3 files changed, 11 insertions, 13 deletions
diff --git a/polymatrix/polymatrix/impl.py b/polymatrix/polymatrix/impl.py
index 85f56bf..2ac4dc0 100644
--- a/polymatrix/polymatrix/impl.py
+++ b/polymatrix/polymatrix/impl.py
@@ -19,7 +19,7 @@ class BroadcastPolyMatrixImpl(BroadcastPolyMatrixMixin):
 
 @dataclassabc.dataclassabc(frozen=True)
 class PolyMatrixAsAffineExpressionImpl(PolyMatrixAsAffineExpressionMixin):
-    data: PolyMatrixAsAffineExpressionMixin.MatrixType
+    affine_coefficients: PolyMatrixAsAffineExpressionMixin.MatrixType
     shape: tuple[int, int]
     slices: dict[MonomialIndex, PolyMatrixAsAffineExpressionMixin.MatrixType]
     degree: int
diff --git a/polymatrix/polymatrix/init.py b/polymatrix/polymatrix/init.py
index 6fcdcb1..332977e 100644
--- a/polymatrix/polymatrix/init.py
+++ b/polymatrix/polymatrix/init.py
@@ -79,4 +79,4 @@ def to_affine_expression(p: PolyMatrixMixin) -> PolyMatrixAsAffineExpressionMixi
     max_degree = max(m.degree for m in slices.keys())
 
     return PolyMatrixAsAffineExpressionImpl(
-            data=data, shape=p.shape, slices=slices, degree=max_degree)
+            affine_coefficients=data, shape=p.shape, slices=slices, degree=max_degree)
diff --git a/polymatrix/polymatrix/mixins.py b/polymatrix/polymatrix/mixins.py
index ce6d09b..c7a1b00 100644
--- a/polymatrix/polymatrix/mixins.py
+++ b/polymatrix/polymatrix/mixins.py
@@ -177,6 +177,11 @@ class PolyMatrixAsAffineExpressionMixin(
     where each matrix :math:`A_\alpha \in \mathbf{R}^{n\times m}`. In the
     context of this class we will call the :math:`A_\alpha` matrices
     `affine coefficients`.
+
+    **Note:** In the example above, all monomials powers upt to degree 2 are
+    present, however in general some monomials may be missing. In that case
+    this class does not store those as they are all zeros. See also the code of
+    :py:meth:`affine_coefficient`.
     """
 
     # Type of matrix that stores affifne coefficients
@@ -186,7 +191,7 @@ class PolyMatrixAsAffineExpressionMixin(
 
     @property
     @abc.abstractmethod
-    def data(self) -> MatrixType:
+    def affine_coefficients(self) -> MatrixType:
         r"""
         The big matrix that store all :math:`A_\alpha` matrices:
 
@@ -197,9 +202,8 @@ class PolyMatrixAsAffineExpressionMixin(
             \in
             \mathbf{R}^{n \times mN},
             \quad
-            N = \sum_{k = 0}^d {q + k \choose k}
+            N \leq \sum_{k = 0}^d {q + k \choose k}
         """
-        ...
 
     @property
     @abc.abstractmethod
@@ -344,12 +348,6 @@ class PolyMatrixAsAffineExpressionMixin(
         # Sort the values by monomial index, which have a total order
         return dict(sorted(monomial_values.items()))
 
-    def affine_coefficients(self) -> MatrixType:
-        r"""
-        Get the large matrix
-        :math:`A = \begin{bmatrix} A_{\alpha_1} & A_{\alpha_2} & \cdots & A_{\alpha_N} \end{bmatrix}`
-        """
-        return self.data
 
     def affine_coefficient(self, monomial: MonomialIndex) -> MatrixType:
         r""" Get the affine coefficient :math:`A_\alpha` associated to :math:`x^\alpha`. """
@@ -358,7 +356,7 @@ class PolyMatrixAsAffineExpressionMixin(
             return np.zeros((nrows, 1))
 
         columns = range(*self.slices[monomial])
-        return self.data[:, columns]
+        return self.affine_coefficients[:, columns]
 
     def affine_coefficients_by_degrees(self) -> Iterable[tuple[int, MatrixType]]:
         """
@@ -418,7 +416,7 @@ class PolyMatrixAsAffineExpressionMixin(
         
         # Evaluate the affine expression
         _, ncols = self.shape
-        return self.data @ (np.kron(mvalues, np.eye(ncols)).T)
+        return self.affine_coefficients @ (np.kron(mvalues, np.eye(ncols)).T)
 
     def affine_eval_fn(self) -> Callable[[MatrixType], MatrixType]:
         r"""