Fixes

Author: blegat

src/MultivariateBases.jl

@@ -72,4 +72,13 @@ function MA.promote_operation(
     return Algebra{BT,B,M}
 end
 
+const _APL = MP.AbstractPolynomialLike
+# We don't define it for all `AlgebraElement` as this would be type piracy
+const _AE = SA.AlgebraElement{<:Algebra}
+
+Base.:(+)(p::_APL, q::_AE) = +(p, MP.polynomial(q))
+Base.:(+)(p::_AE, q::_APL) = +(MP.polynomial(p), q)
+Base.:(-)(p::_APL, q::_AE) = -(p, MP.polynomial(q))
+Base.:(-)(p::_AE, q::_APL) = -(MP.polynomial(p), q)
+
 end # module

src/monomial.jl

@@ -112,6 +112,8 @@ function SubBasis{B}(
     )
 end
 
+SubBasis{B}(monos::Tuple) where {B} = SubBasis{B}([monos...])
+
 function Base.copy(basis::SubBasis)
     return typeof(basis)(copy(basis.monomials))
 end

src/polynomial.jl

@@ -1,5 +1,5 @@
 # TODO Add to MultivariatePolynomials
-MP.variables(p::SA.AlgebraElement) = MP.variables(SA.basis(p))
+MP.variables(p::SA.AlgebraElement) = MP.variables(explicit_basis(p))
 Base.keytype(p::MP.AbstractPolynomialLike) = MP.monomial_type(p)
 Base.valtype(p::MP.AbstractPolynomialLike) = MP.coefficient_type(p)
 #Base.keys(p::MP.AbstractPolynomial) = MP.monomials(p)

test/runtests.jl

@@ -54,6 +54,7 @@ function api_test(B::Type{<:MB.AbstractMonomialIndexed}, degree)
     @test full_basis[mono] == p
     @test polynomial_type(mono, String) == polynomial_type(typeof(p), String)
     a = MB.algebra_element(p)
+    @test variables(a) == x
     @test typeof(polynomial(a)) == polynomial_type(typeof(a))
     @test typeof(polynomial(a)) == polynomial_type(typeof(p), Int)
     @test a ≈ a
@@ -72,6 +73,11 @@ function api_test(B::Type{<:MB.AbstractMonomialIndexed}, degree)
           "\$\$ " *
           _wrap(MB.SA.trim_LaTeX(mime, sprint(show, mime, p.monomial))) *
           " \$\$"
+    const_mono = constant_monomial(prod(x))
+    @test const_mono + MB.algebra_element(MB.Polynomial{B}(const_mono)) == 2
+    @test MB.algebra_element(MB.Polynomial{B}(const_mono)) + const_mono == 2
+    @test iszero(const_mono - MB.algebra_element(MB.Polynomial{B}(const_mono)))
+    @test iszero(MB.algebra_element(MB.Polynomial{B}(const_mono)) - const_mono)
 end
 
 function univ_orthogonal_test(