Add parent for simple basis

src/fixed.jl

@@ -24,6 +24,10 @@ end
 
 implicit_basis(basis::SimpleBasis) = SA.basis(first(basis.elements))
 
+# Needed by SumOfSquares' `_combine_with_gram` which calls `parent` on each
+# gram basis to verify the algebras match.
+Base.parent(b::SimpleBasis) = implicit_basis(b)
+
 """
     struct SemisimpleElement{P}
         elements::Vector{P}

test/fixed.jl

@@ -25,6 +25,15 @@ end
     @test MA.promote_operation(MB.implicit_basis, typeof(sb)) ==
           typeof(MB.implicit_basis(sb))
 
+    @testset "parent" begin
+        # `Base.parent(::SimpleBasis)` is used by SumOfSquares'
+        # `_combine_with_gram` to check that the gram basis lives in the
+        # same algebra as the polynomial basis.
+        @test parent(sb) === MB.implicit_basis(sb)
+        sb1 = MB.SimpleBasis([ae1])
+        @test parent(sb1) === MB.implicit_basis(sb1)
+    end
+
     @testset "length" begin
         @test length(sb) == 3
     end

test/lagrange.jl

@@ -11,14 +11,14 @@ function _test(B::Type)
     implicit =
         MB.ImplicitLagrangeBasis(x, MB.BoxSampling([-1, -1], UInt32[1, 1]))
     point = zeros(2)
-    poly = implicit[x => point]
+    poly = implicit[x=>point]
     @test poly isa MB.LagrangePolynomial
     @test poly.variables == x
     @test poly.point === point
     err = ErrorException(
         "Variables `$([x[1]])` do not match Lagrange basis variables `$x`",
     )
-    @test_throws err implicit[[x[1]] => [0.0]]
+    @test_throws err implicit[[x[1]]=>[0.0]]
     monos = monomials(x, 0:2)
     coeffs = collect(eachindex(monos))
     sub = MB.SubBasis{B}(monos)