From cf69f93de4251c6c5b9732283b4c5ae5ae59f0ec Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Beno=C3=AEt=20Legat?= <benoit.legat@gmail.com>
Date: Wed, 27 May 2026 21:41:02 +0200
Subject: [PATCH 1/2] Generalize implicit_basis

---
 src/bases.jl     |  2 +-
 test/subbasis.jl | 20 ++++++++++++++++++++
 2 files changed, 21 insertions(+), 1 deletion(-)
 create mode 100644 test/subbasis.jl

diff --git a/src/bases.jl b/src/bases.jl
index 9153661..15751d4 100644
--- a/src/bases.jl
+++ b/src/bases.jl
@@ -111,7 +111,7 @@ function algebra_type(::Type{BT}) where {B,M,BT<:MonomialIndexedBasis{B,M}}
     return Algebra{BT,B,M}
 end
 
-implicit_basis(basis::SubBasis) = parent(basis)
+implicit_basis(basis::SA.SubBasis) = parent(basis)
 implicit_basis(basis::FullBasis) = basis
 
 function implicit(a::SA.AlgebraElement)
diff --git a/test/subbasis.jl b/test/subbasis.jl
new file mode 100644
index 0000000..f619d73
--- /dev/null
+++ b/test/subbasis.jl
@@ -0,0 +1,20 @@
+using Test
+import StarAlgebras as SA
+import MutableArithmetics as MA
+using MultivariateBases
+const MB = MultivariateBases
+
+@testset "implicit_basis on generic SA.SubBasis" begin
+    # `MB.implicit_basis` was historically only defined on `MB.SubBasis`
+    # (= `SA.SubBasis{Polynomial}`). It is now defined on any `SA.SubBasis`,
+    # so that a `SubBasis` whose parent is a non-polynomial `SA.ImplicitBasis`
+    # (such as the `SA.DiracBasis` wrapping a custom algebra of monoid elements
+    # used by the CHSH tutorial) routes through the same fallback.
+    parent_basis = SA.DiracBasis(["a", "b", "c"])
+    sub = SA.SubBasis(parent_basis, ["a", "b"])
+
+    @test sub isa SA.SubBasis
+    @test !(sub isa MB.SubBasis)  # not a polynomial-typed SubBasis
+    @test MB.implicit_basis(sub) === parent_basis
+    @test MA.promote_operation(MB.implicit_basis, typeof(sub)) == typeof(parent_basis)
+end

From 9a13fd227cca677f9851cfa6ee440e043991098c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Beno=C3=AEt=20Legat?= <benoit.legat@gmail.com>
Date: Wed, 27 May 2026 21:51:55 +0200
Subject: [PATCH 2/2] Fix format

---
 src/scaled.jl    | 2 +-
 test/lagrange.jl | 4 ++--
 test/monomial.jl | 6 +++---
 test/subbasis.jl | 3 ++-
 4 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/scaled.jl b/src/scaled.jl
index 4790379..7e02aa8 100644
--- a/src/scaled.jl
+++ b/src/scaled.jl
@@ -71,7 +71,7 @@ function Base.promote_rule(
 end
 
 function scaling(exp)
-    return √(factorial(sum(exp)) / prod(factorial, exp; init = 1),)
+    return √(factorial(sum(exp)) / prod(factorial, exp; init = 1))
 end
 unscale_coef(t::MP.AbstractTerm) = MP.coefficient(t) / scaling(MP.monomial(t))
 function SA.coeffs(
diff --git a/test/lagrange.jl b/test/lagrange.jl
index 56857d1..c84215d 100644
--- a/test/lagrange.jl
+++ b/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)
diff --git a/test/monomial.jl b/test/monomial.jl
index 1781b7e..168e648 100644
--- a/test/monomial.jl
+++ b/test/monomial.jl
@@ -124,9 +124,9 @@ function test_monomial(x, y)
     # (Tuple for TypedPolynomials, Vector for DynamicPolynomials)
     full = MB.FullBasis{MB.Monomial}(x * y)
     # Get the exponent keys from the FullBasis directly
-    e_x = MB.sparse_coefficients(x + 0 * y).basis_elements[1]
-    e_y2 = MB.sparse_coefficients(y^2 + 0 * x).basis_elements[1]
-    e_00 = MB.sparse_coefficients(1 * one(x * y)).basis_elements[1]
+    e_x = MB.sparse_coefficients(x+0*y).basis_elements[1]
+    e_y2 = MB.sparse_coefficients(y^2+0*x).basis_elements[1]
+    e_00 = MB.sparse_coefficients(1*one(x*y)).basis_elements[1]
 
     @testset "sparse_coefficients ordering" begin
         p = x + y^2  # mixes degree 1 (x) and degree 2 (y²)
diff --git a/test/subbasis.jl b/test/subbasis.jl
index f619d73..89cbf07 100644
--- a/test/subbasis.jl
+++ b/test/subbasis.jl
@@ -16,5 +16,6 @@ const MB = MultivariateBases
     @test sub isa SA.SubBasis
     @test !(sub isa MB.SubBasis)  # not a polynomial-typed SubBasis
     @test MB.implicit_basis(sub) === parent_basis
-    @test MA.promote_operation(MB.implicit_basis, typeof(sub)) == typeof(parent_basis)
+    @test MA.promote_operation(MB.implicit_basis, typeof(sub)) ==
+          typeof(parent_basis)
 end